Algebra - · PDF fileAlgebra Student Book - Series H 2 Contents Topics Topic 1 ... EXCEL STEP-BY-STEP MATHS YEAR 7 Topic 4: Algebraic abbreviations Pages 186, 252–254. 5 Algebra

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Algebra

Mathletics Instant

Workbooks

Student Book - Series H-2

7(4x - y) = ___

Algebra

Student Book - Series H 2

Contents

Topics

Topic 1 - Algebraic expressions __/__/__

Date completed

Topic 2 - Simplifying algebraic expressions __/__/__ Topic 3 - Collecting like terms __/__/__ Topic 4 - Algebraic abbreviations __/__/__ Topic 5 - Substitution __/__/__ Topic 6 - Index notation __/__/__ Topic 7 - Index laws __/__/__ Topic 8 - Grouping symbols __/__/__ Topic 9 - Equations __/__/__ Topic 10 - Problem solving with algebra __/__/__

Algebra

Mathletics Instant Workbooks – Series H Copyright © 3P Learning

Author of The Topics and Topic Tests: AS Kalra

Practice Tests

Topic 1 - Topic test A __/__/__ Topic 2 - Topic test B __/__/__ Topic 3 - Topic test C __/__/__

1

Algebra

Algebra

Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

Topic 1: Algebraic expressions

69Chapter 6: Algebra

Algebra

UNIT 1: Algebraic expressions

QUESTION 1 Write an expression for the following.

a The sum of 2a and 3b = __________________________________________________________________

b 8 less than 5a = ________________________________________________________________________

c The double of 6x = ______________________________________________________________________

d The difference between x and y =___________________________________________________________

e Two thirds of x = ________________________________________________________________________

QUESTION 2 Write an algebraic expression for the following.

a Nine times the number n minus 3 = _________________________________________________________

b The sum of 3x and 56 = __________________________________________________________________

c The sum of 2l, 5m and 3n = _______________________________________________________________

d The product of 3x and 6y = ________________________________________________________________

e The average of 4a and 8a = _______________________________________________________________

QUESTION 3 If x represents any number, write an algebraic expression for the following.

a Nine times the number plus 5 = ___________________________________________________________

b One fifth of the number minus seven = ______________________________________________________

c The sum of the number and 15 = ___________________________________________________________

d The difference between the number and 9 = __________________________________________________

e Five more than the number = ______________________________________________________________

QUESTION 4 Show the sum of each of the following.

a 15 and x = ____________________________________________________________________________

b 5m and 3n = ___________________________________________________________________________

c 2x, 3y and 5z = ________________________________________________________________________

d 8a, 5b and 7c = ________________________________________________________________________

e 15l, 12m and 4n = ______________________________________________________________________

QUESTION 5 Write algebraic expressions for the following.

a To the sum of 8x and 5y, add 9z = __________________________________________________________

b From the product of 2m and 3n, take away 5 = ________________________________________________

c Divide 2m by 3n and then take away 10 = ____________________________________________________

d Divide the sum of x and y by 20 = __________________________________________________________

e 16 plus y, all divided by 7 = ______________________________________________________________

CHAPTER 6EXCEL STEP-BY-STEP MATHSYEAR 7

Page 186

2

Algebra

Algebra


Topic 2: Simplifying algebraic expressions

70 EXCEL ESSENTIAL SKILLS: YEAR 7 MATHEMATICS REVISION AND EXAM WORKBOOK 2 – EXTENSION

Algebra

UNIT 2: Simplifying algebraic expressions

QUESTION 2 Circle the like terms.

a 3b, 5a, 9a _______________ b 4x, 5y, 6x ______________ c 9x, 3a, 5x ________________

d 9a, 3d, 6a _______________ e 8y, 3a, 3y ______________ f 3l, 5m, 5l ________________

g 3d, 2c, 5c _______________ h 9, 8x, 5x ______________ i 10y, y, x _________________

QUESTION 1 Write down the coefficient for each of the following terms.

a 9a ______________ b 6y ______________ c 12t _____________ d 84x _____________

e 53y _____________ f 32m ____________ g 82c _____________ h 5y ______________

i 16n _____________ j 43a _____________ k 14b _____________ l 32m ____________

QUESTION 3 Simplify the following.

a 2x + 3x = ________________ b a + a + a + a = __________ c y + y + y + y + y + y = _______

d y + y + y + y = ____________ e m + m + m + m + m =_____ f c + c + c + c = _____________

g 3d + 9d = ________________ h 9k + 3k +7k = ___________ i 5a + 11a = ________________

QUESTION 6 Write the following expressions in expanded form.

a 16xy = __________________________________ b 6abc = ___________________________________

c 5ab = ___________________________________ d 18xyz = __________________________________

e 9mnp = _________________________________ f 45mn2 = __________________________________

g 7abc = __________________________________ h 6a2b = ___________________________________

i 6xyz = __________________________________ j 5a3 = ____________________________________

k 15abc = _________________________________ l 12a2b2 = __________________________________

m 9m = ___________________________________ n 18d2e3 = __________________________________

QUESTION 4 Simplify the following expressions.

a 15x – 3x = _______________ b 27b – 18b = ____________ c 28a – 10a = _______________

d 18a – 5a = _______________ e 18x – 7x =______________ f 15a – 6a = ________________

g 11b – 4b = _______________ h 15p – 6p = _____________ i 20y – y = _________________


a 8 × d = __________________ b 8 × a × c = _____________ c x × y × z = ________________

d 5 × x × y = _______________ e 45 × m × n × l = _________ f 5 × a × c = ________________

g a × b × 14 = ______________ h 9 × 2 × m × n =__________ i 15 × b × d × e = ___________

EXCEL STEP-BY-STEP MATHSYEAR 7

Pages 186, 252–254, 259

3

Algebra

Algebra


Topic 3: Collecting like terms


Algebra

UNIT 3: Collecting like terms

QUESTION 1 Collect like terms to simplify the following.

a x x x y y+ + + + = _______________________ b m m m m n n n+ + + + + + = __________________

c a a a a a b+ + + + + = _____________________ d l l l m m m+ + + + + =_______________________

e e e f f f f f+ + + + + + = _________________ f u u u v v v v v+ + + + + + + = ________________

QUESTION 2 Simplify the following by collecting like terms.

a 5 7 4 11x x+ + + = ________________________ b 9 15 6 13a a+ + + = ________________________

c 8 3 9 2a b a b+ + + = _______________________ d 8 2 6x y x+ + = ____________________________

e 9 3 8 4m n m n+ + + = ______________________ f 2 3 9 10x y x y+ + + = _______________________


a 18 7 2 3a a a b− − + = _______________________ b 9 7 6 14x y x y+ − + = _______________________

c 8 9 6 3m n m n+ + − = _______________________ d 8 3 15 8p p q q− + − = _______________________

e 17 42 15x x+ + = _________________________ f 16 12abc abc− = ___________________________

g 18 6 8 20 6l l m m m− + + − = _________________ h 8 7 10 4 2x y x y y+ + − − = __________________


a 8 2x x x− − = ____________________________ b 6 4 9z z z− + = ____________________________

c 5 8 32 2 2x x x+ − = ________________________ d 9 6 2a a a− − = ____________________________

e 5 6 7a b a b− − − = _________________________ f x x x+ − =5 7 _____________________________

g 8 7x x x+ − = ____________________________ h 9 7 2h h h h− − − = _________________________

QUESTION 6 Collect like terms and simplify.

a ab bc ab bc ac+ − − + = ____________________ b 9 5 3 22 2 2 2a b ab ab a b− − + = __________________

c 9 10 32 2 2x x x+ − = _______________________ d 19 6 4 5xyz y xyz y+ + − = ___________________

e 18 15 4xyz xyz xy+ − = _____________________ f 36 15 142 2 2a b a+ − = _______________________

g 8 9 4 62 2 2 2x y x x y x+ + + = _________________ h 9 8 3 63 3 3 3a a b b+ − + = _____________________


a 8 3b b b− − = ____________________________ b m m m2 6 12− − + = ________________________

c 8 6x y y− − = ___________________________ d p p p2 4 6 7− + − = _________________________

e 9 4 8a b b a+ − − = ________________________ f 4 9 6 3x y x y+ + − = ________________________

g xy y xy+ + =5 4 _________________________ h ab b ab b+ − + =3 4 9 _______________________


Pages 259–263

4

Algebra

Algebra



Algebra

UNIT 4: Algebraic abbreviations

QUESTION 1

a Write 12 × p in a shorter way. ___________________

b Write 5 × 3 × y in a shorter way. ___________________

c Write 9 × x × x × x in another way. ___________________

d Write 8ab, showing multiplication signs. ___________________

e What is the difference between 36x and 3 × 6 × x? ____________________________________________

QUESTION 2 Write the following expressions without multiplication or division signs.

a 5 4× × =p ______________ b 8 5× × =m _____________ c x y+ × =4 _______________

d 6 2 3× +( ) =a ____________ e 2 3a ÷ = _______________ f x y z× × = ______________

g 3 9× × =b ______________ h 2p q q× × = ____________ i 5 6× × × =a b ____________

j 3 6× − =m ______________ k 5 8+ × =x _____________ l 8 5× + × =x y ____________

m 15 ÷ =x ________________ n 5 17x ÷ = _____________ o k ÷ =15 _________________

p a b+( ) ÷ =7 _____________ q 9 2 3a a÷ +( ) = __________ r 9 7 4a a+( ) ÷ = ____________

QUESTION 4 Write the following in a shortened form.

a 7 × × × × =a b b c _________________________ b 9 × × × × =m m n n _________________________

c 6 3× +( ) =a _____________________________ d 4 8× −( ) =x ______________________________

e 5 3× × +( ) =p q ___________________________ f 3 4 7× × −( ) =a ___________________________

g a b c× × +( ) =5 ___________________________ h 5 8 2× × −( ) =a ___________________________

i 9 3 6 3+ × + ×( ) =a _______________________ j 7 8 3× × − ×( ) =y z ________________________

k 2 1 3x x+( ) × +( ) = ________________________ l 6 5 6 7p p+( ) × −( ) = ________________________

m a a a× × × =5 ___________________________ n 9 7× × × × =b b b __________________________

o y y y y a a× × × × × = _____________________ p 2 1 3 2× +( ) × × −( ) =x x ____________________

q n n+( ) × +( ) =3 2 5 ________________________ r m m−( ) × −( ) =3 3 5 ________________________

QUESTION 3 Write the following expressions by showing all multiplication or division signs.

a 7m = ___________________ b 5x = _________________ c 16y = ___________________

d 8 3n − = ________________ e 6 7m + = _______________ f 30 5− =a ________________

g xy − =5 ________________ h 8 3k l− = ______________ i x yz2 = __________________

j 15xyz = _________________ k 7 32a + = ______________ l m n3 3− = ________________


Pages 186, 252–254Topic 4: Algebraic abbreviations

5

Algebra

Algebra


Topic 5: Substitution


Algebra

UNIT 5: Substitution

QUESTION 4 Complete the table.

QUESTION 1 If a = 5, find the value of each expression.

a 7a = ____________________ b 9a + 1 = _______________ c 9a – 1 = __________________

d a2 = ____________________ e 5a2 = __________________ f (a + 1)(a – 1) = ____________

g a3 = ____________________ h a2 – 2a = _______________ i (2a + 7) × 3a = ____________

j 7a – 12 = ________________ k 180 ÷ 6a = _____________ l (a – 2) ÷ 15 = _____________

QUESTION 2 If a = 3, b = 5, c = 8 and d = 10, find the value of each of the following expressions.

a a + b = __________________ b a + b + c + d = __________ c abc – d2 =_________________

d abc = ___________________ e 2a + 3b + 4c = __________ f 3b + 5c – d = ______________

g 16bc = __________________ h 8c – d = _______________ i 8d ÷ b = __________________

j 5a – a2 = ________________ k (c + d) – a2 = ___________ l b2 + d2 – abc = _____________

QUESTION 3 Complete the following.

a b a

a

b

= +2 1

0 1 2 3 4

b y x

x

y

= −3 2

1 2 3 4

c m l

l

m

= −15 2

0 1 2 3 4

d y x

x

y

= −4 2

1 2 3 4 5 6

e p q

q

p

= +5 7

0 1 2 3 4

f v u

u

v

= −30 7

1 2 3 4 5 6

x y x + y x – y yx x2 y2 4x 5+ y

a 5 2

b 6 1

c 9 3

d 8 1

e 01 2

f 4 1

g 7 3

h 9 6

i 3 5


Pages 187, 264–265

6

Algebra

Algebra


Topic 6: Index notation


Algebra

UNIT 6: Index notation

QUESTION 3 Find the value of each of the following when x = 3 and y = 2

a x2 = ___________________ b x6 = __________________ c xy3 = ____________________

d x3 = ___________________ e y 4 = __________________ f x y2 5 = __________________

g y3 = ___________________ h y5 = __________________ i 5xy = ____________________

j x5 = ___________________ k x y2 2 = ________________ l 6 4xy = ___________________

QUESTION 1 Write each of the following in simplest index notation.

a p p p p p× × × × = ________________________ b q q q q q q× × × × × = ______________________

c x x x x x x× × × × × = _____________________ d a a b b b× × × × = _________________________

e m m m× × = _____________________________ f c c c c d d× × × × × = ______________________

g a a a a× × × = ___________________________ h y y y y y z z× × × × × × = __________________

QUESTION 2 Write each of the following in expanded form.

a x5 = ___________________________________ b m6 = ____________________________________

c a7 = ___________________________________ d n8 = ____________________________________

e e3 = ___________________________________ f p10 = ____________________________________

g y 4 = ___________________________________ h l9 = ____________________________________

QUESTION 4 Write each of the following in simplest index form.

a 15 × × × =a a a __________________________ b p p p p p× × × × × =5 ______________________

c m m m× × × =7 __________________________ d 6 2× × × × × =m m m m _____________________

e 16 × × × × =x x x x _______________________ f h h h× × × × =3 5 __________________________

g 4 3× × × × =y y y ________________________ h 8 2× × × × =b b b __________________________

QUESTION 5 Expand each of the following.

a 6 2a = __________________________________ b 8 3x = ___________________________________

c 9 3y = __________________________________ d 5 7m = ___________________________________

e 15 2b = _________________________________ f 16 5y = __________________________________

g 7 4a = __________________________________ h 3 2 3a b = __________________________________

QUESTION 6 Evaluate the following when a = 5 and b = 6

a a b2 + = _________________________________ b a b3 = ____________________________________

c a b2 2+ = ________________________________ d ab3 = ____________________________________

e a b3 2+ = ________________________________ f a b2 2 = ___________________________________


Pages 253–254, 265

7

Algebra

Algebra


Topic 7: Index laws


Algebra

UNIT 7: Index laws

QUESTION 1 Simplify the following, writing your answer in index form.

a x x2 3× = _______________ b y y3 3× = ______________ c a a3 4× = ________________

d m m3 4× = ______________ e p p3 7× = ______________ f n n10 3× = ________________

g a a a2 3 4× × = ____________ h x x x5 2× × = __________ i y y5 9× = ________________


a x x9 3÷ = _______________ b x x12 4÷ =______________ c x x7 ÷ = _________________

d y y7 4÷ = _______________ e y y9 2÷ = _____________ f a a9 ÷ = __________________

g m m25 14÷ = ______________ h m m12 10÷ = ____________ i m m15 11÷ = _______________


a a2 3( ) = __________________ b b5 4( ) = ________________ c a5 6( ) = ___________________

d x3 7( ) =__________________ e b2 7( ) = ________________ f x7 8( ) = __________________

g 3 3 2x( ) = _________________ h 3 2 4

x( ) = _______________ i 3 4 3b( ) = __________________


a 5 4 5x x× = _______________ b 9 5 2x x× = _____________ c a a11 53× = _______________

d m m7 25× = ______________ e 8 73 5k k× = _____________ f 5 87 6a a× = _______________

g m n m n3 2 5 7× = ____________ h x y x y2 4 5 7× = __________ i x y x y2 2 4 2× = _____________


a a b2 3 3( ) = ________________ b x y5 6( ) = _______________ c m n5 6 3( ) =_________________

d x x x5 6 7× × = ____________ e x x x8 4 3÷ ÷ = __________ f a a a6 7 5× ÷ = _____________

ga a

a

9 9

3

× = _______________ ha a

a

15 5

7

× = _____________ ib b

b

12 12

10

× = ________________


ax x

x

8 6÷ = _______________ b x x13 8÷ = _____________ c x x x17 13 4÷ × = ___________

d 2 7 3x( ) = _________________ e x x x6 4 3× ÷ = __________ f x x x9 4 7× ÷ = ____________

g a a a4 5 2× ÷ = ____________ h x x9 2÷ = ______________ i a a a7 8 2× ÷ = _____________


Pages 253–258

8

Algebra

Algebra


Topic 8: Grouping symbols


Algebra

UNIT 8: Grouping symbols

QUESTION 1 Expand the following expressions.

a 2 3a b+( ) = ______________ b 8 2a b+( ) = _____________ c 3 5a b+( ) = _______________

d 5 2 5m n+( ) =______________ e 7 5m n−( ) =_____________ f 5 3 8x y+( ) = ______________

g 6 3x y+( ) = ______________ h 9 6 5a b−( ) = ____________ i 6 4 2a b−( ) = ______________

QUESTION 2 Expand.

a 6 2 7a +( ) = ______________ b y y +( ) =7 _____________ c 10 3 8x y−( ) = _____________

d m m2 3+( ) = ______________ e 9 5x y−( ) = _____________ f 2a a b+( ) = ______________

g k k3 2−( ) = ______________ h x x +( ) =15 _____________ i 3 7p p −( ) = ______________

QUESTION 3 Remove the grouping symbols.

a a a3 5+( ) = ______________ b 3 2 9m m −( ) = ___________ c p p3 7+( ) = _______________

d x x5 3−( ) = ______________ e 8 3 10y y −( ) =___________ f 6 4 1p p −( ) = ______________

g m m4 7−( ) = _____________ h 5 3 7x x +( ) = ____________ i 6 3 9a a −( ) = ______________

QUESTION 4 Expand.

a 7 4 5y +( ) = ______________ b 3 7 2a b−( ) =_____________ c 9 2x y−( ) = ______________

d 9 8 2y −( ) = ______________ e 5 5 3a b−( ) =_____________ f 3 3 5a b−( ) = ______________

g 6 3 4x y−( ) =______________ h p p4 9−( ) =_____________ i 19 2a b+( ) = ______________

QUESTION 5 Expand the following expressions.

a am m2 1−( ) = _____________ b x x2 9−( ) = _____________ c a a3 7−( ) = _______________

d q q p8 3+( ) = _____________ e 3 4 3m m n−( ) = __________ f 9 5 6p −( ) = _______________

g 7 6 10x y−( ) =_____________ h 7 3 4p p −( ) = ___________ i 10 5 9a b−( ) = _____________

QUESTION 6 Expand.

a 2 10 3x x y−( ) = ___________ b x x x3 4 2−( ) = ___________ c 5 6 7a a b−( ) = _____________

d x x2 4 7−( ) = _____________ e x x5 3−( ) = _____________ f 6 52 3a a +( ) = _____________

g a a a3 2 −( ) = _____________ h x x x7 2 −( ) = ___________ i 7 3 2 3a b a b+( ) = ____________

j m m n4 5−( ) = ____________ k xy x y2 2−( ) = ___________ l 8 2a b a b+( ) = _____________

m 6 3 2mn m n−( ) = ___________ n mn m n−( ) = ____________ o 9 2 2a a b+( ) = _____________

Algebra EXCEL STEP-BY-STEP MATHSYEAR 7

Page 256

9

Algebra

Algebra


Topic 9: Equations


Algebra

UNIT 9: Equations

QUESTION 1 By substituting back into the equation, see if the given value of the pronumeral is correct orincorrect.

a x x+ = =[ ]3 15 12 ______________________ b y y+ = =[ ]3 12 8 ________________________

c a a− = =[ ]5 17 20 _______________________ d b b− = =[ ]6 14 20 ________________________

e p p+ = =[ ]4 10 6 _______________________ f q q+ = =[ ]3 12 15 ________________________

g m m+ = =[ ]7 11 4 _______________________ h n n− = =[ ]2 7 9 __________________________

QUESTION 2 Solve the following equations.

a x + =3 10 ___________________________ b m + =5 16 ___________________________

c y + =9 15 ___________________________ d n + =9 27 ___________________________

e p + =7 21 ___________________________ f q + =7 7 ___________________________

g a + =5 13 ___________________________ h b + =8 24 ___________________________

QUESTION 3 Solve the following.

a a − =9 11 _______________________________ b x − =5 17 ________________________________

c b − =3 7 ________________________________ d t − =7 15 ________________________________

e y − =1 8 ________________________________ f x − =6 36 ________________________________

g m − =2 13 _______________________________ h n − =3 25 ________________________________

QUESTION 4 Find the solutions to the following.

a 3a = 21 _________________________________ b 2x = 20 __________________________________

c 5a = 35 _________________________________ d 5x = 55 __________________________________

e 4y = 32 _________________________________ f 8x = 64 __________________________________

g 8a = 48 _________________________________ h 6y = 42 __________________________________

QUESTION 5 Solve.

ax3

9= __________________________________ bx8

3= ___________________________________

cx5

7= __________________________________ dx5

15= __________________________________

em7

3= __________________________________ fa3

20= __________________________________

gx6

4= __________________________________ hm5

16= __________________________________

ix7

2= __________________________________ jn7

9= ___________________________________


Pages 272–273

10

Algebra

Algebra


Topic 10: Problem solving with algebra


Algebra

UNIT 10: Problem solving with algebra

1 Find an expresion for the perimeter of a square with side length of 2x units.

_______________________________________________________________________________________

2 If a bag contains 3m marbles, how many marbles are in six similar bags?

_______________________________________________________________________________________

3 A fence is y metres long. A further 3y metres is added. How long is the fence now?

_______________________________________________________________________________________

4 The sum of a number and 7 is 22. What is the number?

_______________________________________________________________________________________

5 Maddy has $y and gets $9x from the bank. How much does she have now?

_______________________________________________________________________________________

6 The product of a number and 9 is 72. What is the number?

_______________________________________________________________________________________

7 If a number is multiplied by 8, and 5 is added to the product, the result is 37. What is the number?

_______________________________________________________________________________________

8 If 9 is subtracted from a number, the result is 23. What is the number?

_______________________________________________________________________________________

9 The sum of a number and 12 is 36. What is the number?

_______________________________________________________________________________________

10 If a number is divided by 15, the result is 6. What is the number?

_______________________________________________________________________________________

11 If 7 is subtracted from the product of 5 and a number, the result is 43. What is the number?

_______________________________________________________________________________________

12 A photograph is 2a cm long and b cm wide. Find its area.

_______________________________________________________________________________________

13 A room is 4x metres long and 5y metres wide. Find its area.

_______________________________________________________________________________________

14 I walked 7x km on Monday and 8y km on Tuesday. How many kilometres did I walk altogether?

_______________________________________________________________________________________

15 Find the perimeter of a rectangular block of land 9p metres long and 5q metres wide.

_______________________________________________________________________________________


Pages 186, 274–275


Algebra

TOPIC TEST PART A

1 2x + 3x equals

A 5x2 B 6x2 C 6x D 5x

2 If 3y = 15 the y equals

A 3 B 5 C 15 D 45

3 3 × x + 4 × y equals

A x3 + y4 B 12xy C 3x + 4y D 7xy

4 If a = 2 and t = 6 then 12

2at equals

A 72 B 36 C 12 D 9

5 a3 + a3 equals

A a6 B a9 C 2a3 D 2a6

6 3y2 – 2y + 5y + 4y2 equals

A 7y2 + 3y B 7y2 – 7y C 7y3 + 3y D 7y4 – 7y

7 3ab2 equals

A 3 × a × b × b B 3 × a × b × 2 C 3 × ab × ab D 3ab × 3ab

8 7t3 × (–4t2) equals

A 3t5 B 3t6 C –28t5 D –28t6

91 1a b

÷ equals

A1ab

B ba

C ab

D ab

10 3(x + 4) – x =

A 12 B 15 C 2x + 4 D 2x + 12

Marks

1

1

1

1

1

1

1

1

1

1

Algebra

Instructions • This part consists of 15 multiple choice questions

• Fill in only ONE CIRCLE for each question• Each question is worth 1 mark• Calculators are NOT allowed

Time allowed: 15 minutes Total marks = 15


Algebra

TOPIC TEST PART A

1 2x + 3x equals

A 5x2 B 6x2 C 6x D 5x

2 If 3y = 15 the y equals

A 3 B 5 C 15 D 45

3 3 × x + 4 × y equals

A x3 + y4 B 12xy C 3x + 4y D 7xy

4 If a = 2 and t = 6 then 12

2at equals

A 72 B 36 C 12 D 9

5 a3 + a3 equals

A a6 B a9 C 2a3 D 2a6

6 3y2 – 2y + 5y + 4y2 equals

A 7y2 + 3y B 7y2 – 7y C 7y3 + 3y D 7y4 – 7y

7 3ab2 equals

A 3 × a × b × b B 3 × a × b × 2 C 3 × ab × ab D 3ab × 3ab

8 7t3 × (–4t2) equals

A 3t5 B 3t6 C –28t5 D –28t6

91 1a b

÷ equals

A1ab

B ba

C ab

D ab

10 3(x + 4) – x =

A 12 B 15 C 2x + 4 D 2x + 12

Marks

1

1

1

1

1

1

1

1

1

1

Algebra

Instructions • This part consists of 15 multiple choice questions

• Fill in only ONE CIRCLE for each question• Each question is worth 1 mark• Calculators are NOT allowed


11Algebra


AlgebraTopic Test PART AInstructions This part consists of 12 multiple-choice questions

Each question is worth 1 marks

Fill in only ONE CIRCLE for each question

Calculators are NOT allowed


Marks


Algebra

Total marks achieved for PART A

Marks

1

1

1

1

15

1

11 (4x3)2 =

A 4x5 B 4x6 C 16x5 D 16x6

1262

2aab

equals

A 3ab B 3ab

C 6b D 6b

13 3ab – b + ab – 2b =

A 2ab – b B 2ab – 3b C 4ab – b D 4ab – 3b

14x x

x

4 6

2

× =

A x5 B x8 C x12 D x22

15m

m

6

2

2

equals

A m5 B m6 C m8 D m9


Algebra

Total marks achieved for PART A

Marks

1

1

1

1

15

1

11 (4x3)2 =

A 4x5 B 4x6 C 16x5 D 16x6

1262

2aab

equals

A 3ab B 3ab

C 6b D 6b

13 3ab – b + ab – 2b =

A 2ab – b B 2ab – 3b C 4ab – b D 4ab – 3b

14x x

x

4 6

2

× =

A x5 B x8 C x12 D x22

15m

m

6

2

2

equals

A m5 B m6 C m8 D m9

12Algebra


AlgebraTopic Test PART A continued

15Total marks achieved for PART A

Marks

Instructions This part consists of 15 questions


Write answers in the answers-only column


Questions Answers only

Total marks achieved for PART B 15

Marks

AlgebraTopic Test PART B

13Algebra



Algebra

Total marks achieved for PART B

TOPIC TEST PART B

Marks

Algebra

Instructions • This part consists of 15 questions

• Each question is worth 1 mark• Write answers in the ‘Answers only’ column


15


1 Simplify 5 × m × 9 × p ___________________

2 Simplify 12x + 7y – 3x – y ___________________

3 Write in a shorter way: 8 × 7(5 × a – 3) ___________________

4 If a = 7, find 3a2 ___________________

5 If x = 5 and y = 7, find 5x + 7y ___________________

6 Find the sum of 8x + 9y and 56 ___________________

7 To the sum of 9x and y, add 6y ___________________

8 Divide 6a by 5b and then add 10 to the result. ___________________

9 Write in a shorter way: 23 plus y, all divided by 9 ___________________

10 Divide the difference of a and b by the sum of a and b ___________________

11 What is the product of 6, x and 9? ___________________

12 What is 8m subtracted from the product of 2m and 3n? ___________________

13 Simplify 9x3 × 5x2 ___________________

14 Simplify a a

a

6 4

3

×___________________

15 Expand 8(5x – 12) ___________________

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1


Algebra


TOPIC TEST PART B

Marks

Algebra




15


1 Simplify 5 × m × 9 × p ___________________

2 Simplify 12x + 7y – 3x – y ___________________


4 If a = 7, find 3a2 ___________________

5 If x = 5 and y = 7, find 5x + 7y ___________________








13 Simplify 9x3 × 5x2 ___________________

14 Simplify a a

a

6 4

3

×___________________

15 Expand 8(5x – 12) ___________________

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1


Algebra


TOPIC TEST PART B

Marks

Algebra




15


1 Simplify 5 × m × 9 × p ___________________

2 Simplify 12x + 7y – 3x – y ___________________


4 If a = 7, find 3a2 ___________________

5 If x = 5 and y = 7, find 5x + 7y ___________________








13 Simplify 9x3 × 5x2 ___________________

14 Simplify a a

a

6 4

3

×___________________

15 Expand 8(5x – 12) ___________________

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

Instructions This part consists of 4 questions


Show all necessary


Questions

Total marks achieved for PART C 20

Marks

AlgebraTopic Test PART C

14Algebra

Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning82 EXCEL ESSENTIAL SKILLS: YEAR 7 MATHEMATICS REVISION AND EXAM WORKBOOK 2 – EXTENSION

Algebra

Total marks achieved for PART C

TOPIC TEST PART C

Marks

Algebra


• Each question is worth 5 marks• Show all necessary working


20

1 Find the value of the expression if x = 3, y = 4 and z = 2

a 3x + 5y __________________________ b y2 ÷ z _____________________________

cy z

x−

___________________________ d –y3 _______________________________

e x2 + y2 – 4xz _______________________________________________________________

2 Solve the following equations.

a 9 + a = 28 _________________________________________________________________

b 85 – y = 46 ________________________________________________________________

c 6x = 54 ___________________________________________________________________

Write in short-hand notation, using indices where necessary.

d 5 × a × a × a = _____________________________________________________________

e 4 × 7 × a × a × b × c = _______________________________________________________

3 Simplify the following.

a m4 x m7 = _______________________ b (3x3)2 = ___________________________

c 9m7 x 3m5 = ____________________ d 24x12y18 ÷ 3x8y9 = __________________

e p p

p

9 5

2 3

×

( ) = _______________________

4 a The product of a number and 7 is 63. What is the number? __________________________

b When 5 is added to the product of 4 and a number, the answer is 21. What is the number?

__________________________________________________________________________

Solve the following inequations.

c x – 3 > 9 _______________________ d 5x < 15 ____________________________

ex7

6> _________________________

5

5

5

5


Algebra

Total marks achieved for PART C

TOPIC TEST PART C

Marks

Algebra


• Each question is worth 5 marks• Show all necessary working


20

1 Find the value of the expression if x = 3, y = 4 and z = 2

a 3x + 5y __________________________ b y2 ÷ z _____________________________

cy z

x−

___________________________ d –y3 _______________________________

e x2 + y2 – 4xz _______________________________________________________________

2 Solve the following equations.

a 9 + a = 28 _________________________________________________________________

b 85 – y = 46 ________________________________________________________________

c 6x = 54 ___________________________________________________________________

Write in short-hand notation, using indices where necessary.

d 5 × a × a × a = _____________________________________________________________

e 4 × 7 × a × a × b × c = _______________________________________________________

3 Simplify the following.

a m4 x m7 = _______________________ b (3x3)2 = ___________________________

c 9m7 x 3m5 = ____________________ d 24x12y18 ÷ 3x8y9 = __________________

e p p

p

9 5

2 3

×

( ) = _______________________

4 a The product of a number and 7 is 63. What is the number? __________________________

b When 5 is added to the product of 4 and a number, the answer is 21. What is the number?

__________________________________________________________________________

Solve the following inequations.

c x – 3 > 9 _______________________ d 5x < 15 ____________________________

ex7

6> _________________________

5

5

5

5

Documents

Algebra - · PDF fileAlgebra Student Book - Series H 2 Contents Topics Topic 1 ... EXCEL STEP-BY-STEP MATHS YEAR 7 Topic 4: Algebraic abbreviations Pages 186, 252–254. 5 Algebra