Vedanta Excel in Mathematics Book 9 Final (2078)

Answers

12. (i) 35 VB 13. (i) MS 14. (i) 13 IC
(ii) 60 25 35 20 (ii) 75 135 75 90 (ii) 37 25 2 13
(iii) (iii) 90 (iii)
(iv) 225 37

15. 15 16. 3550 17. (i) T C 18. 10 19. (i) 1000 (ii) 900
(ii) 3 : 5

20. (i) ZG 20 10 40
(ii) 50 32 3 5 5
(iii) 10
(iv) 47

10

Profit and Loss

1. 1137% profit 2. 20% 3. Rs 22,80,000 4. 2.5% loss 5. Rs 2,200 6. 10%
9. 1191% 10. Rs 150 11. 12.5%
7. Rs 8 8. 21% 16. Rs 55 17. 5% 12. Rs 51 13. 1% loss
22. Rs 1,000
14. 20% 15. 14 2 % 18. Rs 1,000 profit
7
19. 1% loss 20. No gain, no loss 21. 1% loss 23. Rs 700 24. 12%

25. Rs 1,750 26. Rs 1,500 27. 30.95% 28. Rs 100 29. Rs 80 30. 2,000

31. Rs 640, 25% 32. Rs 3,238.40 33. Rs 6,000 34. Rs 800 35. Rs 225 36. 15% 37. 15%

38. Rs 4,000 39. 40% 40. 20% 41. 2% 42. Rs 1800 43. Shop - A by 1.9%

44. Shop A 45. Rs 40,680, 17% 46. Rs 60,000, Rs 1,014

Commission and Taxation

1. Rs 10,000 2. Rs 5,00,000 3. Rs 24,82,500 4. Rs 5,700 5. Rs 26,250 6. Rs 16,000
7. 2% 11. Rs 6,01,800
12. Rs 35,156.25 8. Rs 30,000 9. Rs 11,170 10. Rs 98,000

13. 12% 14. Rs 1,50,00,000

Household Arithmetic

1. a) Rs 162 2. Rs 1,302 3. a) 130 units 4. (i) 15 units, 27 units, 45 units (ii)

Rs 73.50, Rs 152.39, Rs 289.10 (iii) 89.71% 5. Rs 728.44 6. a) 224 b) Rs 309.50

7. Rs 758.23 8. 425 calls 9. Rs 1,140 10. Rs 14,301 11. Rs 230 12. 2 km 13. 6 km

Mensuration

1. 12 cm 2. 40 cm, 25 cm 3. 77 cm2 4. Rs 3,000 5. Increased by 30.8 %

6. 31.68 km/hr 7. 3 ft. 8. 5 cm 9. 400 10. 7200 ft2

11. Rs 1,92,000 12. Rs 13,40,000 13. Rs 57,024 14. (i) Rs 2,25,600 (ii) Rs 1,37,700

15. Rs 6,450 16. Rs 10,080 17. Rs 1,875 18. 5 cm 19. (i) 2571 cm3

(ii) Rs 14,140.50 (iii) 48 20. Rs 3,600 21. Rs 3,360

22. (i) 61,200 (ii) Rs 74,340 23. (i) 4,410 m3 (ii) 1254 m2, Rs 6,270

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 351 Vedanta Excel in Mathematics - Book 9

Answers

Algebraic Expressions

1. a) (x + y + 3)(x + y – 3) b) (a + b + c) (a + b – c) c) (p + q + r) (p – q – r)

d) (4x2 + 2x – 1) (4x2 – 2x + 1) e) (a – b + c + d) ( a – b – c – d) f) (x – a) ( x – b)

g) (ab + a –b + 1) (ab – a + b + 1) h) (a2b-2 + ab-1 + 1)( a2b-2 – ab-1 + 1)

i) (x2 + xy + y2) (x2 – xy + y2) (x4 – x2y2 + y4) j) (b – d) (b2 + b + bd + d + d2)

k) (p + 1) (p2 + p + 1) l) (2m + 1)(2m – 1) (4m2 + 2m + 1)

m) (4 – 3x)3 n) (a – 1) (a – 2) (a – 3) (a – 4)

o) (a + b + c) (a2 + b2 + c2 – ab – bc – ca) p) (x – y – z) (x2 + y2 + z2 + xy – yz + zx)

2. a) 4a2 b) 0 c) 4 d) 0 e) 8x3y f) 1
x(x+2a) (a – 1) (a – 5) x4 – y4 1–a

g) 1 h) 0 i) 3 j) 1
a+c

Indices x2 x
f) a2(p2 – n2) (a – x)x y
1. a) 1 b) 1 c) 1 d) 1 e) 1 g) h) i) 1 j) 1
b) 1 c) 0
3. a) 1 d) 2 e) 0 f) 1 g) 1 h) 1 i) ± 2 j) 0, 2
2 2 3

Simultaneous Linear Equation

1. a) x = 29, y = 5 b) x = 34, y = 6 c) x = 4, y = 7 d) x = 2, y = 4

e) x = -3, y = 9 f) x = 2, y = 2 g) x = 5, y = 5 h) x = 1, y = 5

i) x = 5, y = 3 j) x = 8, y = 2

2. a) 30, 25 b) 44, 18 c) 20, 5 d) Rs 150, Rs 60 e) 42 yrs, 12 yrs

f) 47 yrs, 7 yrs g) 15 yrs, 21 yrs h) 46 yrs, 18 yrs i) 59 j) 38

Quadratic Equation

1. a) 1, 1032 b) 4c , – 5c c) – q ± q2 – 4pr d) 1, 2b e) 6, – 16 f) 3, – 1
3 4 2p a–b 3 2
9 2 a br – cq
g) –4, 4 h) 4, – 9 i) 0, 4 j) ± 5 k) ± 2 l) ± 5 m) –a, –b n) cp – ar

o) a + b + c, a + b + c

2. a) 7, 4 b) 6, 4 c) 63 or, 36 d) 3, 4, 5 e) 25, 20 3. –1, 3
2

1. 1 : 6 b) 1 : 12 Ratio and Proportion
2. a) 45, 60 b) 40, 50, 60
c) 16, 24 d) 15 : 8 e) 3 : 5 3. a) 3 b) 14, 56 c) 9, 36

1. 76° 2. 58° Triangle

3. 30°

1. a) 1 cm b) 17 cm Circle

Vedanta Excel in Mathematics - Book 9 352 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Answers

Trigonometry

1. a) sinD = CD , cosT = AC 2. sinT 45 , cosT 53, tanT 43, sinD 153, cosD 1132, tanD 152
BD BC

3. a) sinT = 3 , cosD 12 b) sinT = 3 , cosD 45 4. 1 10. 30° 11. 45°
5 13 5 2
12. 45° 13. 8 cm 14. 3 cm

17. a) 30° b) 45° c) 30° d) 30°

Statistics

1. Show to your teacher. 2. Show to your teacher.

3. a) 270 b) 213 c) 432 4. a) 54 inches b) 26 c) 10 d) 35
e) 8
5. a) 33.5, 30, 30 b) Rs 800, Rs 800, Rs 800 6. a) 11 b) 8 c) 9, 11 d) 6, 4

7. a) Q1 = 20, Q2 = 30, Q3 = 50 b) Q1 = 10, Q2 = 20, Q3 = 25

Probability

1. 1 2. 4 3. 2 4. A 1 , B 1 , C 1
4 17 25 2 4 4

5. (i) 1 (ii) 1 (iii) 1 (iv) 1 (v) 2 (vi) 4 (vii) 51
13 52 4 2 13 13 52

(viii) 3 (ix) 3 (x) 3
4 4 13

6. (i) 4 (ii) 5 (iii) 4 (iv) 4 (v) 2 (vi) 1
9 9 9 9 9 3

7. (i) 2 (ii) 3 (iii) 5 (iv) 1
5 5 9 3

8. 7 (i) 6 (ii) 2 (iii) 9 9. 2
26 25 5 25 3

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 353 Vedanta Excel in Mathematics - Book 9

Ministry of Education, Science and Technology ,
Curriculum Development Centre
Curriculum of Class 9 (2071)

Area Subject Matters No. of
Periods

1. Set * Review of set 8
* Union, intersection, difference of two sets, complement

of set
* Problem solving of simple verbal problems in two sets

by using Venn-diagram

* Problems related to profit and loss

* Problems related to Commission, discount, tax, 20
dividend 24
2. Arithmetic

* Household arithmetic (Electricity bill, water bill,
telephone bill, taximeter)

3. Mensuration * Simple problems related to area (carpeting the floor,
paving stones, construction paths, colouring and
* plastering, etc.) and expense on it.
* Surface area, area of cross-section and volume of prism,
cube, cuboid
Project work and problem collections related to
mensuration in real life situations

4. Algebra * Factorization of the expressions of the form
a4 + a2b2 + b4
30
* Problems related to indices (Simplification of negative
and fractional indices)

* Exponential equations (excluding the quadratic form)
* Simple problems related to ratio and proportion
* Solution of simultaneous linear equations (substitution

method, elimination method and graphical method)
* Solution of quadratic equations (factorization method,

completing square method and by using formula)

5. Geometry Verification of properties of triangles (use of
experimental and theoretical verifications)
* The sum of three angles of triangle is two right angles 55
(only theoretical proof)
* The exterior angle formed by producing a side of a
triangle is equal to the sum of two opposite interior
angles (only theoretical proof)

Vedanta Excel in Mathematics - Book 9 354 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Area Subject Matters No. of
Periods
* The base angles of an isosceles triangle are equal (only
theoretical proof) 44

* The sides opposite to two equal angles of a triangle are
also equal (Theoretical proof)

* The angular bisector of vertical angle of an isosceles
triangle is perpendicular to the base and bisects the
base and its converse theorem (Theoretical proof)

* The sum of any two sides of a triangle is greater than
the third side (experimental verification)

* In any triangle, the side opposite to the greater angle is
longer than the side opposite to the smaller angle and
its converse theorem (Experimental verification)

* Of all straight line segments drawn to a given line from
an external point, the perpendicular is the shortest one
(Experimental verification)

* Pythagoras Theorem (Experimental verification)
* Discussion on the interrelationship of the properties of

sides and angles of triangle
* A straight line segment joining the mid-points of any

two sides of a triangle is parallel to the third side and
it is equal to half of the length of the third side and its
conversion theorem (only theoretical proof)
Verification of properties of parallelograms
* The straight line segments that join the ends of two
equal and parallel line segments towards the same
sides are also equal and parallel (Theoretical proof)
* The opposite sides of a parallelogram are equal
(Theoretical proof)
* The opposite angles of a parallelogram are equal
(Theoretical proof)
* The diagonals of a parallelogram bisect each other
(Theoretical proof)
* The theoretical proofs of the converse of theorems
mentioned above
* Discussion of the interrelationship of quadrilaterals
(parallelogram, rectangle, square, rhombus)
Construction
* Construction of quadrilaterals (square, rectangle,
rhombus, parallelogram and trapezium)
Similarity
* Review of similarity
* Simple problems on similar polygons

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 355 Vedanta Excel in Mathematics - Book 9

Area Subject Matters No. of
Periods
Circle
* The perpendicular drawn from the centre of a circle to

a chord, bisects the chord (Theoretical proof)
* The line joining the mid-point of a chord and the centre

of a circle is perpendicular to the chord (Theoretical
proof)
* Equal chords of a circle are equidistant from the centre
and its converse theorem (Theoretical proof)

6. Trigonometry * Introduction of trigonometric ratios on the basis of 12
* right-angled triangle 13
* Measurement and problem solving related to the ratios
sine, cosine and tangent
Problems related to sine, cosine and tangent of the
angles 0°, 30°, 45°, 60° and 90° in right-angled triangles.

7. Statistics * Introduction and construction of line graph, pie-chart,
histogram and ogive by using the collected data

* The other information of the data from histogram and
ogive

* Calculation of mean, median, mode and quartiles of
ungrouped data

8. Probability * Introduction to probability
*
* Definition of probability and basic concepts

Use of simple probability and introduction of
probability scale (0 - 1)

* Introduction and use of formula to estimate probability

a) Empirical probability 8

P = Number of observed outcomes
Total number of experiments

b) Probability of an event
Favourable number of cases
P = Exhaustive number of cases

Vedanta Excel in Mathematics - Book 9 356 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 357 Subject: Compulsory Mathematics Specification grid Time: 3 hours
Secondary Level (Class 9) HA Total Remarks

Full Marks: 100 -4

Cognitive Units KC A
domain 1×4
1×4
Subject area
1×4
1 Set 1 Set --
2×4
2 Profit and loss
3×4
2 Arithmetic 3 Commission, discount, tax, 1×1 2×2 1×4 1×5 14
dividend 1×4

4 Household arithmetic -
10
5 Area of plane surface 40

3 Mensuration 6 Surface area and area of 1×1 3×2 1×5 16
cross-section and volume of
prisms, cube and cuboid

7 Factorisation

8 Indices

4 Algebra 9 Exponential equation 1×1 5×2 1×5 24

Vedanta Excel in Mathematics - Book 9 10 Ratio and proportion

11 Equations

12 Triangle and parallelogram

5 Geometry 13 Construction 2×1 3×2 1×5 25
14 Similarity

15 Circle

6 Trigonometry 16 Trigonometry - 1×2 -6

7 Statistics 17 Statistics 1×1 1×2 -7
8 Probability 18 Probability - 2×2 -4
6 4 37
Total no. of question 6 17 20 100
Total marks 34

MODEL QUESTION SET Maximum Marks: 100
Time: 3 hrs.
Class: IX
Subject: Compulsory Mathematics

Attempt all the questions

Group-A (6 × 1 = 6 )
1. (a) Write down the formula to find the rate of discount when the marked price and
selling price after discount of an item are given.
(b) From the figure alongside, what is the area of path? d
b

2. (a) If (am × an) ÷ ap = ax then express x in terms of m, n and p. l

(b) The adjoining line graph depicts the average Rainfall in (mm)100
rainfall in mm during 5 months of 2020. In April80
which month was the maximum average rainfall? May60
How much was the average rainfall recorded in June40
August? July20
August
Months
A

3. (a) In the ∆ABC alongside, M and N are the middle MN
points of sides AB and AC respectively, write BC
the relation between MN and BC.

(b) In the given figure; O is the centre of circle. If OM P MQ
A PQ, ON A XY and OM = ON. Write the relation O
between the chord PQ and XY. N

Group-B (17 × 2 = 34) X

4. (a) A noodle factory made a profit of Rs. 2750000 in the last year. If the management
decided to distribute 16% bonus from the profit to its 80 employees equally, find
the bonus amount received by each employee.

(b) The meter reading of Rajani’s house on Falgun1st was 7410 and that on Chaitra 1st
was 7439. If the electricity charge up to 20 units is Rs. 3 per unit and Rs 7 from
21 to 30 units, find the amount of the bill to be paid of the month of Falgun with
electricity service charge of Rs 30.

5. (a) The frame of the window given alongside is made of a rectangle 140cm
with a semi-circular top. Find its perimeter.
210cm
(b) How many bricks each of 15cm × 10cm × 5cm are required to 2cm
construct a wall of 20m long, 3m high and 20 cm wide? Find it. 3cm

(c) Find the volume of the prism given alongside. 2cm

4cm

Vedanta Excel in Mathematics - Book 9 358 5cm
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

6. (a) Resolve into factors: x4 + 2x2 + 9

(b) Simplify: 3 (x + y)–8 ÷ (x + 2

y) 3

7. (a) If a = 9m, b = 9n and a n b m = 81, prove that mn = 1.

(b) What must be subtracted from each term of the ratio 3:4 so that the result may be
equal to 4:3?

(c) Solve the given simultaneous equations: 3x + y = 5, x –2y = 4 A

8. (a) In the figure alongside, ‘ABC = 6x, ‘BAC = 5x and ‘ACD = 110° 5x
1100, find the actual measure of ‘ABC. 6x
DC B

M

(b) In the adjoining figure; ∆MAN a ∆MEN, ‘MAN = ‘NME. Find
the length of MN.

A 5cm E 4cm N

(c) In the given circle, O is the centre and OW A XY. If XY= 6cm and O

OX = 5cm then find the length of radius OW of the circle. X WY

P

9. (a) In the adjoining figure alongside; ‘PQR = 900, ‘PRQ = T, 30cm
PQ = 30 cm and QR = 40 cm, find the value of cosT.
T R
(b) Find the first quartile from the data given below: Q 40cm

5kg, 12kg, 33kg, 56kg, 24kg, 15kg, 74kg

10. (a) A bag contains a dozen of pencils of same shape and size. Out of them 4 are red

and the rest are yellow. If a pencil is taken from the bag at random, what is the

probability that the pencil so chosen is yellow?
(b) A card is drawn from a well shuffled deck of 52 plying cards. What is the probability
that the card drawn will be a queen?

Group-C (10 × 4 = 40)
11. In a place, 400 people were asked whether they like television shows ‘Comedy Champion’
or ‘Nepal Idol’. 200 liked ‘Comedy Champion’, 250 liked ‘Nepal Idol’ and 10 disliked both
the shows.

(i) How many people liked both the shows?

(ii) How many people liked ‘Nepal Idol’ only?

(iii) Draw a Venn-diagram to show the above information.

12. A man bought two school-bags for Rs. 2020. He sold one of them at 20% profit and the
other at 20% loss. Find his gain or loss percent in this transaction if the selling prices of
both bags are same.

13. A rectangular park is 60 m long and 40 m broad. Two crossing paths at right angle each
of 3m wide are running across the middle of the park. Calculate the cost of gravelling
the path at Rs. 45 per square meter.

14. If a = b = c , prove that: a3 + b3 + abc = a
bcd b3 + c3 + bcd d
x–4 + x+4 331
15. Solve the given equations: x+4 x–4 =

16. Prove that the opposite sides of a parallelogram are equal.
17. Explore experimentally the relation between the sum of the length of any two sides of a
triangle and that of the third side. (Two figures of different measurements are necessary)

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 359 Vedanta Excel in Mathematics - Book 9

18. Construct a quadrilateral ABCD in which AB = BC = 5.5 cm, CD = AD = 4.8 cm and
‘ABC = 600.
A

19. In the given figure, AED is a right angled triangle and BCDE 62cm
is a rectangle. Find the length of CD.

20. The heights of plants planted by the students of class- IX in an E 45°
afforestation program are given below. The average height of D
plants is 36 cm.
B 60m C

Height (in cm) 5 15 25 35 45 55
Number of plants 8 5 12 p 24 16

(i) Find the value of p. (ii) Find the total number of plants.

Group-D (4 × 5 = 20)

21. The present rate of income tax fixed by Inland Revenue Department (IRD) is given below.

Status: Unmarried Status: Married

Income slab Tax rate Income slab Tax rate

Up to Rs 400000 1% Up to Rs 450000 1%

Rs 400000 – Rs 500000 10% Rs 450000 – Rs 10%

550000

Rs 500000 – Rs 700000 20% Rs 550000 – Rs 20%

750000

The monthly salary of an unmarried manager of an office and a married cashier of a
bank is Rs 55000 each. Then according to the above table, who pays the more income
tax and by how much? Find it.

22. Express the area of four walls of a room in terms of perimeter of its floor (P) and the
height (h). The cost of carpeting a squared hall at the rate of Rs 200 per sq. metres is
Rs 64800. If the cost of plastering its walls at Rs 50 per sq. metre is Rs 16200, find the
length and height of the room. By how much percentage is the height of the room less
than its length? Find it.
111

23. The expression 1 + xa – b + xc – b + 1 + xb – c + xa – c + 1 + xc – a + xb – a was given to
Chhiring, Amrita and Rohan to evaluate in a mathematics speed test. Chhiring’s answer

was 0, Amrita’s answer was 1 and Rohan’s answer was x a+ b + c. Simplify it and find
whose answer was correct.

A

24. In the figure alongside, X and Y are the centres of two intersecting P Y
circles. If AB intersects the circle with centre X at P and Q, and
AB A XY at E, prove that: XE
(i) AP = BQ (ii) AQ = BP Q
B

Vedanta Excel in Mathematics - Book 9 360 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur