Vedanta Excel in Mathematics Book 9 Final (2080)_compressed

Revision and Practice Time Revision and Practice Time Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 351 Vedanta Excel in Mathematics - Book 9 Revision and Practice Time Dear students let’s revise the overall contents by practicing the additional problems given below. You have to do these problems independently as far as possible. Set 1. Let U = {x: 10 ≤ x ≤ 20, x∈ N} be a universal set. P and Q are the subsets of U such that P ={y: y is an even number} and Q = {z: z is a multiple of 3} (a) List the elements of P – Q. (b) Draw a Venn-diagram to show the relation of the sets U, P and Q. (c) Prove that P ∪ Q = P ∩ Q. (d) What is the cardinal number of (P ∆ Q)? 2. Let, U = {u, n, i, v, e, r, s, a, l} is a universal set. A = {l, i, v, e, r}, B = {v, i, r, u, s} and C = {r, e, a, l} are the subsets of U. (a) Write A ∩ B ∩ C in listing method. (b) Find A ∪ B in listing method. (c) Find A ∪ B – C and show it in Venn-diagram by shading. (d) Is B ∩ C an improper subset of A ∩ B ∩ C? Give reason. 3. During the lockdown due to pandemic of corona virus, out of 50 schools of a municipality; 35 schools managed their regular classes virtually using zoom platform, 8 used google meet platforms and 3 schools used both of these platforms. (a) Draw a Venn-diagram to represent the above information. (b) Find the number of schools of the municipality that could not manage their virtual classes during lockdown. Taxation 1. Mr. Gurung is the proprietor of a garment factory. His annual income is Rs 10,50,000. If the tax up to Rs 6,00,000 is exempted, 10% tax is charged for the income of Rs 6,00,001 to Rs 8,00,000 and 20% tax is charged for the income of Rs 8,00,001 to Rs 11,00,000 respectively. (a) Define income tax. (b) Find his taxable income. (c) Calculate the annual income tax that should be paid by him. 2. Mrs. Ghising deposited Rs. 6,00,000 for 3.5 years at 10% p.a. simple interest in her fixed account at a commercial bank. (a) Write the formula to calculate simple interest. (b) Calculate simple interest. (c) How much net interest would she get if 5% of interest is paid as income tax? 3. Mr. Rawal is the Branch Manager of a bank. His monthly salary is Rs 95,000 and 10% of his salary is deducted as provident fund. He pays Rs. 55,000 as the premium of his life

Revision and Practice Time Revision and Practice Time Vedanta Excel in Mathematics - Book 9 352 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur insurance. If 1% social security tax is levied upon the income of Rs. 5,00,000, 10% and 20% taxes are levied on the next incomes of Rs. 2,00,000 and Rs. 3,00,000 respectively, answer the following questions. (a) Find his annual income. (b) Find his taxable income. (c) How much income tax should he pay in a year? 4. Mr. Tamrakar marked the price of a camera Rs 32,000 in his shop and he announces a discount of 8%. (a) What is the formula to calculate discount amount when the marked price and discount percent are given? (b) Find the price of the mobile set after allowing discount. (c) How much will a customer have to pay for buying it if 10% VAT was levied on it? 5. After allowing 25% discount on the marked price and then levying 13% VAT, Mr. Tharu sold a cycle to Mr. Tamang. Mr. Tamang got a discount of Rs 750 on it. (a) What was the marked price of the cycle? (b) How much VAT was levied on the price of the cycle? (c) If only 20% discount was given, by how much would the cost of the cycle with VAT be decreased? 6. The price of a refrigerator is tagged as Rs 40,000. The store allows 10% discount on its tagged price. (a) How much should a customer pay for it with 13% value added tax? (b) By what percentage is the VAT amount more than the discount amount? 7. A wholesaler bought a generator for Rs 2,00,000 without VAT. He made a profit of Rs 10,000 and sold it to a retailer. The retailer spent Rs 6,000 for transportation and Rs 4,000 for the local tax. The retailer sold it to a customer at a profit of Rs 20,000. (a) What was the cost price of retailer? (b) How much did the customer pay for it with 13% VAT? Commission, Bonus and Dividend 1. By selling a piece of land for Rs 25,00,000, a real estate agent receives 1 % commission on the first 10 lakhs and 0.5 % commission on the remaining amount of selling price. (a) How much commission does the agent get? (b) How much money does the owner of the land receive? (c) If he had taken 1.5% commission on all, by how much more or less amount of commission would he get? 2. The monthly salary of a sales girl in a cosmetic shop is Rs 11,000 and a certain commission is given as per the monthly sales. The sales of a month is Rs 5,00,000 and the total income of the girl in that month is Rs 21,000. (a) What is her commission amount? (b) What is the rate of commission? (c) What would be the income of the girl, if the sales of the month is Rs. 7,77,000? 3. A cement factory made a net profit of Rs 3,60,00,000 in the last year. The management of the factory decided to distribute 16% bonus from the profit to its 120 employees.

Revision and Practice Time Revision and Practice Time Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 353 Vedanta Excel in Mathematics - Book 9 (a) Find the bonus amount. (b) By what percent should the bonus be increased so that each employee can receive Rs 60,000? (c) What should be the profit of the company so that it can provide Rs 75,000 to each employee at 20% bonus? 4. A group of youths of a village who returned from foreign employment, established a company. They sold 20,000 kitta shares each of Rs. 100. Mr. Limbu bought 500 kitta shares of the company. The company earned a net profit of Rs 12,50,000 in a year and it decided to distribute 10% cash dividend to its shareholders. (a) Define dividend. (b) What was the dividend amount? (c) How much dividend did Mr. Limbu receive? (d) If 15% of net profit had distributed as dividend, by how much more cash dividend would he receive? Household Arithmetic 1. The meter reading for the consumption of electricity of a household was 1248 units on 1 Mangsir and 1388 units on 1 Poush. Answer the following questions under the given rates and billing system. Units 0-20 21-30 31-50 51-100 101-250 Rate per unit Rs 3 Rs 6.50 Rs 8.00 Rs 9.50 Rs 9.50 Service charge Rs 30 Rs 50 Rs 50 Rs 75 Rs 100 (a) What do you mean by 1 unit of electricity? (b) How many units are consumed in the month of Mansir? (c) Calculate the amount required to pay the electricity bill when the payment is made on 6th days of meter reading? (d) How much more amount would she require if she had paid the electricity bill on 20th day than it was paid on 6th day after meter reading? 2. Mr. Manandhar has installed a metered tap using half-inch pipe in his house in Kathmandu. The consumption of water in the month Chaitra is 18 units. According to Kathmandu Upatyaka Khanepani Limited (KUKL), the minimum charge up to 10 units is Rs 100 and Rs 32 per unit for additional consumption of water, and 50% of the total charge is to be paid as sewerage service charge. Answer the following questions. (a) How many litres of water was consumed in the month of Chaitra? (b) How much sewerage service charge did he pay? (c) Find the total bill including 50% sewerage service charge. (d) If he paid only Rs 630 for the consumption of water in Falgun, how many units of water was consumed in the month of Falgun? 3. An office made a total of 2175 calls in a month. According to Nepal Telecommunication Authority (NTA), the minimum charge up to 175 calls is Rs 200 and Re 1 for each additional call. 13% TSC and 13% VAT are applied as per Government rule. (a) How much monthly rental charge is fixed? (b) What is the sub total amount of telephone bill? (c) What is the telephone charge with TSC? (d) How much amount should the office pay with VAT to clear the bill? Payment Rebate/fine Within 7 days 2% rebate 8th – 15th days - 16th – 30th days 5% fine 31st -40th days 10% fine

Revision and Practice Time Revision and Practice Time Vedanta Excel in Mathematics - Book 9 354 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 4. The latest rates of taxi fare implemented by NBSM are given in the table below. Time Minimum fare Fare of per 200 meters Waiting charge 6: 00 am - 9:00 pm Rs 50 Rs 10 Rs 10 per 2 minutes 9: 00 pm - 6:00 am Rs 75 Rs 15 Rs 15 per 2 minutes The distance from Kirtipur, Kathmandu to Sanothimi, Bhaktapur is 14.2 km. Rojina asked a metered taxi to wait for 4 minutes and travelled from Kirtipur to Sanithimi at 11:00 am. (a) Which department is responsible for implementation of the rates of taxi fare? (b) What was the minimum fare appeared immediately after the meter was flagged down? (c) Calculate the total fare paid by her. (d) If she hired a taxi and returned back to Kirtipur again through the same route, how much more or less fare did she pay than travelling to Sanothimi? Mensuration 1. In this rainy season, Samjhana bought an umbrella from a shop for her son Jivesh. Jivesh observed that the umbrella is made by stitching 8 triangular pieces of cloth, each piece measuring 61 cm, 61 cm and 22 cm. (a) What is the formula to find the area of an isosceles triangle? (b) How much cloth is required for the umbrella? (c) If 5% extra cloth is used for sewing, stitching and pasting, how much cloth is required for making the umbrella? 2. The measurements of a few plots of lands given alongside are shown in the given table. Plot no. Shape Dimensions 410 Square Length = 25 m 411 Rectangular l = 65 m, b = 25 m 413 Rectangular l = 80 m, b = 25 m 414 Triangular 130 m, 120 m, 50 m (a) Calculate the area of plot 410 in Ropani,Aana and Paisa. [1 Ropani = 508.72 m2 ] (b) Calculate the area of plot 414 in Kattha and Dhur. [1 Kattha = 338.63 m2 ] 3. A room of class IX is 30 ft. long, 15 ft. wide and 10 ft. high. It contains a door of size 4 ft. × 6 ft. and two windows each of 5 ft. × 4.5 ft. (a) What is the area of its four walls? (b) What is the cost of plastering the walls at Rs. 150 per sq. feet? (c) If 80% of the floor is covered with seats, each seat covers 9 sq. ft. and no seat is found vacant, how many students are there in the class? 4. The following figure shows a closed victory stand made up of wood. (a) Find its volume (b) Find its lateral surface area. (c) Find its total surface area. 30cm 30cm 30cm 40cm 30cm 30cm 1 2 3

Revision and Practice Time Revision and Practice Time Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 355 Vedanta Excel in Mathematics - Book 9 5. In a cylindrical bucket, the internal diameter is 21 cm and height 25 cm. (a) Write down the formula to find the volume of the bucket. (b) Find the internal volume of the bucket. (c) How many litres of water can it hold when it is completely filled with water? 6. The capacity of a cylindrical vessel is 539 litres and its height is 1.4 m. (a) Find the volume of the vessel. (b) Find the radius of its base. (c) What is the internal curved surface area of the vessel? 7. A cylindrical roller made up of iron is 1.05 m long. Its internal radius is 50 cm and the thickness of the iron sheet used in making the roller is 5 cm. (a) If it takes 400 complete revolutions to level a playground, find the cost of levelling the ground at Rs 15 per sq. metre. (b) If 1 cm3 of iron weighs 7.8 g, find the mass of the roller. 8. 50 circular plates, each of radius 7 cm and thickness 5 mm are placed one above the other to form a cylindrical shape. Find the volume of the cylinder so formed. 9. How many cubic meters of earth must be dug out to construct a cylindrical well which is 25 m deep and the radius of the base is 3.5 m? 10. The adjoining cylindrical vessel is 70 cm high and the radius of its base is 35cm. If it contains some water up to the height of 20 cm, how much water is required to fill the vessel completely? Sequence and Series 1. A given series is 3+9+27+81+243. (a) What type of series is it? (b) What is its common ratio? (c) What is its general term? (d) Rewrite the series in sigma notation. 2. Each organic compound contains Carbon atoms (C) and Hydrogen atoms (H). The structure of a few organic compounds are shown in the diagrams below. , , , ... H H H H H H H H H H H H H C H H C C H H C C C H | | | | | | | | | | | | | | | | | | | | | (a) Draw one more diagram in the same pattern. (b) Find the nth term formula of the sequence for the number of Hydrogen atoms (H). (c) Find the number of Hydrogen atoms (H) in 10th diagram. 3. In an arithmetic sequence, the third and the ninth terms are 4 and –8 respectively. (a) Find the common difference and the first term. (b) Find the corresponding series. 4. In an arithmetic sequence, the fourth term is equal to 3 times its first term and seventh term exceeds twice the third term by 1. (a) Find the common difference and the first term. (b) Find the sequence. 35cm 70cm 20cm

Revision and Practice Time Revision and Practice Time Vedanta Excel in Mathematics - Book 9 356 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 5. A person saves Rs.10 on the first day, Rs.20 on the second day, Rs.40 on the third day and so on. (a) How much amount will he save on the 10th day? (b) On which day will he / she save Rs. 640? Factorisation 1. Resolve into factors. a) 4x4 + 81 b) x4 + 625y4 c) a4 + a2 b2 + b4 d) a4 + 2a2 + 9 e) x4 – 39x2 + 25 f) x4 y4 + x2 y2 + 1 g) 8x3 + 27 h) 135a6 x + 5a3 x4 i) 16a5 b – 54a2 b4 j) a2 – 8a – 9 + 10b – b2 k) x2 – 10x + 24 + 6y – 9y2 l) (1 – x2 )(1 – y2 ) + 4xy m) (x2 – 4)(y2 – 9) – 24xy H.C.F. and L.C.M. 1. Find the H.C.F. and L.C.M. of the following expressions. a) x2 + 2x , x3 – 4x b) 3x2 – 15x , 3x3 – 75x c) a2 – 6a + 6b – b2 , b2 + ab – 6b d) m2 – n2 - m - n, m2 n – mn2 –mn e) 16a4 – 4a2 + 4a – 1, 8a3 + 1 f) 1 + 4x + 4x2 –16x4 , 1 – 8x3 g) x4 + 4x2 + 16, x3 + 8 h) 16a4 + 4a2 b2 + b4 , 8a3 + b3 i) x4 + x2 + 169, x3 + x (x + 13) + 4x2 j) x3 – 3x2 – x + 3 , x3 – x2 – 9x + 9 k) x2 – 14x – 15 + 16y – y2 , x2 – y2 +2y – 1 2. Find the H.C.F. and L.C.M. of the following expressions a) 6(a3 – 4a), 8(a3 b – a2 b – 6ab), 9(a2 b – ab – 2b) b) 8m4 +27mn3 , 8m3 n + 2m2 n2 – 15mn3 , 4m3 n – 9mn3 c) x3 – y3 , x4 + x2 y2 + y2 , x3 + x2 y + xy2 d) y3 – 1, y4 + y2 + 1, y3 + 2y2 + 2y + 1 Indices 1. Simplify. a) 2x + 3 – 2x + 2 2x + 2 b) 3x + 2 + 3x + 1 3x + 1 + 3x c) 11m – 11m–1 5 × 11m–1 d) 6n + 2 + 7 × 6n 6n + 1 × 8 – 5 × 6n e) 8n + 2 + 9 × 8n 8n + 1 × 10 – 7 × 8n 2. Simplify. a) xa(b – c) xb(a – c) × xa xb c b) xa – c x– b a – b × xb – a x– c b – c × xc – b x– a c – a c) xa xb a2 + ab + b2 × xb xc b2 + bc + c2 × xc xa c2 + ca + a2 d) xb xc b + c – a × xc xa c + a – b × xa xb a + b – c e) xa xb 1 ab × xb xc 1 bc × xc xa 1 ca f) xp + q xp – q r – p × xq + r xq – r p – q × xp + r xr – p q – r g) (am . an) m – n ap an n + p × ap am p+m

Revision and Practice Time Revision and Practice Time Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 357 Vedanta Excel in Mathematics - Book 9 h) x a b x b a ab × x b c x c b bc × x c a x a c ca i) x 1 b x 1 c 1 bc × x 1 a x 1 b 1 ab × x 1 c x 1 a 1 ca j) 1 1 + xb – a + xc – a + 1 1 + xc – b + xa – b + 1 1 + xa – c + xb – c 3. a) If abc = 1, prove that: (1 + a + b–1) –1 + (1 + b + c–1) –1 + (1 + c + a–1) –1 = 1 b) If p + q + r = 0, prove that: (1 + xp + x–q) –1 + (1 + xq + x–r) –1 + (1 + xr + x–p) –1 = 1 c) If a+ b+c = p, show that x2a x2a + xp–b + x p–c + x2b x2b + xp–c + xp–a + x2c x2c + xp–q + x p–b = 1 d) If x2 + 2 = 3 2 3 + 3– 2 3 , show that 3x (x2 + 3) = 8. e) If x = (ab) 1 3 – (ab)– 1 3 , prove that abx (x2 + 3) = a2 b2 – 1 Simultaneous Equations 1. The cost of tickets to enter in the central zoo is Rs 150 for adult and Rs 50 for a child. If a family paid Rs 700 for 6 tickets altogether. (a) Express the above statements in the form of linear equations. (b) How many tickets were purchased in each category? (c) If the cost of tickets of each category is decreased by 10%, how many tickets of each category can be bought for Rs 540? 2. Five years ago, father’s age was 4 times his son’s age. Now the sum of their ages is 45 years. (a) Write the above statements in the form of linear equations. (b) Find their present ages. (c) What was the age of the father when his son was just born? 3. 6 years ago a Rita’s age was six times the age of his son. 4 years hence, thrice her age will be equal to eight times his son Bishwant’s age. (a) Write the above statements in the form of linear equations. (b) Find their present ages. (c) If Rita gave birth to her son Bishwant after 2 years of marriage, how old was Rita when she got married? 4. Mr. Thapa was four times as old as his son was in B.S. 2074 but he was only three times as old as his son in B.S. 2079. (a) Write the above statements in the form of linear equations. (b) Find their ages of the year 2074 B.S. (c) Find their birth years. 5. A number of two digits is six times the sum of its digits. If 9 is subtracted from the number, the digits are reversed. (a) What is a two digit number in which x and y are the digits at ten's and one's places respectively?

Revision and Practice Time Revision and Practice Time Vedanta Excel in Mathematics - Book 9 358 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur (b) Write the above statements in the form of linear equations. (c) Find the number. 6. A number of two digits is equal to the four times the sum of its digits. If 18 is added to the number, the digits are reversed. (a) Write the above statements in the form of linear equations. (b) Find the number. 7. A number consists of two digits whose sum is equal to 10. If 36 is subtracted from the number, the digits are reversed. Find the number. 8. A number between 10 and 100 exceeds 4 times the sum of its digits by 9. If the number is increased by 18, the result is equal to the number formed by interchanging its digits. Find the original number. 9. Two buses were coming from two villages situated just in the opposite direction. The average speed of one bus is 8 km/hr more than that of another one and they had started their journey in the same time. If the distance between the villages is 360 km and they meet after 4 hours, find their average speed. 10. Koshi bus started its journey from Kathmandu to Dharan at 4 p.m. at the average speed of 50 km/hr. 1 hour later Makalu bus also started its journey from Kathmandu to the same destination at the average speed of 60 km/hr. At what time would they meet each other? Geometry-Triangle 1. When a side BC of a triangle ABC is produced to an exterior point D, answer the following questions. (a) Write down the relation between ∠ACD and ∠ABC + ∠BAC. (b) Verify experimentally that the relationship between ∠ACD and ∠ABC + ∠BAC. (Two triangles of different shapes and sizes are necessary) (c) If the triangle ABC were an isosceles right angled triangle right-angled at B, what would be the ratio of measurements of ∠ABC and ∠ACD? 2. In an isosceles triangle ABC; bisector of vertical ∠BAC is drawn to a point D on its base BC. (a) What is the relation between AD and BC? (b) What is the relation between BD and CD? (c) Draw two triangles ABC and verify experimentally verify that the bisector of the vertical angle of an isosceles triangle is perpendicular bisector of the base. 3. The diameter of a circular lake is 198 m. A temple is situated on an island at the centre of the lake. If the height of the temple above the water surface is 20 m, what is the distance between the top of the temple from ends of the diameter of the lake? 4. In the adjoining figure, BX ⊥ AC, CY ⊥ AB and BX = CY. Prove that AB = AC. A B Y X C

Revision and Practice Time Revision and Practice Time Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 359 Vedanta Excel in Mathematics - Book 9 5. In the given figure, AB // PQ and AC // PR. If BQ = CR, prove: (i) AB = PQ (ii) AC = PR 6. In the given figure, BA ⊥ AC, RQ ⊥ PQ, AB = QR, and BP = CR. Prove that AC = PQ. Geometry-Parallelogram 1. The figure of rhombus ABCD is given. (a) What is the relation between the diagonals of rhombus? (i) Equal (ii) Perpendicular to each other. (iii) Long diagonal is twice the shorter diagonal. (iv) Only one diagonal bisects the other diagonal. (b) If AB = (2x – 3) cm and BC = (x + 2) cm, find the value of x. (c) Construct a rhombus ABCD having diagonals AC = 6 cm and BD = 8 cm. 2. A quadrilateral ABCD is given alongside. (a) Which of the following conditions is necessary for the quadrilateral ABCD to be a parallelogram? (i) AB = DC and BC = AD (ii) ∠ABC = ∠ADC and ∠BAD = ∠BCD (iii) OA = OC and OB = OD (iv) Any one of the above (b) If ABCD is a parallelogram with OA = (x – 6) cm and OC = (9 – 2x) cm, what is the value of x? (c) Construct a quadrilateral ABCD in which AB = BC = 5 cm, CD = AD = 4.5 cm and ∠ABC = 60o . 3. A quadrilateral ABCD is given alongside. The figure is not drawn to scale. Answer the following questions. (a) If AB = CD, name the special type of the quadrilateral. (b) If ABCD were a parallelogram with ∠BAD = (2x + 45o ) and ∠BCD = (x + 60o ), what would be the value of x? (c) Construct the given quadrilateral ABCD with exact measurements. P B Q C R A A B C P Q R A B C D A B C O D D A B C 4.5 cm 5 cm 4 cm 5 cm 5.2 cm

Revision and Practice Time Revision and Practice Time Vedanta Excel in Mathematics - Book 9 360 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 4. A trapezium PQRS is given alongside. The figure is not drawn to scale. Answer the following questions. (a) What is the measure of ∠QRS? (b) Write any one of the necessary condition for the trapezium PQRS to be a parallelogram. (c) Construct the given trapezium PQRS with exact measurements. Geometry-Circle 1. In a given circle with centre O, perpendicular line OP is drawn from centre O to the chord AB. (a) What type of triangle is ∆OAB? (b) If chord AB = 16 cm and OP = 6 cm, what is the radius of the circle? (c) Can a circle of radius 10 cm be drawn passing through points A and B? Write with reason. 2. In the circle given alongside; O is the centre, OM ⊥ AB, AB = 8 cm and OM = 3 cm. (a) Write down the relation between AM and AB. (b) Find the length of radius OA. (c) If OM is produced to meet the circumference at N, what is the length of MN? 3. In the figure given alongside; O is the centre of circle, OPQR is a rectangle. If PR = 17 cm and PQ = 8 cm, answer the following questions. (a) Write the relation between the OP and TQ. (b) Find the length of OS. (c) Find the length of RS. 4. In the given figure, O is the centre of the circle. If AB = 8 cm, CD = 6 cm, OA = 5 cm, AB // CD and ON ⊥ CD, answer the following questions. (a) Write the relation between the OM and AB. (b) What is the length of OM? (c) What is the length of MN? 5. In the figure given alongside; O is the centre of circle, OX ⊥ PQ , OY ⊥ RS and OX = OY, answer the following questions. (a) Write the relation between the chords PQ and RS. (b) If PX = 7 cm, find the length of RS. (c) If another chord TU is drawn in the circle such that TU is longer than PQ and OZ ⊥ TU, what is the relation between OX and OZ? 6. In the figure; O is the centre of circle, AB and BC are equal chords, OP ⊥ AB and OQ ⊥ BC; and R is the mid-point of the chord AC, answer the following questions. (a) Identify the name of shaded portion. (b) Write down the relation between OP and OQ. (c) If OP = OR, write the type of the ∆ABC with reasons. P Q R 4 cm 4.3 cm 6 cm 60° S A B O P A B O M Q O R T S P A B O M C N D R P Q S Y X O A B Q C P O R

Revision and Practice Time Revision and Practice Time Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 361 Vedanta Excel in Mathematics - Book 9 7. In the figure alongside, A and B are the centres of two intersecting circles and CD intersects AB perpendicularly at P. (a) Write down the relation between CP and PD. (b) Is CM = DN? Give reason. (c) If CN = 5 cm, find the length of MD. 8. In the adjoining figure, equal chords AB and CD of a circle with centre O, cut at E. If M and N are the mid-points of AB and CD respectively, answer the following questions. (a) Write down the relation between OM and AB. (b) If OM = 3 .5 cm, what is the length of ON? (c) If ∠MEN = 90o , show that OMEN is a square. Statistics 1. The ages (in years) of members of 5 families of a community are given below. 20, 30, 5, 10, 35, 50, 80, 40, 10, 40, 30, 60, 90, 50, 60, 20, 35, 30, 5, 40, 10, 20, 35, 25, 60, 40, 20, 25, 30, 25 (a) Name the type of the series. (b) Present this series into a discrete series with tally bars. (c) Find the mean from the discrete series. (d) How many people are older than 20 years? 2. The speeds of the vehicles of a highway during 10 a.m. to 12 noon were recorded as follows: Speed in km/hr <30 <40 <50 <60 <70 <80 No. of vehicles 2 3 7 10 8 4 (a) Form the frequency distribution table. (b) Add the cumulative frequency column in the same table and fill up the cumulative frequencies. (c) Draw the histogram of the data. (d) How does histogram differ from bar graph? 3. Mr. Chaudhary has a garment factory. He recorded the monthly remuneration of the labourers of his factory as shown in the table below. Salary (in Rs 000) 10 20 30 40 50 60 No. of employees 5 8 10 9 p 1 (a) Write the formula to calculate the mean of discrete series. (b) Construct the fx column and fill it up in the same table. (c) If the average remuneration is Rs. 32,000, find the value of p. (d) How much amount should be managed by Mr. Chaudhary in a month for the remuneration of the labourers? A M C P N D B M A N E D C B O

Revision and Practice Time Revision and Practice Time Vedanta Excel in Mathematics - Book 9 362 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 4. The following table shows the marks obtained by the students of grade IX in mathematics test. Marks obtained 15 30 45 60 75 90 No. of students 2 3 7 10 8 4 (a) What type of data is it? (b) Construct a cumulative frequency distribution table? (c) Calculate the median mark. (d) Calculate the mean mark of the students who secured more than median mark. 5. The table given below shows the weight of the teachers of a school. Weight (in kg) 55 58 60 65 70 75 No. of teachers 3 4 6 10 2 1 (a) What is the modal weight? (b) Name the quartile which divides the data in the ratio of 3: 1 from the bottom. (c) Construct a cumulative frequency distribution table. (d) Calculate the upper quartile. Probability 1. From a married couple, a child is born. Answer the following questions. (a) Write down the sample space of this event. (b) Find the probability of the brith of a son. (c) Find the probability of the birth of a daughter. (d) Are the events of the birth of son or daughter equally likely? Give reason. 2. A normal die is rolled once. Answer the following questions. (a) Define sample space. (b) Find the probability of getting an odd number. (c) Find the probability of getting the face with the number 3. d) Are the events of getting numbers from 1 to 6 equally likely? Give reason. 3. From a well shuffled pack of 52 playing cards, a card is randomly drawn. Answer the following questions. (a) What is the probability of an impossible event? (b) What is the probability of getting an ace? (c) What is the probability of getting a card of diamond? (d) What is the probability of not getting a jack? 4. A boy writes down at random a whole number larger than 1 and smaller than 11. Find the probability that it is (a) an odd (b) an even (c) a prime (d) a factor of 12 (e) a perfect square (f) a power of 2

Revision and Practice Time Revision and Practice Time Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 363 Vedanta Excel in Mathematics - Book 9 Trigonometry 1. In the given right angled triangle ABC; ∠ABC = 90o and ∠ACB =θ. Answer the following questions. a) Which trigonometric ratio is represented by AB BC ? b) What is the value of AB AC 2 + BC AC 2 = 1? c) If AC = 20 cm and cosθ = 4 5 , find the length of BC. d) If the length of AC were twice the length of AB, what would be the value of θ? 2. In the adjoining figure; AB ⊥ BC, BD ⊥ DC, AB = 12 cm, BD = 3 cm, DC = 4 cm, ∠BCD = θ and ∠BAC = α. a) Find the length of BC. b) Find the value of sinθ. c) Find the length of AC. d) If the length of BC were 3 times the length of AB, what would be the value of a? 3. In the given figure; AB = height of water tank, CD = height of house, BD = distance between the water tank and the house. If AB = 30 m, BD = 40 m and ∠ACE = 30o , answer the following questions. a) What is the value of tan30°? b) Find the length of AE? c) What is the height of the house? d) If the length of AE and AC were equal, what would be the value of ∠ACE? 4. In the given figure; AB = length of the ladder and AC = height of a wall. If AC = 30 ft and ∠ABC = 60o , answer the following questions. a) Which trigonometric ratio is useful to find the length of the ladder? b) What is the value of sin60o ? c) Find the length of the ladder? d) What is the distance of the foot of the ladder from the base of the wall? e) If the length of BC and AC were equal, what would be the value of ∠ABC? A B C q A B C 12 cm θ 3 cm 4 cm D a 40 m A B D 30 m E 30° C A B C 60° 30ft.

Vedanta Excel in Mathematics - Book 9 364 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 1. Sets Exercise : 1.1 1. a) P ∪ Q b) P ∩ Q c) P – Q d) Q – P e) P f) Q g) P ∪ Q h) P ∩ Q g) P – Q 2. a) A ∪ B b) A ∪ B c) A ∩ B d) A ∩ B e) A – B f) Y – X g) (A ∪ B ∪ C) h) P ∩ Q ∪ R 3. a) (i) A ∪ B = {1, 2, 3, 5, 6, 7, 9} , A ∪ B = {4, 8, 10} (ii) A ∩ B = {1, 3}, A ∩ B = {2, 4, 5, 6, 7, 8, 9, 10} (iii) A – B = {5, 7, 9}, A – B = {1, 2, 3, 4, 6, 8, 10} (iv) B – A = {2, 6}, B – A = {1, 3, 4, 5, 7, 8, 9, 10} b) (i) P ∪ Q ∪ R = {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15} (ii) P ∩ Q ∪ R = {6} (iii) P ∪ Q ∪ R = {7, 11, 13, 14} (iv) P ∩ Q ∩ R = {1, 2, 3, 4, 5, 7, 8, ..., 15} (v) (P ∪ Q ) ∩ R = {3, 6, 12} (vi) (P ∩ Q) ∪ R = {2, 3, 4, 6, 9, 12, 15} 4. a) (i) A ∪ B = {a, b, e, h, l, n, p} (ii) A ∩ B = {a, n} (iii) A – B = {e, p, l} (iv) B – A = {b, h, u, t} b) (i) P ∪ Q = {1, 2, 3, 4, 5, 6, 7, 8, 9} (ii) P ∩ Q = {1, 2, 4, 8} (iii) P – Q = {3, 5, 6, 7, 9} (iv) Q – P = φ c) (i) M ∪ N = {11, 13, 15, 17, 19, 23} (ii) M ∩ N = {17, 19} (iii) M – N = {11, 13, 15} (iv) N – M = {23} 5. a) and b) Show to your teacher. 6. a) (A – B) ∪ (B – A) = {1, 2, 6, 10} b) (i) A D B = {a, d, e, h, i, n, r, t} (ii) P D Q = {1, 2, 7} 7. a) (i) A = {2, 4, 6, 8, 10} (ii) B = {1, 4, 6, 8, 9, 10} (iii) A ∪ B = {1, 2, 4, 6, 8, 9, 10} (iv) A ∩ B = {4, 6, 8} (v) A ∪ B = {4, 6, 8} (vi) A ∩ B = {1, 2, 4, 6, 8, 9, 10} (vii) A = {1, 3, 5, 7, 9} (viii) B = {2, 3, 5, 7} b) (i) A = {1, 3, 5, 7, 9, 11, 13, 15} (ii) A ∪ A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} (iii) A ∩ A = φ (iv) U = φ A e B p l a n b h u t A e B p l a n b h u t A e B p l a n b h u t A e B p l a n b h u P t 3 Q 5 6 7 9 2 4 8 1 P 3 Q 5 6 7 9 2 4 8 1 P 3 Q 5 6 7 9 2 4 8 1 P 3 Q 5 6 7 9 2 4 8 1 M N 11 13 15 23 17 19 M N 11 13 15 23 17 19 M N 11 13 15 23 17 19 M N 11 13 15 23 17 19 Answers

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 365 Vedanta Excel in Mathematics - Book 9 8. a), b) and c) Show to your teacher. 9. a), b) and c) Show to your teacher. 10. a) (i) A ∩ B = {3, 5, 7} (ii) n(A – B) = 2 (iii) A ∪ B = {4, 6, 8, 10} iv) A – B is a proper subset of A. b) (i) P ∪ Q = {1, 2, 3, 6, 9 12} (ii) n(Q – P) = 2 (iii) P – Q = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12} iv) P ∩ P is an empty set. 11. a) (i) A ∩ B ∩ C = {3} (ii) A – (B ∩ C) = {1, 5, 7, 9, 11} (iii) A ∪ (B – C) ={6, 8, 10, 12, 13, 14, 15} (iv) A ∩ B ∩ C is a proper subset of A ∩ B. b) (i) X ∪ Y ∪ Z = {a, b, c, d, e, f, g, h} (ii) X ∪ (Y – Z) = {a, b, c, d, f} (iii) X∩ (Y ∪ Z) = {b, e, f, g, h, i, j} X Y Z b a f c d e g h i j (iv) X ∪ Y is a proper subset of X∪Y∪Z. c) (i) U= {1, 2, ..., 20}, A = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}, B = {3, 6, 9, 12, 15, 18}, C = {1, 2, 3, 4, 6, 8, 12} (ii) A B 6 2 1 4 3 9 15 18 10 14 16 20 8 C 5 7 11 13 17 19 12 (iii) Show to your teacher. (iv) n (A ∪ B ∪ C) = 6 12. a) and b) Show to you teacher. 13. a) and b) Complete your project work in a group or individually. Discuss the outcomes in the class. A B 3 4 6 8 10 5 7 1 9 2 P Q 3 4 5 7 8 6 1 2 9 12 10 11 Exercise : 1.2 1. Show to your teacher. 2. a) 9 b) 3 c) 4 d) 5 e) 2 f) 4 g) 6 h) 5 i) 1 j) 2 3. a) (i) 53 (ii) 12 (iii) 8 (iv) 25 b) (i) 85% (ii) 20% (iii) 35% (iv) 30% c) (i) 45 (ii) 40 (iii) 75 (iv) 13 c) (i) 35 100 35 115 F M (ii) 100 4. a) (i) 200 200 150 50 T N (ii) 200 (iii) 150 (iv) 50 b) (i) 325 450 525 200 N C (ii) 200 Answers

Vedanta Excel in Mathematics - Book 9 366 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Answers d) (i) (ii) 10% (iii) 20% 70% 10% 20% C A 5. a) (i) 145 (ii) 300 (iii) 135 145 165 55 B A b) (i) (ii) 325 (iii) 450 275 325 175 125 T C 6. a) (i) 57 (ii) 7 (iii) 27 (iv) 37 20 7 30 18 F C b) (i) 625 (ii) 125 (iii) 385 (iv) 260 125 240 125 P S 7. and 8. Complete your project work in a group or individually. Discuss the outcomes in the class. 2. Taxation Exercise: 2.1 1. a) Rs 4,00,000 b) Rs 4,20,000 c) Rs 5,25,000 d) Rs 10,04,640 2. a) Rs 3,054 b) Rs 5,400 3. a) Rs 14,000 b) Rs 40,000 c) Rs 7,500 d) Rs 45,000 4. a) (i) Answer yourself (ii) Rs 5,66,800 (iii) Rs 11,680 b) (i) Rs 6,06,000 (ii) Rs 6,600 c) Rs 21,000 d) Rs 4,42,600 5. a) (i) Rs 60,000 (ii) Rs 57,000 b) (i) Rs 16,000 (ii) Rs 15,200 c) Rs 1,50,780 d) Rs 27,850 6. a) Rs 20,000 b) Rs 4,000 7. a) (i) Rs 6,75,000 (ii) Rs 6,45,000 (iii) Rs 1, 950 (iv) Rs 17,550 b) (i) Rs 6,24,000 (ii) Rs 1,164 (iii) Rs 10,476 c) (i) Rs 5,51,880 (ii) Rs 5,36,682 (iii) Rs 8,668.20 8. a) (i) Rs 77,200 (ii) Rs 8,56,192 (iii) Rs 37,238.40 b) (i) Rs 72,000 (ii) Rs 8,33,600 (iii) Rs 32,720 9. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 2.2 1. a) R% of Rs x b) y x × 100% c) Rs P + R% of Rs P d) Rs (x – y + z) 2. a) (i) Rs 2,860 (ii) Rs 4,550 (iii) Rs 4,000 b) (i) Rs 4,500 (ii) Rs 7,500 (iii) Rs 66,000 3. a) (i) Rs 390 (ii) Rs 3,390 b) (i) Rs 1,950 (ii) Rs 16,950 c) (i) Rs 5,915 (ii) 51,415 4. a) (i) Rs 3,600 (ii) Rs 468 b) (i) Rs 9,700 (ii) Rs 1,455 c) (i) Rs 23,400 (ii) Rs 3,042 5. a) (i) Rs 585 (ii) 13% b) (i) Rs 819 (ii) 13% c) 13% 6. a) (i) Rs 2,500, Rs 22,500, Rs 2,925, Rs 25,425 (ii) Rs 6,000, Rs 34,000, Rs 4,420, Rs 38,420 (iii) Rs 11,900, Rs 73,100, Rs 9,503, Rs 82,603 (iv) Rs 16,800, Rs 1,03,200, Rs 13,416, Rs 1,16,616 b) (i) Rs 300 (ii) Rs 2,700 (iii) Rs 3,051 c) (i) Rs 1,100 (ii) Rs 4,400 (iii) Rs 4,972 7. a) (i) Rs 2,88,000 (ii) Rs 2,44,800 (iii) Rs 2,76,624 b) (i) Rs 62,500 (ii) Rs 63,562.50 c) Rs 21,696 d) Rs 6,215 8. a) (i) Rs 770 (ii) Rs 870.10 b) Rs 1,118.70 9. a) (i) Rs 3,400 (ii) Rs 4,000 (iii) Rs 600 (iv) Rs 442 b) (i) Rs 6,300 (ii) Rs 7,000 (iii) Rs 700 (iv) Rs 819 c) Rs 663 10. a) (i) Rs 4,400 (ii) Rs 572 (iii) 13% b) (i) Rs 1,700 (ii) 13% 11. a) (i) Rs 10,000 (ii) 25% profit b) (i) Rs 42,000 (ii) 20% profit 12. a) (i) Rs 51,500 (ii) Rs 56,000 (iii) Rs 63,280 b) Rs 3,82,844 c) Rs 88,592 13. a) (i) Rs 9,600 (ii) Rs 10,000 (iii) Rs 8,000 (iv) Rs 9,200 (v) 4% b) 3% 14. (i) Rs 18,00,000 (ii) Rs 21,06,000, Rs 3,06,000 (iii) 10.33% profit 15. Complete your project work in a group or individually. Discuss the outcomes in the class.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 367 Vedanta Excel in Mathematics - Book 9 Answers 3. Commission, Bonus and Dividend Exercise: 3.1 1. a) Rs 60,500 b) Rs 3,60,000 c) Rs 1,20,000 2. a) (i) Rs 3,75,000 (ii) Rs 2,46,25,000 b) (i) Rs 37,500 (ii) Rs 12,12,500 3. a) Rs 1,62,900 b) Rs 1,10,000 c) Rs 1,85,00,000 d) Rs 3,50,000 4. a) 2.5% b) 5.5% 5. a) Rs 70,930 b) Rs 33,250 c) (i) Rs 1,215 (ii) Rs 2,375 (iii) Rs 4,392 6. a) (i) Rs 30,300 (ii) Rs 6,50,000 b) Rs 23,100 c) 1% 7. a) Rs 47,53,000(b) Rs 2,28,300 Exercise: 3.2 1. a) Rs 5,00,000 b) Rs 9,75,000 c) Rs 18,16,100 2. a) Rs 9,180 b) Rs 40,000 3. a) Rs 23,12,500 b) Rs 3,60,00,000 4. a) 12% b) 20% 5. a) (i) Rs 34,560 (ii) Rs 2% (iii) Rs 50,00,000 b) (i) Rs 20,000 (ii) 2% (iii) Rs 3,90,62,500 6. a) Rs 20,832 (b) Rs 28,000 7. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 3.3 1. a) (i) Rs 12,50,000 (ii) Rs 48,00,000 (iii) Rs 78,93,000 b) (i) Rs 1,200 ii) Rs 490 (iii) Rs 560 2. a) (i) Rs 9,60,000 (ii) Rs 960 b) (i) Rs 57,60,000 (ii) Rs 2,304 3. a) (i) 20% (ii) Rs 10,00,000 b) (i) Rs 4,80,000 (ii)20% 4. a) (i) Rs 1,12,00,000 (ii) Rs 22,40,000 b) (i) Rs 48,60,000 (ii) Rs 12,15,000 5. a) Rs 36,210 b) Rs 1,26,360 6. a) (i) 22% (ii) Rs 2,20,000 b) (i) 27% (ii) Rs 1,08,000 7. a) (i) Rs 1,48,00,000 (ii) Rs 77,700 b) (i) Rs 1,25,40,000 (ii) Rs 1,25,400 8. Complete your project work in a group or individually. Discuss the outcomes in the class. 4 . Household Arithmetic Exercise: 4.1 1. a) 17 units n) 1165 units 2. b) 2 units c) 16 units 3. a) Rs 30 b) Rs 30 4. a) (i) Rs 149 (ii) Rs 162 b) Rs 142.50 c) Rs 175 5. a) (i) Rs 300 (ii) Rs 380 b) (i) Rs 425 (ii) Rs 678 c) (i) Rs 430 (ii) Rs 761 6. a) (i) Rs 1,029 (ii) Rs 1,050 (iii) Rs 1,102.50 (iv) Rs 1,155 b) Rs 283.50 more 7. a) 35 units b) 110 units 8. a) 30 units b) Bhadra c) (i) Rs 210.70 (ii) Rs 267.75 9. a) Rs 320 b) Rs 321.20 10. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 4.2 1. a) 1000 l b) Rs 110 c) Rs 3,420 2. a) 20 units b) 371 units c) 1125 units 3. a) (i) Rs 352.50 (ii) Rs 690 b) (i) Rs 534 (ii) Rs 1,590 4. a) (i) 25000 l (ii) Rs 242.50 (iii) Rs 727.50 (iv) 18 units b) (i) 30 unit (ii) Rs 1,061.50 (iii) Rs 3,184.50 (iv) 35 units 5. a) Rs 960.30 b) Rs 9,882 6. a) (i) Rs 4,088.55 (ii) Rs 4,215 (iii) Rs 5,058 (iv) Rs 6,322.50 b) (i) Rs 8,241.12(ii) Rs 9,345.60 (iii) Rs 12,744 7. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 4.3 1. a) 500 calls b) Rs 1,125 2. a) Rs 1,276.90 b) Rs 2,553.80 3. a) (i) Rs 200 (ii) Rs 2,200 (iii) Rs 286, Rs 323.18 (iv) Rs 2,809.18 b) (i) 2,163 calls (ii) Rs 2,188 (iii) Rs 284.44, Rs 321.42 (iv) Rs 2,993.86 c) Rs 638.45 d) Rs 15.96 e) Rs 127.69 4. a) (i) Rs 452 (ii) Rs 400 (iii) 375 calls b) (i) Rs 1,130 (ii) Rs 1,000 (iii) 975 calls 5. a) (i) Rs 390.73 (ii) 51 minutes 11.9 seconds b) (i) Rs 390.75 (ii) 4 hours 15 minutes 55.8 seconds 6. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 4.4 1. Answer the questions yourself and discuss in the class. 2. a) Rs 350 b) Rs 500 c) Rs 1,200 3. a) (i) Rs 50 (ii) Rs 30 (iii) Rs 310 (iv) Rs 30 less b) (i) Rs 75 (ii) Rs 30 (iii) Rs 1,230 (iv) Rs 430 less 4. a) (i) Rs 100 (ii) Rs 300 (iii) 6 km b) (i) Rs 75 (ii) 7 km

Vedanta Excel in Mathematics - Book 9 368 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Unit 5 Mensuration-I (Area) Exercise: 5.1 1. a) 1 2 xy cm2 b) 1 2 mn cm2 c) 3 4 x2 cm2 d) q 4 4p2 – q2 cm2 e) x + y + z 2 cm f) s(s – a) (s – b) (s – c) cm2 g) 1 4 (p + q + r) (p + q – r) (p + r – q) (q + r – p) cm2 2. a) (i) 24 cm2 (ii) 84 cm2 (iii) 90 cm2 (iv) 360 cm2 b) 210 ft2 . c) 16,296 m2 d) 168 cm2 e) 4 3 cm2 3. a) 168 cm2 b) 336 cm2 c) 126 cm2 d) 192 cm2 e) 240 cm2 f) 222 cm2 4. a) (i) 9 cm, 12 cm, 15 cm (ii) 54 cm2 b) (i) 26 m, 28 m, 30 m (ii) 336 m2 c) 60 m d) 108 m 5. a) 180 m2 b) 2340 m2 c) 216 m2 d) 0.96 hectare 6. a) (i) 5376 cm2 (ii) Rs 806.40 b) (i) 528 cm2 (ii) Rs 1,320 c) (i) 2016 cm2 (ii) Rs 3,024 Exercise: 5.2 1. a) 16 Aana b) (i) 4 Paisa (ii) 64 Paisa c) (i) 4 Daam (ii) 16 Daam (iii) 256 Daam d) 20 Kattha e) (i) 20 Dhur (ii) 400 Dhur f) 13.31 Ropani 2. a) (i) 96 Aana (ii) 167 Aana (iii) 810 Paisa (iv) 1343 Paisa (v) 100 Kattha (vi) 129 Kattha (vii) 2947 Dhur (viii) 3390 Dhur b) (i) 2 Ropani (ii) 3.5 Ropani (iii) 2.5625 Ropani (iv) 20.375 Ropani (v) 5 Bigha (vi) 2.5 Bigha (vii) 20.5125 Bigha (viii) 11.225 Bigha 3. a) 69-3-1-2.25 (Ropani) b) 140-1-1-2.46 (Ropani) c) 5-10-10 (Bigha) d) 2-4-16 (Bigha) 4. a) 3.93 Ropani b) 40 Aana c) 4.784 Bigha d) 4.96 Dhur 5. Show to your teacher. 6. a) (i) A = 1 2 d1 × d2 (ii) 60000 m2 (iii) 117-15-0-1.43 Ropani b) (i) A = 1 2 d (a + b) (ii) 140000 m2 (iii) 20-13-8.75 Bigha c) Rs 1,00,00,000 7. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 5.3 1. a) Equal b) Equal 2. a) (i) xy m2 (ii) xy m2 (iii) 2xy m2 (iv) 2xz m2 (v) 2yz m2 (vi) 2z (x + y) m2 (vii) xy +2z (x + y) m2 (viii) xy +2z (x + y) m2 b) PQ m2 c) 4xy m2 d) 5a2 ft2 e) (2A+B) m2 3. a) 100 m2 b) 625 ft2 c) 576 m2 d) 144 m2 e) 300 sq. ft. f) 240 ft2 g) 209 m2 4. a) (i) 150m2 (ii) 150m2 (iii) 150m2 (iv) 100m2 (v) 250m2 (vi) 550 m2 b) (i) 288 m2 (ii) 240 m2 (iii) 528 m2 c) (i) 450 ft2 (ii) 900 ft2 (iii) 1,350 ft2 5. a) 5m b) 20 ft. c) 9.6 ft. 6. a) 128 m2 b) 300 sq. ft. 7. a) 102 m2 b) 276 m2 c) 3170 ft2 8. a) (i) 124 m2 (ii) 31 b) (i) 13 (ii) 200 9. a) 29 b) 605 10. a) 10 ft. b) 4 m 11. Complete your project work in a group or individually. Discuss the outcomes in the class. Unit 6 Mensuration-II (Prism) Exercise: 6.1 1. Answer the given questions yourself and discuss in the class. Then show to your teacher. 2. a) 540 cm3 b) 480 cm2 c) 255 cm2 d) 648 cm2 3. a) 150 cm2 b) 64 cm3 c) 6 cm, 516 cm2 d) 4 cm e) 50 4. a) 96 cm2 , 288 cm2 , 480 cm2 , 576 cm3 b) 38 cm2 , 170 cm2 , 246 cm2 , 190 cm3 c) 48 cm2 , 204 cm2 , 300 cm2 , 288 cm3 d) 32 cm2 , 150 cm2 , 214 cm2 , 160 cm3 e) 69 cm2 , 240 cm2 , 378 cm2 , 345 cm3 f) 600 cm2 , 3,600 cm2 , 4,200 cm2 , 18,000 cm3 5. a) (i) 2,16,000 cm3 , 60 cm (ii) 21,600 cm2 b) (i) 10 m2 (ii) 3,000 l (iii) Rs 12,000 c) (i) 960 (ii) 10 cm 6. a) 6 cm b) 20 cm c) 20 cm d) 27 7. a) 9.6 l b) 10 cm, 4 l Exercise: 6.2 1. a) (i) 1 2 xy (ii) (x+y+z)×l (iii) xy+(x+y+z)×l (iv) 1 2 xyl b) (i) 1 4 (p + q + r) (p + q – r) (p + r – q) (q + r – p) (ii) (p+q+r)×h Answers

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 369 Vedanta Excel in Mathematics - Book 9 (iii) 1 2 (p + q + r) (p + q – r) (p + r – q) (q + r – p) + (p+q+r)×h (iv) 1 4 (p + q + r) (p + q – r) (p + r – q) (q + r – p) ×h c) (i) 3 4 a2 cm2 (ii) 3ah cm2 (iii) ( 3 2 a2 + 3ah) cm2 (iv) 3 4 a2 h cm3 2. a) 24 cm2 b) 36 cm2 c) 270 cm2 d) 20 cm e) 366 cm2 f) 288 cm2 3. a) 410 cm3 b) 180 cm3 c) 8 cm 4. a) (i) 750 cm3 (ii) 270 cm3 (iii) 1200 cm3 (iv) 1080 cm3 (v) 1200 cm3 (vi) 3840 cm3 b) (i) 128 cm2 , 147.6 cm2 (ii) 103.2 cm2 ,113.4 cm2 (iii) 360 cm2 , 408cm2 (iv) 900 cm2 , 960 cm2 (v) 450 cm2 , 536.6 cm2 (vi) 380 cm2 , 414.1 cm2 5. a) 8 cm b) 18 cm c) 30 cm 6. a) 24 cm b) 10.5 cm 7. a) (i) 1650 cm3 (ii) 1232 cm2 b) (i) 2160 cm2 (ii) 2412 cm2 c) (i) 432 cm2 (ii) 432 cm3 8. a) (i) 230 3 cm2 (ii) 450 cm3 b) (i) 152 sq2 , 96 ft3 9. a) 5 m b) 10 m 10. a) 146.83 ft3 b) 8 inch 11. Complete your project work in a group or individually. Discuss the outcomes in the class. 7. Mensuration-II (Cylinder and Sphere) Exercise: 7.1 1. a) (i) 2πxy cm2 (ii) 2πx(x +y) cm2 (iii) πx2 y cm3 b) (i) 2πb (A + a) cm2 (ii) 2π(A+a)(b+A-a) cm2 (iii) πb (A+a)(A-a) cm3 c) (i) πpq cm2 (ii) pq(π+2) cm2 (iii) pq(π+2) + πp2 cm2 (iv) 1 2 πp2 q cm3 2. a) 440 cm2 b) 330 in2 c) 770 cm3 3. a) (i) 1100 cm2 (ii) 1408 cm2 (iii) 3850 cm3 b) (i) 1056 cm2 , 1282.29 cm2 , 3168 cm3 c) (i) 880 cm2 , 1188 cm2 , 3080 cm3 d) (i) 5500 in2 , 7425 in2 , 48125 in3 4. a) (i) 6600 cm2 , 9372 cm2 , 69300 cm3 b) (i) 55 in2 , 74.25 in2 , 48.125 in3 5. a) 3080 l b) 269.5 l c) 30.8 m3 6. a) 297 cm2 b) 2013 cm2 7. a) 68750 cm3 b) 20944 cm3 c)264 cm2 d) 1188 cm2 8. a) 2156 cm3 b) 179.67 cm3 9. a)4620 cm3 b) 3080 cm3 c)1188 cm2 10. a) 720cm2 , 874 cm2 , 1540 cm3 b) 5400 cm2 , 6786 cm2 , 34650 cm3 c) 297 m3 11. a) 1760 cm3 b) 352 cm3 c) 2.112 kg d) 13.31 kg 12. a) 25 cm b) 5600 13. a) Bucket-B can hold 4.048 l more water than bucket-A b) Tank-Y can hold 4455 l more water than tank-X. 14. a) 35,200 l b) 19.25 l 15. a) 2904 m2 b) 8.8 m3 16. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 7.2 1. a) (i) 4πx2 cm2 (ii) 4 3 πx3 cm3 b) (i) 2πp2 cm2 (ii) 3πp2 cm2 (iii) 2 3 πp3 cm3 c) 12.57 cm2 , 4.19 cm3 2. a) (i) 616 cm2 , 1437.33 cm3 (ii) 498.96 cm2 , 1047.82 cm3 (iii) 5544 cm2 , 38808 cm3 (iv) 221.76 cm2 , 310.46 cm3 b) (i) 2772 cm2 , 4158 cm2 , 19404 cm3 (ii) 1232 cm2 , 1848 cm2 ,5749.33 cm3 (iii) 443.52 cm2 , 665.28 cm2 , 1241.86 cm3 (iv) 49.28 cm2 , 73.92 cm2 , 45.99 cm3 3. a) 154 cm2 , 179.67 cm3 b) 1386 cm2 , 220.5 m3 c) 21999494092 km3 4. a) 11.21 kg b) 4365.9 cm3 c) 154 cm2 d) 1386 cm2 5. a) 1039.4 cm2 , 2425.5 cm3 b) 27.72 cm2 , 19.404 cm3 6. a) 718.67 cm3 b) 2887.5 cm2 7. a) 0.262 cm3 b) 462 cm2 c) 1527.43 cm3 8. a) 924 cm2 b) 8316 cm2 9. a) 3 cm b) 7 cm c) 21 cm 10. a) 38808 cm3 b) 5544 cm2 11. a) (i) 2772 cm2 (ii) 4158 cm2 (iii) 19404 cm3 b) (i) 1232 cm2 (iii) 5749.33 cm3 c)693 cm2 , 1039.5 cm2 12. a) 3 times b) (i) 16:1 (ii) 64:1 c) (i) 2:3 (ii) 4:9 13. a) 9 cm b) 12 cm c) 4 cm 14. a) 6.5 cm b) 0.63 cm c) 16 15. a) 1.44 m b) 2 cm c) 5 16. a) (i) 77.44 kg (ii) 11088 cm2 b) (i) 6.04×1024 kg (ii) 1.55 ×108 km2 Exercise: 7.3 1. a) Rs xy b) Rs PQ c) Rs AB d) Rs 21,600 e) Rs 39,000 2. a) Rs 35,100 b) Rs 6,600 c) Rs 4,500 3. a) (i) Rs 13,500 (ii) Rs 12,750 (iii) Rs 12,000 b) (i) Rs 10,800 (ii) Rs 10,000 (iii) Rs 11,520 4. a) Rs 16,900 b) Rs 18,900 c) Rs 11,520 5. a) Rs 8,100 b) Rs 25,050 , Rs 22,545 6. a) 5m b) Rs 11,520 c) Rs 7,200 d) 5 m e) 6 m Answers

Vedanta Excel in Mathematics - Book 9 370 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 7. a) Rs 10,800 b) Rs 9,200 8. a) Rs 10,800 b) 4 m c) Rs 6,480 d) Rs 6,336 e) 4.5 m 9. a) Rs 8,100 b) 4.2 m 10. Complete your project work in a group or individually. Discuss the outcomes in the class. 8. Sequence and Series Exercise: 8.1 1. Answer the questions yourself and discuss in the class. 2. a) 24, 29 b) 8, 5 c) 16, 32 d) 6, 3 e) 25, 36 f) 5 36 , 6 49 3. a) 5, 8, 11, 14 b) –2, 3, 8, 13 c) 2, 6, 12, 20 d) –2, 3, –4, 5 e) 1, 3, 6, 10 f) 0, 1 3, 1 2, 3 5 g) 1 4, 1 3, 5 16, 7 25 h) –1 3 , 2 7 , –3 13, 4 21 4. a) 4n, 24, 36 b) 5n+1, 31, 46 c) 13 – 4n, –11, –23d) n2 , 36, 81 e) (–1)n+1.2n, –64, 512 f) n n + 1, 6 7, 9 10 g) n2 (n + 1)2, 36 49 , 81 100 h) n2 + 2, 38, 83 5. a) 3, 6, 12, 24, 48 b) 4, –3, 1, –2, –1, –3 c) 15, 101 6. a) (i) (ii) 3n+2 (iii) 32 b) (i) (ii) 3n – 2 (iii) 28 c) (i) (ii) n2 (iii) 100 d) (i) (ii) 4n+2 (iii) 42 Exercise: 8.2 1. Answer the questions yourself and discuss in the class. 2. a) sequence b) series c) sequence d) series 3. a) 5 + 10 + 15 + 20 + 25 b) 1 – 2 + 4 – 8 + 16 c) –7 – 3 + 1 + 5 + … d) 1+1 2+1 4+1 8+... 4. a) 5 b) 4 c) 5 d) 8 5. a) 50 b) 120 c) 42 d) 62 e) 138 f) 6 g) 4 6. a) 3 b) –3 7. a) 6, 10, 4 b) 20, 35, 15 8. a) tn = 3n –1, 6 n = 1 (3n – 1) b) tn = 4n – 14, 6 n = 1 (4n – 14) c) tn = 3n, 5 n = 1 3n d) tn = 4n–1, 9 n = 1 4n – 1 e) tn = (–1)n+1.n , 10 n = 1 ( –1)n + 1.n f) tn =(–1)n.2n , 12 n = 1 (–1)n.2n g) tn= n n + 1, 7 n =1 n n + 1 h) tn = ( n n + 1) 2 , 9 n =1 ( n n + 1) 2 i) tn = n + 1 2n + 1, 8 n =1 n + 1 2n + 1 j) tn = (–1)n 5n (n + 1)2, 10 n =1 (–1)n 5n (n + 1)2 k) tn = n(n+1), 7 n =1 n(n + 1) l) tn =n2 + 2n + 3, 10 n =1 (n2 + 2n + 3) Exercise: 8.3 1 Answer the questions yourself and discuss in the class. 2. a) tn = a+(n-1)d b) t6 = a+5d 3. a) A.P. b) A.P. c) Not an A.P. d) Not an A.P. 4. a) 2n+1 b) 4n – 9 c) 17 – 7n d) 1 – 3n 5. a) 21 b) 61 c) 55 6. a) 3 b) 4 c) -5 d) 13 7. a) 16 b) 37 c) 40 8. a) 19th b) 21st 9. a) Yes b) Yes c) No 10. a) 2, 3, 50 b) 7, 4, 63 c) -28, 3, 29 11. a) 3+8+13+18+… b) 50+47+44+41+… 12. a)12th b) 15th 13. b) 0 14. a) Rs 23,000 b) Rs 300 c) 50 15. a) Offer B b) (i) 170, (ii) B.S.2086 16. a) 7 b) 10th day c) 21 years d) 16 days 17. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 8.4 1 Answer the questions yourself and discuss in the class. 2. a) tn = arn–1 b) t4 = xy3 3. a) G.P. b) G.P. c) G.P. d) Not an G.P. Answers

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 371 Vedanta Excel in Mathematics - Book 9 4. a) 2, 6, 18 b) –9, –27, –81 c) 1 8, -1 4 , 1 2 d) 27, 9, 3 5. a) 384 b) 1 c) 144 6. a) 2 b) 4 c) 3 d) 1 2 7. a) 7 b) 5 8. a) 9th b) 8th 9. a) Yes b) Yes 10. a) 1536 b) 1458 c) 16 11. a) 5 + 15 + 45 + 135 + ... b) 9 + 18 + 36 + 72 + ... 12. a) 64 b) 324 c) (i) 40 (ii) 160 13. a) Rs 87,846 b) Rs 20,480 c) 8,09,112 d) Rs 2,45,650 14. Answer yourself and discuss in the class. 15. Complete your project work in a group or individually. Discuss the outcomes in the class. 9. Factorisation of algebraic expressions Exercise: 9.1 1. a) x (x + 1) b) x (x + 2) c) (x+ 2) (x + 1) d) (a + 3) (a + 3) 2. a) 2x (a + 2b) b) 2p(p – 3) c) 3ab (2a + 3b) d) 2px (x – 2 + 3p) e) 3x2 y2 (2x + 3y – 1) f) (2x + 3y) (a + b) g) (3a – 1) (x – y) h) (x + 3) (x + 2) i) (t – 1) (2t – 1) 3. a) x2 + 5x + 6 = (x + 3) (x + 2) b) (x2 + x – 6) = (x + 3) (x – 2) c) x2 – 7x + 12 = (x – 4) (x – 3) d) 2x2 + 7x + 3 = (2x + 1) (x + 3) e) 2x2 + x – 6 = (2x – 3) (x + 2) f) 2x2 – 5x + 3 = (2x – 3) (x – 1) 4. a) (a + b) (x + y) b) (m + n) (p – q) c) (a + b) (a + c) d) (x2 + y2 ) (m – n) e) (x – 2) (y + 3) f) (x + 4) (x + 3) g) (p – 8) (p – 1) h) (4x – 1) (4x – 1) i) (a – c) (a – b) j) (x – y) (x + 3) k) (pr – q) (qr – p) l) (x + y + z) (y + z) 5. a) (x + 1) (x + 3) b) (x – 8) (x + 1) c) (a – 15) (a – 12) d) (x + 2) (2x + 3) e) (p – 3) (3p + 2) f) (x – y) (2x + 5y) g) (a – b) (3a – 13b) h) abx (3a + 5b) (3a – b) i) (3a b + 4) (4a b – 5) j) ( x y – 3y x ) (x y + y x) k) (x + y + 1) (2x + 2y + 7) l) (x – y – 2) (3x – 3y – 4) 6. a) (i) (x + 5) m, (x + 3) m (ii) (4x + 16) m b) (i) (x + 8) m, (x + 5) m (ii) (x2 + 9x + 18) sq. m. c) (2x2 + 13x + 6) sq. m. 7. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 9.2 1. a) (3x + 2) (3x – 2) b) (5ab + 1) (5ab – 1) c) 3a (4x + 5y) (4x – 5y) d) (x2 + y2 ) (x + y) (x – y) e) xy(4x2 + 9y2 ) (2x + 3y) (2x – 3y) f) (25a2 + 16b2 ) (5a + 4b) (5a – 4b) g) (2 + m – n) (2 – m + n) h) (1 + a – b) (1 – a + b) i) (4 + 5p – 5q) (4 – 5p + 5q) j) 3(a – b) (a + b) k) (a + b + c) (a + b – c) l) (p + q + r) (p – q – r) m) (a + b – 2) (a – b + 2) n) (4a2 + 2a + 1) (4a2 – 2a – 1) o) (x + y) (ax – ay – 1) p) (a – b) (a + b – x) 2. a) 96 cm2 b) 216 cm2 c) 299 m2 d) 392 m2 e) 544 sq.ft. f) 756 m2 3. a) (x + y + 5 (x – y + 1) b) (a + b – 2) (a – b – 8) c) (p + q – 14) (p – q + 2) d) (x2 + y – 5) (x2 – y + 13) e) (3a + 4x – 4) (3a – 4x – 6) f) (25y + z – 2) (25y – z + 18) g) (4p – 8q + 3r) (4p – 10q – 3r) h) (5x + 3y – z) (5x – 7y + z) 4. a) (ac + ab – bc + bd) (ac – ad + bc + bd) (b) (xy + x + y – 1) (xy – x – y – 1) c) (3p + 2q + pq – 6) (3p + 2q – pq + 6) d) (30 – xy + 10x + 3y) (30 – xy – 10x – 3y) 5. a) 544 cm2 b) 18,900 m2 6. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 9.3 1. a) (x2 + 2x+2)(x2 – 2x+2) b) (2a2 + 2a+1)(2a2 – 2a+1) c)(p2 +4pq+8q2 )(p2 – 4pq+8q2 ) d) (9m2 +6mn+2n2 )(9m2 – 6mn+2n2 ) e) (8a2 +12ax+9x2 )(8a2 – 12ax+9a2 ) f) (25b2 +10bd+2d2 )(25b2 – 10bd+2d2 ) g) (m2 +m+1 2)(m2 – m+1 2) h) (10c2 +2t+t 2 5)(10c2 – 2t+t 2 5) 2. a) (x2 + xy+y2 )(x2 – xy+y2 ) b) (a2 + 2a+4)(a2 – 2a+4) c)(6p2 +3p+1)(6p2 – 3p+1) d) (3m2 +4mn+5n2 )(3m2 – 4mn+5n2 ) e) (2x2 +5xy+3y2 )(2x2 – 5xy+3y2 ) f) (15x2 +11xy+4y2 )(15x2 – 11xy+4y2 ) g) 2(4x2 +xy+y2 )(4x2 – xy+y2 ) h) 5(2b2 +by+3y2 )(2b2 – by+3y2 ) (i) 3mn(4m2 +5mn + 3n2 ) (4m2 – 5mn + 3n2 ) 3. a) (2x2 +2x – 3)(2x2 – 2x – 3) b) (3p2 +2p – 4)(3p2 – 2p – 4) Answers

Vedanta Excel in Mathematics - Book 9 372 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur c)(5a2 +3a – 1)(5a2 – 3a – 1) d) (y2 +3yz – 2z2 )(y2 – 3yz – 2z2 ) e) (9a2 +3ax – 5x2 )(9a2 – 3ax – 5x2 ) f) (11p2 +pq – 6q2 )(11p2 – pq – 6q2 ) g) x (2x2 +6xy – 5y2 )(2x2 – 6xy– 5y2 ) h) 3p(3b2 +bp – p2 )(3b2 – bp – p2 ) (i) 15ab(2a2 +2ab – 3b2 ) (2a2 – 2ab – 3b2 ) 4. a) (x+1)(x – 1)(3x+4)(3x – 4) b) (y+1)(y – 1)(2y+1)(2y – 1) c)(m+1)(m – 1)(5m+2)(5m – 2) d) (a+b)(a – b) (3a +5b)(3a – 5b) e) 25(c + d)(c – d) (2c + d)(2c - d) f) (p+q)(p – q)(13p +14q) (13p – 14 q) 5. a) x2 y2 + x y + 1 x2 y2 – x y + 1 b) a2 b2 + b2 a2+ 1 a2 b2 + b2 a2 – 1 c) x + 1 + 1 x x – 1 + 1 x d) x2 y2 + 3x y + 1 x2 y2 – 3x y + 1 e) m2 n2 + 5m n – 2 m2 n2 – 5m n – 2 f) b2 d2 + b d – 10 b2 d2 – b d – 10 6. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 9.4 3. a) (2x + 5)3 b) (3a + 4)3 c) (4y – 5)3 d) (7m – 6)3 e) (10a – 3b)3 f) (2x + 11y)3 4. a) (2a + 3) (2a + 3) (2a + 3) b) (5x + 1) (5x + 1) (5x + 1) c) (3p – 4) (3p – 4) (3p – 4) d) (9w – 8) (9w – 8) (9w – 8) e) (6m – 5n)(6m – 5n)(6m – 5n) f) (13e + 7g) (13e + 7g) (13e + 7g) 5. a) (2x + y) (4x2 – 2xy + y2 ) b) (1 + 3a) (1 – 3a + 9a2 ) c) 2t(4t – 1)(16t2 + 4t + 1) d) y(x – 4y)(x2 + 4xy + 16y2 ) e) (a2 +b) (a4 – a2 b+ b2 ) f) (4x2 y - 5) (16x4 y2 + 20x2 y+25) g) (a+2)(a – 2) (a2 + 2a + 4) (a2 – 2a + 4) h) (3x + y)(3x– y) (9x2 + 3xy+ y2 ) (9x2 – 3xy + y2 ) 6. a) (a+b+1)(a2 +2ab+b2 – a – b + 1) b) (x – 1) (x2 + 7x + 19) c) –(x+3y)(7x2 + 6xy + 3y2 ) d) p + 1 p p2 – 1 + 1 p2 e) a b – b a a b + 1 + b a a b – 1 + b a f) x x + 1 x x2 – 1 + 1 x2 g) y y + 1 y y – 1 y y + 1 + 1 y y – 1 + 1 y y2 – 1 + 1 y2 h) p q p – q p p2 + q + q2 p2 7. a) (3x + 4y) (9x2 – 2xy + 16y2 ) b) (2 + 3a) (4 – 9a + 9a2 ) c) (4m – 5n) (16m2 + 13mn + 25n2 ) d) (p – 2) (2p2 – 3) (p2 + 2p + 4) e) (2a – 1) (5a2 + 2) (4a2 + 2a + 1) f) (x -1) (2x – 1) (x2 + x + 1)(4x2 + 2x + 1) 8. a) (i) (2a +1) ft., (a +1) ft., (a – 1) ft. (ii) (2a2 + 3a + 1) sq. ft. b) (i) 27 cm3 (ii) (x3 – 27) cm3 9. Complete your project work in a group or individually. Discuss the outcomes in the class. 10. H.C.F. and L.C.M. Exercise: 10.1 1. Answer the questions yourself and discuss in the class. 2. a) 2x (x + 2) b) 2xy (x – 1) c) 3a2 b2 (2a + 3b) d) 4a2 b2 (a + b – 2) e) p – q 3. a) a + b b) a (a – 2) c) x + 3 d) x + y e) 4 (x + 5) f) x (x + 2) g) a – b – 1 h) x2 + 2xy + 4y2 i) p +2 j) x2 + 2xy + 2y2 4. a) a2 + a + 1 b) p2 – 2p + 4 c) 4x2 + 2x + 1 d) 9a2 – 3a + 1 e) 18x (x – 3y) f) 10 (x – 10y) g) x2 + 5x + 12 h) a2 + 4a + 10 i) a + 1 j) x – 1 5. a) a +2 b) x – 3 c) 2x + 3 d) x – 2 e) a + 2 f) m – 1 g) x – 4y h) x (x + 5) i) 4x2 – 6xy + 9y2 j) x2 – xy + y2 6. a) x2 + x + 1 b) p + 2 c) a – b d) a2 + ab + b2 e) a + b + c f) 3x + 2y + 2z g) x – y + 1 h) a – b + 1 i) 4x2 + 2x + 1 j) 9x2 +3x + 1 7. a) (x + 15) m b) (x – 2) m 8. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 10.2 1. Answer the questions yourself and discuss in the class. 2. a) 6x2 (x2 – 1) (x + 3) b) 12x2 (x + 2)(x2 – 9) c) 24a2 b2 (a + b) (a3 – b3 ) d) (x2 – 4) (x2 – 9) e) (a – 3) (a – 4) (a – 5) 3. a) 6x2 (x + 2) b) ax (x2 – 1) c) 10x4 y4 (2x + y) d) xy (x2 – y2 ) e) 2x (4x2 – 1) f) a3 – b3 g) (x + 3) (x2 – 4) h) 3 (x2 – 9) (x2 – 3x + 9) i) a2 b2 (a2 – b2 ) (a2 + ab + b2 ) j) (x2 – xy + y2 )(x3 – y3 ) k) (a2 +ab + b2 ) (a3 + b3 ) l) 2x(2x – 1) (27x3 + 1) Answers

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 373 Vedanta Excel in Mathematics - Book 9 4. a) 4 (x3 + 125y3 ) (x2 + 5xy + 25y2 ) b) 6a (8a3 – 27b3 ) (4a2 + 6ab+ 9b2 ) c) (1 – 8x3 )(1 + 2x – 4x2 ) d) (2a + 1) (8a3 – 1) (4a2 – 2a – 1) e) x (x2 + 5x + 9)(x2 – 5x + 9) f) y (10y2 + 4y – 1)(10y2 – 4y – 1) 5. a) (a+2)2 (a3 – 8) b) (a – 3)2 (a3 + 27) c) a (a – 1)2 (a2 – 4) d) (x + y)(x2 + y2 )(x3 – y3 ) e) 2x2 (2x – 1) (3x – 2) (x3 + 8) f) x2 (x + 1)(x + 3)(x3 – 27) g) a2 (a +1)(a +2)(a3 – 8) h) a (a3 – 1) i) (x – y)(x2 + y2 )(x3 + y3 ) j) (x +1)(x +2)(x+3) 6. a) (a + b + c) (a + b – c) (b + c – a) (c + a – b) b) (x + y + z) (x – y – z) (y – z – x) (z – x – y) c) (3x + 2y + 2z) (3x -2y + 2z) (3x – 2y – 2z) (2z – 3x – 2y) d) (x2 – a2 )(x2 – b2 ) e) (x2 – 1)(x2 – 4) f) a (a + b + 5) (a + b – 5) (a – b +1) g) xy (x + 3y + 11)(x – 3y + 11)(x – 3y – 3)(x – 3y – 11) 7. a) 4a (a – b)2 b) x3 + 1 8. Complete your project work in a group or individually. Discuss the outcomes in the class. 11. Indices Exercise: 11.1 1. a) am + n b) 1 c) 1 d) 2 2. a) 8 b) 5 c) 1 121 d) 125 e) 1 16 f) 1 2 g) 81 16 h) 14 13 i) 1 2 j) 25 k) 7 l) 2 5 m) 1 2 n) 2 3 o) 10 p) 3 3. a) 1 b) 1 c) 2 5 d) 2 3 4. a) 9 4a2 x2 b) 16 25p2 q2 c) 2 5 d) 5 7 5. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 g) 1 ab h) xy x2 + y2 7. a) 1 6 b) 1 c) 2 d) 2 e) 2 5 f) 1 8. a) 15a2 b b) a2 c)1 d) 2p q e) 6m2 n f) 1 (a + b)2 g) 1 (2x – y)2 h) (a – b) 9. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 g) 1 h) 1 i) x y 2a j) a b a + b 10. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 12. Simultaneous Equations Exercise: 12.1 1. a) 1 b) –4 c) y = –2, x = 2 d) 4 e) 6 2. a) (5, 2) b) (1, 4) c) (–3, 1) d) (3, 5) e) (5, 2) 3. a) x = 3, y = 2 b) x = 4, y = 1 c) x = 1, y = 3 d) x = 2 , y = 1 e) x = 3 , y = –1 f) x = 2, y = –1 g) x = –1, y = 1 h) x = 3, y = –2 i) x = 5, y = 0 j) x = 1, y = 0 k) x = 1, y = 1 l) x = 1, y = 1 m) x = 2, y = 3 n) x = 3, y = –2 o) x = 10, y = 3 4. a) x = 3, y = 6 b) x = 2, y = 10 c) x = 1, y = –4 d) x = 6, y = 4 e) x = 2, y = –1 f) x = 1, y = 4 g) x = 2, y = 1 h) x = 5, y = 2 i) x = 3, y = 2 j) x = 3, y = –2 k) x = 4, y = 1 l) x = 3, y = 0 m) x = 5, y = 7 n) x = 4, y = 6 o) x = 5, y = 5 Exercise: 12.2 1. a) (i) x + y = 60, x – y = 10 (ii) 35, 25 b) (i) x + y = 77, x – y = 55 (ii) 66, 11 c) (i) x = 2y, x + y = 30 (ii) 20, 10 d) (i) x = 3y, x + y = 80 (ii) 60, 20 e) (i) x + y = 59, y = x – 7 (ii) 33, 26 f) (i) x – y = 12, x = 3y (ii) 18, 6 g) (i) x + y = 14, x – y = 4 (ii) 9, 5 2. a) (i) x + y = 1000, x – y = 200 (ii) Rs 600, Rs 400 b) (i) x + y = 5000, x – y = 1500 (ii) Rs 3,250, Rs 1,750 c) (i) x + y = 38, x – y = 22 (ii) 30 years, 8 years d) (i) x = 6y, x – y = 35 (ii) 42 years, 7 years 3. a) (i) x = 2y, 4x + 6y = 1540 (ii) Rs 220, Rs 110 b) (i) x = 4y, 2x + 3y = 3300 Answers

Vedanta Excel in Mathematics - Book 9 374 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur (ii) Rs 1,200, Rs 300 c) (i) x + y = 5, 150x + 5oy = 550 (ii) 3, 2 d) (i) x + y = 7, 200x + 25y = 700 (ii) 3, 4 4. a) (i) x + 2y = 70, 2x + y = 95 (ii) 40 years, 15 years b) (i) x + y = 44, x – 2y = 8 (ii) 32 years, 12 years c) 42 years, 12 years d) 14 years, 10 years e) 47 years, 7 years f) 45 years, 13 years g) 29 years, 5 years h) 58 years, 25 years i) 29 years, 5 years j) 45 years, 15 years k) 15 years, 21 years l) 19 years, 15 years. 5. a) (i) 10x + y (ii) x + y = 16, x – y = 2 (iii) 97 b) (i) x+ y = 10, x – y = –2 (ii) 46 c) 63 d) 39 e) 27 f) 84 g) 38 h) 59 6. a) 7 9 b) 4 9 c) 3 8 d) Rs 25,000, Rs 15,000 e) Rs 8,000, Rs 6,000 7. a) (i) Rs 40, Rs 50 (ii) 5 km b) (i) Rs 25, Rs 5 (ii) 14 days 8. a) (i) 34 years, 6 years (ii) 8 years b) (i) 50 years, 30 years (ii) 26 years 9. a) 5, 7 b) Rs 60, Rs 90 10. a) 12 : 00 b) 65 km/hr, 60 km/hr 11. a) 17 m, 9 m b) 180 12. Complete your project work in a group or individually. Discuss the outcomes in the class. 13. Geometry: Triangle Exercise: 13.1 1 and 2 Answer the questions yourself and discuss in class. Then show to your teacher. 3. a) 23o , 46o , 111o b) 40o , 60o , 80o c) 30o , 35o , 115o d) 72o , 36o , 72o 4. a) a = 60o , b = 50o b) 90o , 140o c) 28o , 112o d) 80o , 120o , 160o e) x = 100o , y = 40o , z = 140o f) x = 50o , y = 40o g) x = 55o , y = 165o h) x = 20o i) x = 50o 5. a) (i) ∠ACD = ∠ABC + ∠BAC (iii) 2 : 3 b) (ii) 120°, 1 : 2 Exercise: 13.2 1. a) (i) longest side AB shortest side AC (ii) longest side DF shortest side DE (iii) longest side PQ shortest side PR b) (i) Greatest angle ∠ Y Smallest angle ∠ Z (ii) Greatest angle ∠ A Smallest angle ∠ B (iii) Greatest angle ∠ F Smallest angle ∠ E c) Longest side BC Shortest side AB d) Longest side QR Shortest side PQ e) Greatest angle ∠ Y Smallest angle ∠ X 2. Answer the questions yourself and discuss in class. Then show to your teacher. 3. a) 3 cm < AC < 13 cm b) 2 cm < c < 10 cm 4. a) S.S.S., ∠ A = ∠ P, ∠ B = ∠ R, ∠ C = ∠ Q b) R.H.S., DF = ZX, ∠ F = ∠ Z, ∠ E = ∠ Y c) S.A.S., BC = QR, ∠ C = ∠ R, ∠ B = ∠ Q d) A.S.A., ∠ F = ∠ S, EF = RS, GF = TS 5. a) S.S.S., a = 70°, x = 50°, b = y = 60° b) A.S.A., x = 6.4 cm, y = 5.8 cm, a = 30° 8 and 9 Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 13.3 1. Answer the questions yourself and discuss in the class. Then show to your teacher. 2. a) 70°, 70°, 40° b) 130° c) 60°, 60° d) 20° e) 110° f) 69°, 69°, 111° g) 70°, 140° h) 65°, 130°, 65° i) 37°, 106° j) 60°, 90° k) 30°, 60° l) 70°, 40° 3. a) 75°, 75°, 30° b) 60°, 70°, 40°, 80° c) 110° 5. a) x = 2, y = 3 b) x = 4 cm, y = 3 cm 6. a) AB ⊥ BC b) BD = CD 11. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 13.4 1. a) 8 cm b) 2 cm c) 10 cm, 9 cm d) 12 cm e) 2 cm 2. a) 4.5 cm b) 7.5 cm, 4.5 cm c) 9 cm, 5 cm d) 3.2 cm, 2.4 cm e) 6 cm 3. a) 18 cm b) 43.01 in c) 72 ft. Answers

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 375 Vedanta Excel in Mathematics - Book 9 14. Geometry: Parallelogram Exercise: 14.1 1. Answer the questions yourself and discuss in the class. Then show to your teacher. 2. a) 10 cm b) 45° c) 40° d) 30° 3. a) w = y = 2x = 72°, z = 3x° = 108° b) a = 4y = 80°, b = 5y = 100° c) p + 10° = 2p – 50° = 70°, p + q = r = 110° d) x = 20°, 2x = 40° e) y = 65°, x = 50° f) x = 125° g) a = 40°, b = 140° h) x = 70°, y = 110° 4. a) 70° b) 70° c) 120° d) 25°, 65° 5. a) 140° b) 33° c) 60°, 120° d) 62°, 28° e) 25°, 115° f) 30°, 60° g) 65° 6. a) x = y = 4 cm b) x = 15, y = 5 c) a = 5, b = 1 d) 8 cm e) p = 3 cm, q = 6 cm 7. a) 75°, 15° b) 15°, 75° 12. Complete your project work in a group or individually. Discuss the outcomes in the class. 15. Geometry: Construction Exercise: 15.1, Exercise: 15.2 and Exercise: 15.3 Complete the construction of quadrilaterals yourself and compare with your friends. Then show to your teacher. 16. Geometry: Circle Exercise: 16.1 1, 2, 3. Answer the questions yourself and discuss in the class. Then show to your teacher. 4. a) (i) 5 cm (ii) 12 cm b) (i) 4 cm (ii) 8 cm c) 24 cm d) (i) 10 cm (ii) 8 cm (iii) 4 cm 5. a) (i) 3 cm (ii) 2 cm b) (i) 8 cm (ii) 5 cm (iii) 10 cm 6. a) 6 cm b) 14 cm c) 6 cm 7. a) (i) 1 cm (ii) 7 cm b) 2.5 cm c) 13 cm 13. a) 10 m b) 48 ft. c) 160 m 14. Complete your project work in a group or individually. Discuss the outcomes in the class. 17. Statistics (I): Classification and Graphical representation of data Exercise: 17.1 1. Answer the questions yourself and discuss in the class. Then show to your teacher. 2 and 3.Draw the cumulative frequency table yourself and discuss in the class. Then show to your teacher. 4. a) p = 4, q = 25, r = 5 b) a = 25, b = 20, c = 100 5, 6, 7 Draw the cumulative frequency table yourself and discuss in the class. Then show to your teacher. 8. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 17.2 1. Answer the questions yourself and discuss in the class. Then show to your teacher. 2. a) (i) 20 (ii) 65 (iii) 30 b) (i) 60 (ii) (30 – 40), 60 (iii) 100 3 and 4 Draw the histograms yourself and discuss in the class. Then show to your teacher. 5. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 17.3 1. Answer the questions yourself and discuss in the class. Then show to your teacher. 2. Draw the histograms and frequency polygons yourself and discuss in the class. Then show to your teacher. 3 and 4 Draw the frequency polygons yourself and discuss in the class. Then show to your teacher. 5. Complete your project work in a group or individually. Discuss the outcomes in the class. Exercise: 17.4 1. a) (i) 50 (ii) 20 (iii) 20 b) (i) 30 (ii) 10-20 (iii) 10 2. a) (i) 20 (ii) 16 b) (i) 75 (ii) 30 Answers

Vedanta Excel in Mathematics - Book 9 376 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 3. Draw the histograms and frequency polygons yourself and discuss in the class. Then show to your teacher. 4. Draw the ogive curves yourself and discuss in the class. Then show to your teacher. 5. Draw the ogive curves yourself and discuss in the class. Then show to your teacher. 18. Statistics (II): Measures of central tendencies Exercise: 18.1 1. a) 34 b) Rs 450 c) 13 years d) 67 2. a) 10 years b) 7 c) 7 3. a) 120 b) 27, 93 c) 5 d) 25 4. a) 66 b) 10.8 years c) 63.44 kg d) 62.2 cm 5. a) 28 b) 7 c) (i) 35 (ii) 100 d) (i) 11 (ii) 50 6. a) 11 b) 20 c) 5 d) 10 Exercise: 18.2 1. Answer the questions yourself and show to your teacher. 2. a) (i) 20 (ii) 28 (iii) 30 (iv) 24 (v) 13 b) 50 kg c) 34 years d) 32 3. a) (i) 12 (ii) 10 (iii) 10 b) (i) 39 (ii) 34 (iii) 70 4. a) 25 b) 158 c) 6 d) 7 5. a) 18 b) 172 c) 3 d) 7 6. a) (i) 7 (ii) 21 kg b) 18 years c) Rs 36 d) 8 to 12 e) Rs 1,500 to Rs 2,000 f) (i) c (ii) f g) 7 h) Rs 150 7. a) (i) 120 cm (ii) 95 cm (ii) 25 cm b) 59 c) 50 8. a) 34.5 years b) Rs 542.85 9. a) 50 b) 20 c) Rs 65 d) 40 kg 10. a) 36 b) 80 c) 27, 37 d) Q1 = 100 cm, Q2 = 120 cm, Q3 = 130 cm 11. Complete your project work in a group or individually. Discuss the outcomes in the class. 19. Probability Exercise: 19.1 1. and 2. Answer the questions yourself and discuss in the class. Then show to your teacher. 3. a) 1 6 b) 1 5 c) 2 5 d) 1 8 4. a) (i) S = {H, T} (ii) 1 2 (iii) 1 2 (iv) Yes b) (i) S = {1, 2, 3, 4, 5, 6} (ii) 1 2 (iii) 1 6 (iv) Yes c) (ii) 1 2 (iii) 1 6 (iv) Sure events 5. a) (i) P (E) = n(E) n(S) (ii) 2 5 (iii) 1 10 (iv) 9 10 b) (i) 1 2 (ii) 3 10 (iii) 1 5 (iv) 1 10 c) (i) 1 8 (ii) 0 (iii) 1 2 (iv) impossible events 6. a) (i) 0 (ii) 1 13 (iii) 1 4 (iv) 12 13 b) (i) 1 26 (ii) 1 26 (iii) 3 13 (iv) 3 4 7. a) (i) 5 8 (ii) 3 8 (iii) 5 8 (iv) 1 5 b) (i) 5 12 (ii) 1 3 (iii) 3 4 c) (i) 1 11 (ii) 2 11 (iii) 2 11 (iv) 10 11 (v) 10 11 (vi) 9 11 d) (i) 1 8 (ii) 1 2 (iii) 1 4 (iv) 3 8 (v) 3 4 (vi) 3 8 Answers

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 377 Vedanta Excel in Mathematics - Book 9 8. a) 0.562 b) 0.001 c) 870 d) (i) 0.27 (ii) 0.38 e) (i) 0.82 (ii) 0.965 (iii) 0.08 9. Complete your project work in a group or individually. Discuss the outcomes in the class. 20. Trigonometry Exercise: 20.1 1. a) sinθ = AB AC , cosθ = BC AC , tanθ = AB BC b) sinα = PQ QR , cosα = PR QR , tanα = PQ PR c) sinβ = YZ XY , cosβ = ZX XY , tanβ = YZ ZX 2. a) sinθ = 3 5 , cosθ = 4 5 , tanθ = 3 4 b) sinα = 3 5 , cosα = 4 5 , tanα = 3 4 c) sinβ = 12 13 , cosβ = 5 13 ,tanβ = 12 5 3. a) sinα = CQ PC , tanθ = CA AB b) sinβ = BY BX , cosθ = AC BC c) tanα = PR PQ, cosθ = PR QR d) sinα = QR PR , cosq = TR QR 4. a) (i) sinθ = AB AC (ii) tanθ (iii) 1 (iv) 15 cm b) (i) PQ PR (ii) sina (iii) 1 (iv) 9 cm 5. a) (i) 5 cm (ii) 3 5 (iii) 12 cm b) (i) 5 cm (ii) 12 5 (iii) 4 cm c) (i) 24 cm (ii) 12 5 (iii) 26 cm 6. a) (i) Right-angled triangle (ii) 5 cm (iii) 3 5 b) (i) Right-angled triangle (ii) 12 cm (iii) 3 5 7. a) (i) 10 cm (ii) 3 5 b) (i) 13 cm (ii) 12 13 Exercise: 20.2 1. a) 3 4 b) 1 2 c) 3 d) 0 e) 3 2 f) 0 g) 1 4 h) 1 i) 1 j) 5 k) 1 l) 1 2 m) 1 2 n) 1 2 o) 1 4 p) 4 3 q) 0 r) 1 s) 2 3 t) 1 u) 1 v) 1 w) 1 x) 3 y) 2 z) 0 3. a) 15 cm, 8.7 cm b) 8 cm, 11.3 cm c) 13.9 cm, 6.9 cm 4. 6.4 cm 5. a) 60°, 30° b) 30°, 60° c) 45°, 45° 6. a) 61.5 m b) 65.82 m 7. a) 10 3 m, b) 25 2 ft., 25 ft. 8. a) 60° b) 30° 9. Complete your project work in a group or individually. Discuss the outcomes in the class. Revision and Practice Time Set 1. a) P – Q = {10, 14, 16, 20} b) d) 5 10 14 16 20 12 18 15 P Q 11 13 17 19 Answers

Vedanta Excel in Mathematics - Book 9 378 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 2. a) A ∩ B ∩ C = {r} b) A ∪ B = {e, i, l, r, s, u, v} (c) (A ∪ B)– C ={n} (d) Yes Taxation 1. b) Rs 4,50,000 c) Rs 70,000 2. a) I = TTR 100 b) Rs 2,10,000 c) Rs 1,29,500 3. a) Rs 11,40,000 b) Rs 9,86,000 c) Rs 82,200 4. a) Discount = D% of MP b) Rs 29,440 c) Rs 32,384 5. a) Rs 3,000 b) Rs 292.50 c) Rs 169.50 more 6. a) Rs 40,680 b) 17% 7. a) Rs 2,20,000 b) Rs 2,48,600 Commission, Bonus and Dividend 1. a) Rs 17,500 b) Rs 24,82,500 c) Rs 20,000 more 2. a) Rs 10,000 b) 2% c) Rs 26,540 3. a) Rs 48,000 b) 4% c) Rs 4,50,00,000 4. b) Rs 1,25,000 c) Rs 3,125 d) Rs 1,562.50 more Household Arithmetic 1. b) 140 units c) Rs 1,117.20 d) Rs 79.80 2. a) 18,000 l b) Rs 178 c) Rs 534 d) 20 units 3. a) Rs 200 b) Rs 2,200 c) Rs 2,480 d) Rs 2,809.18 4. a) NBSM b) Rs 50 c) Rs 780 d) Rs 20 less Mensuration 1. a) b 4 4a2 – b2 b) 5280 cm2 c) 5544 cm2 2. a) 1 Ropani 3 Aana and 2.6 Paisa b) 24 Kattha and 16.12 Dhur 3. a) 900 sq. ft. b) Rs 1,24,650 c) 40 students 4. a) 1,44,000 cm3 b) 12,000 cm2 c) 19,200 cm2 5. a) pr2 h b) 8662.5 cm2 c) 8.6625 l 6. a) 0.539 m3 b) 35 cm c) 30800 cm2 7. a) Rs 11,880 b) 707.85 kg 8. 3,850 cm3 9. 962.5 m3 10. 24,750 l Sequence and Series 1. a) Geometric series b) 3 c) 3n d) 5 n =1 3n 2. a) H H H C H H C H H C H H C H b) tn = 2 (n +1) c) 22 3. a) a = 8, d = –2 b) 8 + 6 + 4 +... 4. a) a = 3, d = 2 b) 3, 5, 7, .... 5. a) Rs 5,120 b) 7th day Factorisation 1. a) (2x2 + 6x + 9) (2x2 – 6x + 9) b) (x2 + 4xy + 8y2 ) (x2 – 4xy + 8y2 ) c) (a2 + ab + b2 ) (a2 – ab + b2 ) d) (a2 + 3a + 3) (a2 – 3a + 3) e) (x2 + 7x + 5) (x2 – 7x + 5) f) (x2 y2 + xy + 1) (x2 y2 – xy + 1) g) (2x + 3) (4x2 – 6x + 9) h) 5a3 x(3a + x) (9a2 – 3ax + x2 ) i) 2a2 b(2a – 3b) (4a2 + 6ab + 9b2 ) j) (a + b – 9) (a – b + 1) k) (x + 3y – 6) (x – 3y – 4) l) (xy + x – y + 1) (xy – x + y + 1) m) (xy + 3x + 2y – 6) (xy – 3x – 2y – 6) 3. a) b) 10 32 3 5 Z G 10 i v u s a n r el Answers

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 379 Vedanta Excel in Mathematics - Book 9 HCF and LCM d) HCF : (m – n – 1) LCM : mn(m + n) (m – n – 1) a) HCF : x(x + 2) LCM : x (x2 – 4) b) HCF : 3x(x – 5) LCM : 3x(x2 – 25) c) HCF : (a + b – 6) LCM : b(a – b) (a + b – 6) 1. e) HCF : (4a2 – 2a + 1) LCM : (8a3 + 1) (4a2 + 2a – 1) f) HCF : (4x2 + 2x + 1) LCM : (1 – 8x3 ) (1 + 2x – 4x2 ) g) HCF : (x2 – 2x + 4) LCM : (x3 + 8) (x2 + 2x + 4) h) HCF : (4a2 – 2ab + b2 ) LCM : (2a + b) (16a4 + 4a2 b2 + b4 ) i) HCF : (x2 + 5x + 13) LCM : x(x4 + x2 + 169) j) HCF : (x – 1) (x – 3) LCM : (x2 – 1) (x2 – 9) k) HCF : (x + 1) (x + 2) LCM : (x2 – 1) (x2 – 4) 2. a) HCF : 1 LCM : 72ab(a + 1) (a – 3) (a2 – 4) b) HCF : mn(2m + 3n) LCF : mn(2m – 3n) (4m – 5n) (8m3 + 27n3 ) c) HCF : (y2 + y + 1), LCM : y6 – 1 d) HCF : x2 + xy + y2 , LCM : x(x2 – xy + y2 ) (x3 – y3 ) Indices 1. a) 1 b) 3 c) 2 d) 1 e) 1 2. a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 g) a2(p2 – n2 ) h) 1 i) 1 j) 1 Simultaneous Equations 1. a) x + y = 6, 3x + y = 14 b) 4, 2 c) 3 2. a) x – 4y = –15, x + y = 45 b) 33 years, 12 years c) 21 years 3. a) x – 6y = –30, 3x – 8y = 20 b) 36 years, 11 years c) 23 years 4. a) x = 4y, x = 3y + 10 b) 40 years, 10 years c) B.S. 2034, B.S. 2064 5. a) 10x + y b) 4x – 5y = 0, x – y = 1 c) 54 6. a) y = 2x, x = y – 2 b) 24 7. 73 8. 57 9. 41 km/hr, 49 km/hr 10. 10 p.m. Geometry-Triangle 1. a) ∠ACD = ∠ABC + ∠BAC c) 2 : 1 2. a) AD ⊥ BC b) BD = CD 3. 101 m Geometry-Parallelogram 1. a) (ii) b) 5 2. a) (iv) b) 5 3. a) Parallelogram b) 15° 4. a) 120° b) PS // QR Circle 1. a) Isosceles triangle b) 10 cm c) Yes 2. a) AB = 2AM b) 5 cm c) 2 cm 3. a) TQ = 2OP b) 17 cm c) 9 cm 4. a) OM ⊥ AB b) 3 cm c) 1 cm 5. a) PQ = RS b) 14 cm c) OX > OZ 6. a) Segment of circle b) OP = OQ c) Equilateral triangle 7. a) CP = PD b) Yes c) 5 cm 8. a) OM ⊥ AB b) 3.5 cm Statistics 1. a) Individual series c) 34.33 d) 21 2. Show to your teacher. 3. c) 7 d) Rs 12,80,000 4. a) Discrete data c) 60 d) 80 5. a) 65 kg b) Q3 c) 65 kg Probability 1. a) S = {S, D} b) 1 2 c) 1 2 d) Yes 2. b) 1 2 c) 1 6 d) Yes 3. a) 0 b) 1 13 c) 1 4 d) 12 13 4. a) 4 9 b) 5 9 c) 4 9 d) 4 9 e) 2 9 f) 1 3 Trigonometry 1. a) tanθ b) 1 c) 16 cm d) 60° 2. a) 5 cm b) 3 5 c) 13 cm d) 60° 3. a) 1 3 b) 20 m c) 10 m d) 45° 4. a) sine b) 2 3 c) 20 3 feet d) 45° Answers

Vedanta Excel in Mathematics - Book 9 380 Students’ Evaluation System (Class 9) (a) Internal (Formative) Evaluation Students’ individual portfolio should be managed with the marks under the following headings. S.N. Area of evaluation Weightage 1. Participation: attendance and participation in classroom activities 3 2. Terminal examinations (Obtained marks from each of 2 terminal exams should be converted in to 3) 6 3. Practical/Project work (at least 1 project work from each area should be prepared and presented in class) 16 Total 25 (b) External (Summative) Evaluation Summative evaluation covers 75% of the entire weightage of the course intended by the curriculum. The items should be chosen from all the chapters of the course of a session for the test paper prepared to the external evaluation. The test should contain knowledge, skill, application and higher ability based items by following specification grid. Specification Grid for External Evaluation F.M.: 75 Time: 3 hours S.N. Area Working hours Knowledge (16%) Understanding (24%) Application (40%) Higher ability (20%) Total no. of items Total no. of questions Total Marks No. of items Marks No. of items Marks No. of items Marks No. of items Marks 1. Set 12 1 1 1 1 1 3 1 1 4 1 6 2. Arithmetic 28 2 2 2 3 3 5 2 3 9 3 13 3. Mensuration 28 2 2 2 3 2 5 2 3 8 3 13 4. Algebra 32 2 2 2 4 3 7 1 2 8 3 15 5. Geometry 28 2 2 2 3 2 5 2 3 8 3 13 6. Statistics and Probability 24 2 2 2 3 2 4 2 2 8 2 11 7. Trigonometry 8 1 1 1 1 1 1 1 1 4 1 4 Total 160 12 12 12 18 14 30 11 15 49 16 75

381 Vedanta Excel in Mathematics - Book 9 MODEL QUESTION SET Class: IX Time: 3 hours Full Marks: 75 Attempt all the questions. 1. If U = {x : x < 10, x ∈N} is a universal set, A = {x: x is a factor of 6}, B = {y: y is a prime number} and C = {z: z is a multiple of 3} are the subsets of U. (a) What is the cardinal number set U? [1] (b) Write (A ∩ B) in listing method. [1] (c) Find (A ∪ B) – C and illustrate it in a Venn-diagram by shading. [3] (d) What is the relation between A ∩ B and A ∩ B ∩ C? Give reason. [1] 2. Mr. Yadav buys 100 cycles of same model from India and marked each cycle with price Rs 5,000. He allows 10% discount in each cycle and sells all the cycles by levying 13% VAT. (a) What is the formula to calculate the price of cycle after allowing discount? [1] (b) Calculate the selling price of all cycles with VAT. [2] (c) If he deposits half of the selling price of all cycles excluding VAT in a bank for next one year at 12% p.a., how much net interest will he get if 5% of interest is charged as income tax%? [2] 3. A group of youths returned from foreign employment of a village wished to run a mini-hydro company to uplift the economic status of the villagers. They sold 4,00,000 shares each of Rs. 100. After 1 year, the company made a net form of Rs. 25,00,000 and the management committee of the company decided to distribute Rs. 5,00,000 cash dividend among the shareholders. (a) From which amount is the cash dividend distributed? [1] (b) What percent of cash dividend was distributed? [1] (c) How much cash dividend would Janak get at the same rate if he had 4,800 shares and the net profit of the company was Rs. 30,00,000? [2] 4. The table given below shows the rate of electricity charge with service charge for a 5A meter box. Case kWh (units) Service charge Energy charge/unit Consumed units is up to 20 units 0-20 Rs. 30.00 Rs. 0.00 Consumed units exceeds 20 units 0-20 21-30 31-50 Rs. 30.00 Rs. 50.00 Rs. 50.00 Rs. 3.00 Rs. 6.50 Rs. 8.00 A 5A transmission line is connected in Bina’s house, and the meter reading of 1 Bhadra and 1 Aswin was recorded as 01045 units and 01070 units respectively. The electricity office is at a distance of 2 km from Bina’s house. The minimum fare of taxi is Rs. 14 and fare per 200 meter is Rs 7.20.

Vedanta Excel in Mathematics - Book 9 382 Answer the following questions. (a) How many unit of electricity was consumed in Bhadra? [1] (b) What was the electricity bill of the month Bhadra? [2] (c) If she used the taxi to go to the electricity office for paying the bill, how much money did she pay for the taxi fare? [1] 5. In Geetanjali Secondary School, the room of class IX is rectangular in shape. It is 15 m long, 10 m broad and 5 m high. Also, it contains two windows of size 2 m × 1.5 m each and a door of size 1 m × 4 m. (a) Write down the formula to calculate the area of four walls. [1] (b) What is the area the ceiling of the room? [1] (c) Find the cost of colouring its walls excluding the windows and door at Rs 250 per sq. metre. [2] (d) By how much more or less does it require to papering the walls at Rs. 275 per sq. metre than couloring the walls? [1] 6. On a sunny day, Mr. Shah was working in the field. He went to a store and bought a cylindrical can completely filled with pineapple juice. The inner radius of base of the of can was 5 cm and height 14 cm. (a) What is the formula to calculate the volume of the can? [1] (A) πr2 h (B) 1 3 πr2 h (C) 2πrh (D) 2πr(r + h) (b) How many liter of juice was filled in the can? Find it. [3] 7. Gopal’s house was completely destroyed due to the devastating earth-quake on 12 Baishakh 2072 B.S. An organization distributed the canvas for making the tent. He made an equilateral triangular tent by using the canvas including the floor for the temporary shelter. The edge of the triangular face was 12 ft. each and length of the tent was 20 ft. (a) How many square feet of canvas was given to him? [2] (b) By how many feet would the length of tent be increased if he didn’t use the canvas on the floor? [2] 8. In a Boost up Test of mathematics held on last Sunday in a school, the marks obtained by a group of students are 16, 24, 36, …., 81. (a) What is the formula to find the general term of a geometric sequence? [1] (A) t n = a + (n – 1)d (B) t n = a + (n – 1)r (C) t n = arn (D) t n = arn – 1 (b) What is the common ratio of the sequence of marks? [1] (c) How many students are there in the group? [2] 15 m 5 m 10 m Model Question Set

383 Vedanta Excel in Mathematics - Book 9 9. Solve the following problems. (a) Find the H.C.F. of 8a3 + b3 and 16a4 + 4a2 b2 + b4 [3] (b) Simplify: a+b xa2 xb2 × b+c xb2 xc2 × c+a xc2 xa2 [3] 10. Zeena bought 3 kg of apples and 5 kg of oranges for Rs 1155 from a fruit corner. At the same time, Chhiring bought 2 kg of oranges with the price of 1 kg of apples from the same corner. (a) Represent the given statements in linear equations. [1] (b) Find the rates of cost of apples and oranges per kg. [2] (c) If the rate of cost of oranges were decreased by 10% and that of apples were increased by 20%, how many kg of oranges and apples of equal quantity would be bought for Rs. 5544? [2] 11. (a) Draw two triangles ABC of different shapes and sizes. Explore the experimentally the relation between the sum of any two sides and the third side. [3] (b) A boy 1.8 m tall casts the shadow of length 3 m at 2:30 p.m., what is the height of the tree which casts the shadow of length 30 m at the same time? [2] 12. A parallelogram ABCD is given aside. (a) What is the relation between the diagonals of parallelogram? [1] (A) equal (B) perpendicular to each other (C) bisect each other (D) bisect each other perpendicularly. (b) If ∠ABC = (30o + p) and ∠ADC = (60o – p), what is the value of p? Find it. [1] (c) Construct a rhombus ABCD in which diagonal AC = 6 cm and diagonal BD = 8 cm. [2] 13.Dipesh draws a circle with centre O and radius 5 cm. He draws a chord PQ of length 6 cm and mark the mid-point M of it. Also, he draws another chord RS and joins centre O to the mid-point N of it. (a) What is the relationship between OM and PQ? [1] (b) Find the length of OM. [2] (c) How should the chord RS be equal to the chord AB with respect to OM and ON? Give reason. [1] A B C D P M Q N S O R Model Question Set

Vedanta Excel in Mathematics - Book 9 384 14.Last week, the mathematics teacher of Children Park English Secondary School administered a class test for class-IX students. He recorded the marks obtained by students in the following table. Marks obtained 15 30 45 60 75 90 No. of students 2 3 7 10 8 4 (a) What type of data is it? [1] (b) Construct a cumulative frequency distribution table? [1] (c) Calculate the median mark. [2] (d) What is the average mark of students who secured more than median mark? [2] 15.A mathematics teacher divides the students into groups of 6/6 students. He rolls a die to select the student of a particular group for solving certain question in the board. If he rolls the die once, answer the following questions. (a) Write down the sample space for the above experiment. [1] (b) What is the probability of selecting the students numbered by an even number in a group? [2] (c) What is probability of not selecting the students numbered by multiple of 3 in a group? [2] 16.In the given figure, a right angled triangle ABC is formed when a ladder AC is rest against a vertical wall AB making an angle of 60o with the ground. The length of the ladder is 18 ft. Answer the following questions: (a) Which trigonometric ratio is represented by AB AC ? [1] (b) What is the value of tan60o ? [1] (c) What is the length of BC? [1] (d) What would be the size of angle ACB when the wall AB and the distance of the foot of the ladder from the base of wall (BC) were equal? [1] ♠♠♠ … The End … ♠♠♠ https://vedantapublication.com.np/model_questions/latest_syllabus_20220412191104.pdf Latest Curriculum of Class 9 (2078) Please! Scan this QR code or browse the link given below: C 60° A B Model Question Set