ALGEBRA CHAPTER52. Look at the number line and fill in the blanks.(a) x represents .................... (b) y represents ......................(c) z represents ...................... (d) 3 is replaced by ...................(e) 7 is replaced by ...................... (f) 10 is replaced by .................(g) x, y, z are called ...................... (h) 3, 7, 10 are called ................3. Study the following and fill in the blanks.(a)There are x marbles.The value of x is ..................(b) xxxxThere are ...................... x.(c) yyyyyyHow many y's?There are ...................... y's.0 1 2 x 4 5 6 y 8 9 z 11 121. Complete the following:(a) + 4 = 117 + = 11 (b) + 4 = 3010 + = 30(c) 9 + = 16+ 7 = 11(d) 10 + = 15+ 5 = 15Warm Up TestAcme Mathematics 5 251
1 Algebraic Term and ExpressionsA. Variable and ConstantAlgebra is a branch of mathematics like Arithmetic and Geometry. In Arithmetic we use numerals like 1, 2, 3, 4 etc. In algebra we use letters to represent the value of a number.Consider an expression x + 7.Here, x is called literal term or a variable.7 is called constant term. The unknown quantity that can take any value is called variable. The known quantity whose value does not change is called a constant.x is a single term.3y is a single term.3ab is a single term.x + y is an expression.3a – 2b is an expression.B. Algebraic Expressionx, 3x, 2y are called algebraic terms.x + 2y, 3x – 7 are called algebraic expressions.An algebraic expression contains both variables and constants connected to each other by +, –, × or ÷ sign. For examples: x + 7, x + y – 3, 2a + bx etc are all algebraic expressions.x + 7 means the sum of x and 7.x – 10 means the difference of x and 10.4x, means the product of 4 and x.x5 , means the quotient of x divided by 5.2s monomialx + 4 binomial3x + y + 3 trinomialOh! Expression contains + or – sign?252 Acme Mathematics 5
C. Base, coefficient and power of a termRead.3x is read as 3 times x. (or simply three x.)x2 3x is read as x square. (or x power 2)2It is baseIt is coefficientIt is powerD. Formation of algebraic expressionSee the following examples.(i) The sum of x and y x + y(ii) x is added to 3 x + 3(iii) 10 is subtracted form y y – 10(iv) 3 times x 3x(v) 'a' is increased by 1 a + 1(vi) one - third of x x3E. Types of expressionThe terms like 2x, x, a, y, etc are called Monomial expressions.The terms like 2x + a, x + y, a + y etc are called Binomial expressions.The terms like 2x + y + a, 3 + x – y etc are called Trinomial expressions.Classwork1. 3x and 4x are .............. terms.2. a + b + c is .............. terms.3. The coefficient of 10x is ................Exercise 5.11. Fill in the blanks:(a) The value of x is 5 only, x is a .......................... (b) x represents 5, 6 or 7, x is called ...............(c) x in the term 3x is called .............These are algebraic expressionsa terma terma term a term a termAcme Mathematics 5 253
2. Write the number of terms of the following algebraic expressions:(a) 4x + 5 (b) 10y – 3 (c) 9x – y + 3 (d) 12x3. List the single term and expression :x a + b 4a 2x + 3 4x – 3a + 3 3y a + b + c 10x xy4. Write monomial, binomial , or trinomial in each box:x2x + 7 + 12a + 2x – y – 105x – 33xy73xy + y75. List the base and coefficient :(a) 3x (b) 10a (c) 8y (d) 100z6. Match the following:(a) The sum of 10 and x. a – 3(b) x is multiplied by 9 y ÷ 4(c) 3 is subtract from a 10 + x(d) y is divided by 4 x + 7(e) x is increased by 7 9x7. Write the number of terms and list the Monomial, Binomial and Trinomial:10 – x + yx – 3a + b + c3a + b4xaxx – y + 10x + y5y3yz + 28. Write the following expression in terms of variable and constants:(a) x added to 10 (b) 5 subtracted from y(c) 12 times x (d) 3 times x added to y(e) 5 less than z (f) the sum of 20 and a(g) 3 times the sum of x and y (h) the product of x, y and 13(i) 5 times the quotient of 'x divided by y'254 Acme Mathematics 5
All are mangoes.All are same.These are like fruits.All are x.All are same.These x, 2x, 3x are like terms.x 2x 3xAll are different fruits.All are not same.These are unlike fruits.All are different letters.All are not same.2x, 2y and 4a are unlike terms.x 2y 4aConsider the terms 4x, 5x, 6x, where variable is x only and coefficient are 4, 5 and 6. Such terms are called like terms.2y and 7y or 10z and 2z are also like terms. 4x and 7y have different variables. They are called unlike terms.Similarly, 2y and 10z are also unlike terms. Like terms can be added and subtracted.A. Addition of Like TermsLook at the following carefullyand3x 2x 5x=2 Like and Unlike TermsAcme Mathematics 5 255
Similarly,x and 3x = 4x → x + 3x = 4x4y and 3y = 7y → 4y + 3y = 7y9a and 7a = 16a → 9a + 7a =16a2a and 8a = 10 a → 2a + 8a = 10a2b and 5b = 7b → 2b + 5b = 7bClasswork1. List the like terms.xy 9x 10ab x + y 2yx 45 3a 4x 5xExercise 5.21. Fill in the blanks. [like terms, unlike terms](a) 3y and y are .................... (b) 4x and 2x are ....................(c) 2x and 2a are .................... (d) 10x and 8x are ....................2. Add the following like terms:(a) 2x and 4x (b) y and 3y (c) z and 9z(d) 3a and 4a (e) 9x and 6x (f) 10z and 8z(g) 5b and 6b (h) 2x, 3x and 4x (i) y, 2y and 6y3. Find the sum: (a) 3x2 + 5x2 (b) 2y3 + 4y3 (c) 2z2 + 10z2(d) 10z3 + 3z3 (e) 5b2 + 10b2 (f) 2x2 + 9x2(g) 6a2 + 12a2 (h) 2y3 + 4y3 (i) 2zx + 3zx4. Add the following like terms.(d) 8x + 3x (e) 4a + 7a (f) 12p + 10p(g) x + 2x (h) 13y + 7y + 6y (i) 15p + 10p + 3p is replaced by x. and → replaced by +256 Acme Mathematics 5
(j) 17xz + 12xz (k) yz + 21yz (l) 6pq + 3pq(m) 9xy + 10xy (n) ab + 4ab (o) 11pq + 2pq(p) 2xz + 3xz + 4xz (q) 4yz + 3yz + 5yz (r) 3mn + 6mn + 9mn5. Add:(a) 4x and 3x + 10 (b) 10x and 2x - 6(c) 2y and 7y - 7 (d) 3a, 4a, 5a and 6a+3(e) 4x, – 6x + 10 and 12x (f) 2m, 10-3m, 4m and 5m(g) 3xy, 5xy, 5– 6xy and 10 xy6. Add:(a) (b) (c)(d) (e) (f)B. Subtraction of Like TermsLook at the following carefully:4x 2x 2xx x x x x x x x x x4x – 2x = 2xSimilarly,5x – x = 4x6a – 4a = 2a10y – 6y = 4y8a – 2a = 6a7b – b = 6b14a + 3a10xy + 4xy4x + 5y + 3x + 2y4m + 3n + 2m – 2nx + 3y 4x – 1y– 3x + 10y – 2x – 8yAcme Mathematics 5 257
Exercise 5.31. Match the following:(a) 5x – 3x 2y(b) 7a – 2a 5b(c) 10y – 8y 2x(d) 6b – b 7x(e) 8x – x 8x(f) 10x – 2x 5a2. Find the difference:(a) 4x – 2x (b) 3z – 2z (c) 7b – 4b (d) 3y – y(e) 2b – b (f) 9b – 5b (g) 6a – 5a (h) 11z – 4z(i) 9a – a (j) 12x – 6x (k) 14x – 2x (l) 12x – 63. Find the answer and go to the home.4. Subtract the following:(a) 4ax – 3ax (b) 10bx – 2bx (c) 8cx – 3cx(d) 4ab – ab (e) 12ab – 3ab (f) 20ab – 12ab(g) 7y2 – 2y2 (h) 13y2 – 7y2 (i) 21y3 – 2y3(j) 9x2y – 7x2y (k) 8ab2 – 4ab2 (l) 11p2q2 – 2p2q25. Subtract:(a) 4x from 10x (b) – 4y from – 8y (c) 10xy from 14xy(d) 7ab from – 10ab (e) –a2b2 from 4a2b2 (f) x2y from 9x2yI can solve it.4x 6x2x10x 3x –+–+258 Acme Mathematics 5
C. SimplificationWe can simplify the algebraic terms like simplification in arithmetic.See some examples.Example 1 : Simplify: 4x + 7x – 2xSolution : Here, 4x + 7x – 2x= 11x – 2x Adding 4x and 7x first= 9x Subtracting 2x from 11x.Example 2 : If x = 2 cm, find the length of the given line segment.2x x 4xSolution : Here, length = 2x + x + 4x= 3x + 4x= 7x= 7 × 2 cm= 14 cmThe length is 14 cm.Classwork1. The sum of 2x and 3x is ................2. Find the sum of 4x, 5x and 6x.3. Find the difference between 12x and 20x.Exercise 5.41. Fill in the blanks. [add or subtract](a) The difference of 5x and 3x = .................... (b) The sum of x and x = .................... (c) 3x + 10x = ....................Sum of 2x and xPutting x = 2 cmAcme Mathematics 5 259
(d) 12y – 2y = .................... (e) 8a – 6a = ....................(f) 7ab – 2ab = .................... (g) 4xy + 5xy = ....................2. Match the followings6x + 2x – x ● ● 2a10xy – 2xy – 7xy ● ● 4a – 9bx2 + 12x2 – x2 ● ● 7x20x2y2 + 3x2y2 – 10x2y2 ● ● xy(a + b) + (a – b) ● ● 12x2(3a – 2b) + (a – 7b) ● ● 13x2y23. Simplify:(a) 3x + 4x – 2x (b) 5x2 – 3x2 – x2(c) 4xy – 2xy – xy (d) – 10ab – 12ab + 20ab(e) (x + 3) + (2x + 14) (f) (2x + 3y) + (– 3x – 4y)(g) (7x – 4y) + (10x + y) (h) (2a2 – 3a) + (4a2 – 7a)(i) (5a + 7b + 9c) + (8a – 4b –6c)(j) (– 4x2y2 – 7xy + 9) + (– 5x2y2 + 11xy + 2)4. A quadrilateral ABCD is given : (a) Find the total length of two sides AB and BC.(b) Find perimeter of quadrilateral ABCD.(c) If x = 3 cm, find the actual perimeter of the given quadrilateral.6x5x2x4xAB CD260 Acme Mathematics 5
3 Algebraic Equation of One VariableA. Mathematical sentencesStudy the following sentences.The sum of 4 and 5 is 9.The difference of 8 and 6 is 4.The product of x and 5 is 20.Which of the above sentences are :(a) A true sentence?(b) A false sentence?(c) Neither true nor false sentence? The sum of 4 and 5 is 9. It is written as 4 + 5 = 9. It is true.Hence, it is true sentence. The difference of 8 and 6 is 4. It is written as 8 – 6. 8-6 is not qeual to 4. It is false.Hence, it is false sentence. The product of x and 5 is 20. It is written as x × 5 = 20. We can not say whether it is true of false. We don't know the value of x.Let us try for x = 1, 2, 3, 4, 5When x = 1, 1 × 5 = 20 it is false.x = 2, 2 × 5 = 20 it is false.x = 3, 3 × 5 = 20 it is false.x = 4, 4 × 5 = 20 it is true.x = 5, 5 × 5 = 20 it is false.x × 5 = 20 is true only for x = 4.Sentence like x × 5 = 20 is an open mathematial sentence.Acme Mathematics 5 261
Classwork1. Write True, False or Open sentence in the blanks:(a) The sum of 2 and 5 is 7. .....................(b) The difference between 10 and 3 is 7. .....................(c) The product of 2 and 7 is 13. .....................(d) The product of 3 and 4 is 12. .....................(e) Triangle has 3 sides. .....................(f) Quadrilateral has x sides. .....................(g) The sum of ‘q’ and 3 is 10. .....................(h) ‘y divided by 3 gives 6. .....................(i) Half of 10 is x. .....................(j) 4 is divisible by 2. .....................Exercise 5.51. Make the open mathematical sentence:(a) x added to 7 is 12 ................(b) y subtracted from 10 is 2. ................(c) the product of 5 and y is 15. ................(d) x increased by 3 is 10. ................(e) y divided by 2 is 5. ................2. Put the correct number in the blank and make true sentence:(a) The sum of 10 and ................ is 12.(b) 4 is double of ................(c) The difference of ................ and 5 is 3.(d) ................ × ................ = 12(e) 10 ÷ ................ = 2(f) ................ is divisible by 5.(g) The number between 10 and 12 is ................x + 7 = 12262 Acme Mathematics 5
B. EquationBiren and Sona play the game 'think a number'.Biren : Think a numberSona : Yes, I thought it.Biren : Multiply your number by 3.Sona : Yes, I did it.Biren : What is the product ?Sona : Twelve.Biren : Your number is 4.Sona : Yes.How can Biren work out Sona's original number ?The problem is related to equation.Biren does it like this3x = 12or,3x3 = 123 [Dividing both sides by 3]or, x = 4 The equation is the statement of equality containing a variable. Variable is an unknown quantity whose values varies and is represented by x, y, z, a, b, c,.... etcSome examples of equations are : 3x + 5 = 8, x2 = 7, x – 2 = 5The value of the unknown quality is called the solution of the equation. In the above example, x = 4, So 4 is the solution.x is unknown. It is Sona's original number.This part is lefthand side (LHS)equal signThis part is righthand side (RHS)Acme Mathematics 5 263
How equation is formed?Look at the following examples.15 cmIt is 15 cm long.x + 2 cmIt is (x + 2) cm longLength of 2 sticks are same.So, we can write x + 2 = 15x + 2 = 15 is an open sentence.It has = (is equal to) sign.Open sentence like x + 2 = 15 is called an equation.Equation can be represented by balance.When we put x = 13 in the left pan,Left pan = right panValue of x is 13.13 is called the solution of x + 2 = 15The process of finding the solution of an equation is called solving equation.C. Solution of an equationTrial and error methodLet us consider the equation x + 9 = 13Here, LHS (left hand side) = x + 9Let us put the values of x till the LHS becomes equal to the RHs.x + 2 15Left pan left hand sideRight pan right hand sideLeft panx + 2 = 13 + 2 = 15Right panx + 2 15264 Acme Mathematics 5
When x = 1, x + 9 = 1 + 9 = 10 not equal to RHS.When x = 2, x + 9 = 2 + 9 = 11 not equal to RHS.When,x = 3, x + 9 = 3 + 9 = 12 not equal to RHS.When x = 4, x + 9 = 4 + 9 = 13 it is equal to RHS.Thus, x = 4 is the solution.Balancing methodAn equation may be compared with a balance used for weight.Now, x + 9 = 13Balance has two sides like LHS and RHS.Equality tells us that the two pans are in equilibrium.Solved ExampleExample 1 : Solve: x + 3 = 5Solution : Here, using balance method.x + 3 equal 5x + 3 = 5 xRemove 3 from the left pan only.x + 3 – 3 ≠ 5not equalxRemove 3 from right pan alsox + 3 – 3 = 5 – 3x = 2xNow, balance is equalSo, value of x is 2.xx + 9 13 represents 1Acme Mathematics 5 265
Short method:x + 3 = 5or, x + 3 – 3 = 5 – 3 3 is taken out from both sides.or, x = 5 – 3or, x = 2Value of x is 2.Rule1. Same number can be added to both sides.2. Same number can be subtracted from both sides.3. Same number can be multiplied on both sides.4. Both sides can be divided by the same number.Rule - 1 We can add the same numbers to both sides.If x – 4 = 6, thenor, x – 4 + 4 = 6 + 4or, x = 10Rule - 2 We can subtract the same number to both sides.If x + 7 = 8 thenor, x+ 7 – 7 = 8 – 7or, x = 8 – 7or, x = 1Rule - 3 We can multiply both sides by the same quantity.If x3 = 6 thenor,x3 × 3 = 6 × 3or, x = 18Rule - 4 We can divide both sides by the same quantity.If 4x = 12 then,or, 4x4 = 124 or, x = 3We continue the process.4 is added to both sides.7 is subtracted from both sides.Both sides are multiplied by 3.Dividing both sides by 4.266 Acme Mathematics 5
4 kg2.5 kg 500 g 350 g4 kg 1 kg1 kg800 g1. Determine the unknown weight to balance each scale.Example 2 : Solve: 5x2 = 10Solution : Here, 5x2 = 10or,5x2 × 2 = 10 × 2 Multiplying both sides by 2.or, 5x = 20or,5x5 = 205 Diving both sides by 5.or, x = 205or, x = 4The value of x is 4.ClassworkAcme Mathematics 5 267
2. Balance the given scale3. Determine the value of each shape.6 + 4 = 3 + .......4 + 8 = 5 + .......12 + 4 = 2 + .......9 + 8 = 5 + .......8 + 10 = 9 + .......8 + 2 = 1 + .......= _____= _____= _____8 6 8105= _____= _____= _____6268 Acme Mathematics 5
1. Fill in the blanks:(a) 3 + ............. = 5 (b) ............. – 2 = 7(c) ............. × 2 = 10 (d) 4 × ............. = 20(e) 10 – ............. = 8 (f) 8 = 42. Fill in the blanks (Guess the value):(a) If x + 2 = 3 then, x = .....................(b) If x + 7 = 13 then, x = .....................(c) If a – 2 = 9 then, a = .....................(d) If a – 1 = 0 then, a = .....................(e) If 2 y = 4 then, y = .....................(f) If 6y = 24 then, y = .....................(g) If p3 = 1 then, p = .....................(h) If p3 = 2 then, p = .....................3. Using Trial and Error method, find the value of x:(a) x – 5 = 2 (b) x + 7 = 12 (c) x – 6 = 1(d) x + 8 = 12 (e) 3x = 12 (f) 5x = 20(g) x3 = 3 (h) x2 = 4 (i) x5 = 204. Solve: (Use Rule 1 or Rule 2)(a) x – 3 = 4 (b) x –5 = 10 (c) x – 15 = 20(d) x + 4 = 8 (e) a + 3 = 7 (f) a + 10 = 20(g) 4 + x = 10 (h) 45 = x + 11 (i) 9 = x – 125. Solve: (Use Rule 3 or Rule 4)(a) x4 = 2 (b) x15 = 2 (c)x9 = 3(d) 3x = 9 (e) 4x = 16 (f) 9x = 27(g) 2x = 4 (h) 3x4 = 12 (i) m2 = 8(j) 5x4 = 20 (k) p3 = 9 (l) 12r6 = 24Exercise 5.6Acme Mathematics 5 269
6. Find the value of x: (use trial method)(a) (b)(c) (d)(e) (f)7. Solve (find the value of x):(a) x + 6 = 12 (b) x – 6 = 12 (c) 5 + x = 6(d) 10 + x = 15 (e) 10 = x + 4 (f) 20 = x – 3(g) x + 16 = 20 (h) x – 2 = 188. Solve:(a) 3x = 18 (b) 4x = 20 (c) x2 = 3(d) x7 = 2 (e) 14x = 28 (f) x19 = 19. Solve these equations:(a) 2x + 6 = 10 (b) 5x + 8 = 28 (c) 8 + x = 2 (d) 25 – x = 1(e) 18x = 9 (f) 100x = 25 (g) 6x4 = 18 (h) 2x5 = 4(i) 3x + 2 = 5 (j) 4x – 3 = 5 (k) x + 32 = 2 (l) x – 24 = 3(m) 2x + 34 = 1 (n) 2x – 17 = 1 (o) 28x – 65 = 104x 8 x + 9 12x 1 1 11 1 11111x xxx x 11 1 1 11 1 1 1x x x1 11 xx x x 1 1 11 1 1 11270 Acme Mathematics 5
10. Make the equations from the information given by the figures and solve:(a)x cm 12 cm20 cm (b)x cm 2x cm 4 cm13 cm(c)a a a15 cm (d)x4 cm 10 cm12 cm(e)11. Make the equation and solve the given problems.(a) The sum of x and 10 is 20. Find the value of x.(b) The sum of 2x and 5 is 40. Find the value of x.(c) 4 times y is 32. Find the value of y.(d) When y is divided by 32, the quotient is 4. Find the value of y.(e) The difference of x and 2 is 7. Find the value of x.12. Solve the equation and find the path to go END.3x3xPerimeter x 32 c m x7x + 1 = 22x5 –3 – 9 = – 15 + 2x – 5 + 7 = 65x + 12 = 32 6x + 5 = 23 x4 4 + 2 = 53– 17348871136253– 86124x + 7 = 19 8 + x– 4 5 + 9x = 104 = 6 1099 87 = 3 + x128 + x45 = – 6 + = – 2 x4 44 – 3565 = 11 + 6x ENDBEGIN8 = x + 93 9 15Acme Mathematics 5 271
1. (a) 'x' is the multiple of 5 less than 20. Find whether x is variable or constant?(b) If x = 2, y = 4 and z = 6, find the product of x, y and z.2. The index of y in 7y3 is .............(a) 7 (b) 10 (c) 3 (d) 213. If a = 1, b = 5 then what is the value of a + b?(a) 1 (b) 4 (c) 6 (d) 214. What is the sum of 3a + 5a?(a) 8a (b) 9a (c) 6a (d) 7a5. Which one is the monomial algebraic expression?(a) 5x (b) 5x + y (c) 3a + b + c (d) 5x2 + y26. If 3y = 9, then what is the value of y?(a) 3 (b) 6 (c) 9 (d) 127. Find the value of 3a + 2b + 4c, when a = 2, b = 3 and c = 4.8. (a) Add: (b) Subtract : 7x + y from 6x + 4y9. Solve the equation : x + 1 = 510. Observe the following figure.P 3a Q 2a R(a) Write algebraic expression for length of line segment PR.(b) Find its actual length if a = 3 cm.(c) Fill the empty space by a suitable number:3 + ...... = 1011. Study the expression : 3x – 2y5z(a) Is the given expression an algebraic expression or not?(b) Write the given expression into words.3x + 2y+ 5x + 4yMixed Exercise272 Acme Mathematics 5
(c) Find the numerical value when x = 3, y = 2 and z = 1.(d) Write down an equation for the following picture.x12. (a) Identify the coefficient of 7x2.(b) Classify 7xyz and 10xyz as like or unlike terms.(c) What is the value of expression if x = 2?(d) Find the length of given line segment when a = 3 cm.P Q a a a13. (a) Identify the base of – 8x.(b) Write the like terms among the following : 5a, 2b, 3a, 6x, 4a(c) If a = 1, b = 2 and c = 3 find the value of : 4a + 6bc14. Find the value of 'a'.(a) a – 1 = 2 a = ______(b) 3 + a = 10 a = ______(c) 7a = 3a = 8 a = ______(d) Write the appropriate number in the given box.a + 5 = 11or, a = ______15. Find the possible values of x and y where x < 4, x + y = 10xy16. Study the given algebraic expression and answer the following questions.3x, 2y, 7m, 7y, 2x(a) Which is the like-term of 3x?(b) Define monomial term.(c) Find the sum of 7y and 2y. Acme Mathematics 5 273
17. One algebraic expression is 4x + 5y and the another is 3x + 2y.(a) Add the given algebraic expression.(b) If x = 2 and y = 3, what will be the sum?(c) Simplify: a + 2b + 3a – b18. Match the following.'A' 'B'(a) The sum of x and y 3x(b) x is added to 3 y – 10(c) 10 is subtracted from y x + y(d) 3 times x x + 319. Write the number of terms and list the monomial, binomial and trinomial.x x + y 3y z + 2 a + b + c x + y + z20. Solve:(a) 4x + 5x + 6x(b) 5x2 – 3x2 – x221. 4x + 3y is an algebraic expression.(a) Write types of algebraic expression.(b) Which type of algebraic expression is given above?(c) Find the constant and variable from 4x.22. Solve:(a) 2a + 1 = a + 2(b) 2x5 + 3 = 723. Study the given figure and answer the given questions.10x cm 4x cm(a) How long is figure?274 Acme Mathematics 5
(b) How more is coloured parts than non-coloured part?(c) What should be added to this figure to make it 20x cm long?24. Study the length of given sticks.2x m (x + 2) mThe total length of sticks is 23 m.(a) How long is first stick?(b) Calculate the length of second stick.(c) Find the value of 'x'.25. A balance is given.x + 9 21(a) Make the equation.(b) Solve for x.(c) What will happen if 21 is replaced by 12?26. Two expressions 3x + y and 2x – 3y are given.(a) List the like terms.(b) Add the expressions.(c) If length of a rectangle is (3x + y) cm and breadth (2x – 3y) cm, find the difference between length and breadth.(d) If x = 4 and y = 1, calculate the actual length and breadth of rectangle.(e) When y = 1, solve: 3x + y = 7Acme Mathematics 5 275
EvaluationTime: 60 minutes Full Marks: 251. State whether the given statement is constant or variable. (a) x represents the number of day in a week. [1](b) y represents the height of tree. [1](c) Fill in the blanks [1](i) .......... + 10 = 15 (ii) 5 × ..... = 20 2. (a) How many terms are there in the algebraic expression 2xy ? [1](b) The expression having only one term is called ……… [1](i) monomial(ii) binomial (iii) trinomial (c) If a =2 and b=3, then find the value of 3a + 2b. [2]3. (a) Are the given terms 4a and 2b like or unlike? [1](b) The sum of a number and 5 is 15. Find the number. [2]4. (a) Simplify: 8m + 2n – 5m+ 3n [1](b) Solve: 4x =12 [1] (c) If p =3 and q =2, then find the value of 5p – 5q. [2] (d) For what value of p, the value of 5p – 5q is 15 ? [2] 5. (a) Identify the coefficient and base of the 5x. [1] (b) How many terms are in the expression (5x–1) ? [1] (c) Express \"Sum of x and 3\" phrases as an algebraic expression. [1] (d) Find the length of given line segment. [1] 6. (a) If x=3, then find the value of (2x+5). [1] (b) Add: (2pq + 3qr + 5pr) and (4pq + 2qr + 7pr) [2](c) Solve: x + 5 = 8 [2]A a B a − 3 C1. In the figure, dice and the angle formed at the point O are given. ABD CO(a) How many corners and the surfaces are on the dice? [1U](b) What type of angle is ∠AOC? [1U](c) Draw an angle which is equal to the ∠AOC. [1A](d) By how much is the measurement of ∠BOC + ∠BOA more or less than the measurement of ∠BOD? Find it. [2HA]2. A quadrilateral is given below in a square grid. DA BC(a) What is the line segment parallel to AB? [1K](b) What are the measurement of ∠ABC and ∠DAB? Using the protractor, measure and write it. [2A] Time – 2 hrsModel QuestionSubject : Mathematics F.M. 50Mathematics-5 277 276 Acme Mathematics 5
1. In the figure, dice and the angle formed at the point O are given. ABD CO(a) How many corners and the surfaces are on the dice? [1U](b) What type of angle is ∠AOC? [1U](c) Draw an angle which is equal to the ∠AOC. [1A](d) By how much is the measurement of ∠BOC + ∠BOA more or less than the measurement of ∠BOD? Find it. [2HA]2. A quadrilateral is given below in a square grid. DA BC(a) What is the line segment parallel to AB? [1K](b) What are the measurement of ∠ABC and ∠DAB? Using the protractor, measure and write it. [2A] Time – 2 hrsModel QuestionSubject : Mathematics F.M. 50Mathematics-5 277Acme Mathematics 5 277
3. The price of house in Kathmandu is Rs. 30720485.(a) Write the number according to national system using comma (,). [1K](b) Write the number 30720485 into words. [1U] (c) Present the given number in the place value table according to the international system. [2A](d) To buy a house, Rs. 50485 is given in advance. Round off 50485 to the nearest thousand. [1A]4. In a test of Mathematics, Rima obtained 13 marks in 20 full marks and Sunita obtained 64 marks in 100 full marks.(a) Write the marks obtained by Rima in fraction. [1K](b) Write the marks obtained by Sunita in percentage. [1K] (c) Among Rima and Sunita, who obtained more marks and by how much? Find it. [2HA]5. When Nabin came from abroad, he bought 5 packets of chocolates containing 30 chocolates in each packet and 8 more chocolates. From these chocolates he distributed 39 chocolates to his relatives.(a) Write the above problems into mathematical sentence. [1U](b) How many chocolates are left with Nabin? Find it. [2A] (c) The number of chocolates distributed to the relatives is '39'. Is it prime or composite number? Write with reasons. [2U]6. Sarita had gone to buy household goods in a wholesale shop. She bought 512 kg Mungi and 2.5 kg Musuro.(a) Convert 2.5 into mixed number. [2A](b) If she has to make 10 12 kg of dal (lentil) by mixing Mugi, Musuro and Mas, how many kgs of Mas should she buy? [2HA] 7. Ranjita boarded a bus from Baglung at 8 am to go to Chitwan via Pokhara to attend her nephew's wedding. She reached Sauraha of Chitwan which is 239 km from Baglung at 2:42 pm.(a) Which basic operation of Mathematics should be used to find the time taken for her to reachSauraha? [1U]278 Model Question 278 Acme Mathematics 5
(b) According to 24 hours’ time, at what time did she reach Sauraha? [1U](c) 18 guests attending the wedding were given the sarbat (a juice) 350 ml each. If 200 ml sarbat remains in the vessel, how many liters sarbat was made in total? Find it. [2A](d) If 3 meter 70 centimeter of clothes is needed to sew a coat and pants for a person, how much clothes is need to sew coats and pants for 5 people? [2A]8. A farmer is cultivating paddy in a rectangular field having 80 meter length and 35 meterbreadth. He bought 3 bundles of wire of equal weight from the market to fence the field 3rounds with the wire to protect it from cattle.(a) When length and breadth of a rectangle are given, what should be done to findits perimeter? [1K](b) If the total weight of the wire is 2 quintal 55 kilogram, what is the weight of 1 bundle of wire? [1A](c) While fencing the field 3 rounds, the farmer was short of 15 meters wire, howmany meters of wire did he purchase? [2HA]9. Maya buys goods from Himchuli food store. She bought following good on 2079 Poush 3.Price listParticulars Unit Rate (Rs.)Rice Sack 2000Oil Liter 220Sugar kg 95Flour kg 80Daal kg 200(a) Which items has the lowest per unit price? [1K](c) Maya has gone to the shop with Rs. 5,000. After paying the amount according to the bill, will the remaining amount be enough to buy fruits worth Rs. 1200 or not? If not, find out how much is not enough for her. [1HA]Details of items bought by MayaRice :1 SackOil : 5 LiterMathematics-5 279 Acme Mathematics 5 279
(b) The sample of the bill given by Himchuli food store to Maya is given below. Prepare a bill on the basis of the goods purchased by Maya. [2U] Himchuli Food StoresPAN: 105998932 Date: 2079/09/03Bill No. 02313 Name of customer: ..................................................S.N. Name of items Quantity Rate Total Price (in Rs.)TotalPrice in words: ....................................................... Kaji Sharpa Sells man10. Sachin gave 12 books of stories, 14 books of poem, 10 books of essay, and 8 books of general knowledge to the school where he studied. (a) Present the number of books given by Sachin to the school in a table. [1A] (b) Draw a bar graph from the given data in a square grid paper. (Square grid paper should be given) [1A]11. The breadth of rectangular ground of a 'Janta Basic School' is (4x + 36) meter. The length of the ground is 10 meter more than its breadth. (a) How many terms are in the expression (4x + 36)? [1K](b) Write the length of ground in terms of x. [1U](c) What is the perimeter of the ground? Find it. [1A](d) If x = 2, what is the breadth of the ground? [1U]12. Pemba has Rs. x. Ram Naresh has Rs. 5 more than Pemba. Both of them have Rs 35 in total.(a) Write the amount with Ram Naresh in terms of x. [1K] (b) How many rupees does each of them have? Find it. [2A](c) How many rupees does his father have to give Pemba to make it twice as much as Ram Naresh has? [1HA]280 280 Acme Mathematics 5