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Algebra

Student Book - Series H-2
7(4x - y) = ___

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Algebra
Student Book - Series H 2

Contents Date completed

Topics __/__/__
__/__/__
Topic 1 - Algebraic expressions __/__/__
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 __/__/__
__/__/__
Practice Tests __/__/__

Topic 1 - Topic test A
Topic 2 - Topic test B
Topic 3 - Topic test C
Author of The Topics and Topic Tests: AS Kalra

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

CHAPTER 6 EXCEL STEP-BY-STEP MATHS
YEAR 7
AAlglgeberabra
Page 186
Topic 1: Algebraic expressUioNnIsT 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 6: Algebra 69
1
Algebra
Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

AAlglgeberabra EXCEL STEP-BY-STEP MATHS
YEAR 7
Topic 2: SimplifyingUaNlgIeTb2ra: iSciemxpprleifsysiinognsalgebraic expressions
Pages 186, 252–254, 259

QUESTION 1 Write down the coefficient for each of the following terms. d 84x _____________
h 5y ______________
a 9a ______________ b 6y ______________ c 12t _____________ l 32m ____________
e 53y _____________ f 32m ____________ g 82c _____________
i 16n _____________ j 43a _____________ k 14b _____________

QUESTION 2 Circle the like terms.

a 3b, 5a, 9a _______________ b 4x, 5y, 6x ______________ c 9x, 3a, 5x ________________
f 3l, 5m, 5l ________________
d 9a, 3d, 6a _______________ e 8y, 3a, 3y ______________ i 10y, y, x _________________

g 3d, 2c, 5c _______________ h 9, 8x, 5x ______________

QUESTION 3 Simplify the following.

a 2x + 3x = ________________ b a + a + a + a = __________ c y + y + y + y + y + y = _______
f c + c + c + c = _____________
d y + y + y + y = ____________ e m + m + m + m + m =_____ i 5a + 11a = ________________

g 3d + 9d = ________________ h 9k + 3k +7k = ___________

QUESTION 4 Simplify the following expressions.

a 15x – 3x = _______________ b 27b – 18b = ____________ c 28a – 10a = _______________
f 15a – 6a = ________________
d 18a – 5a = _______________ e 18x – 7x = ______________ i 20y – y = _________________

g 11b – 4b = _______________ h 15p – 6p = _____________

QUESTION 5 Simplify the following.

a 8 × d = __________________ b 8 × a × c = _____________ c x × y × z = ________________
f 5 × a × c = ________________
d 5 × x × y = _______________ e 45 × m × n × l = _________ i 15 × b × d × e = ___________

g a × b × 14 = ______________ h 9 × 2 × m × n =__________

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 = __________________________________

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

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

AAlglgeberabra EXCEL STEP-BY-STEP MATHS
YEAR 7
Topic 3: Collecting like termUsNIT 3: Collecting like terms
Pages 259–263

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 5x + 7 + 4x + 11 = ________________________ b 9a + 15 + 6a + 13 = ________________________
c 8a + 3b + 9a + 2b = _______________________ d 8x + 2 y + 6x = ____________________________
e 9m + 3n + 8m + 4n = ______________________ f 2x + 3 y + 9x + 10 y = _______________________

QUESTION 3 Simplify the following. b 9x + 7 y − 6x + 14 y = _______________________
d 8p − 3p + 15q − 8q = _______________________
a 18a − 7a − 2a + 3b = _______________________
c 8m + 9n + 6m − 3n = _______________________ f 16abc − 12abc = ___________________________
e 17x + 42x + 15 = _________________________ h 8x + 7 y + 10x − 4 y − 2 y = __________________
g 18l − 6l + 8m + 20m − 6m = _________________

QUESTION 4 Simplify the following. b 6z − 4z + 9z = ____________________________

a 8x − x − 2x = ____________________________ d 9a − 6a − 2a = ____________________________
c 5x2 + 8x2 − 3x2 = ________________________ f x + 5x − 7x = _____________________________
e 5a − 6b − 7a − b = _________________________ h 9h − h − 7h − 2h = _________________________
g 8x + 7x − x = ____________________________

QUESTION 5 Simplify the following. b m2 − 6m − m + 12 = ________________________
d p2 − 4p + 6p − 7 = _________________________
a 8b − b − 3b = ____________________________ f 4x + 9 y + 6x − 3 y = ________________________
c 8x − 6 y − y = ___________________________ h ab + 3b − 4ab + 9b = _______________________
e 9a + b − 4b − 8a = ________________________
g xy + 5 y + 4xy = _________________________

QUESTION 6 Collect like terms and simplify. b 9a2b − 5ab2 − 3ab2 + 2a2b = __________________
d 19xyz + 6 y + 4xyz − 5 y = ___________________
a ab + bc − ab − bc + ac = ____________________ f 36a2 + 15b2 − 14a2 = _______________________
c 9x2 + 10x2 − 3x2 = _______________________ h 9a3 + 8a3 − 3b3 + 6b3 = _____________________
e 18xyz + 15xyz − 4xy = _____________________
g 8x2 y2 + 9x + 4x2 y2 + 6x = _________________

Chapter 6: Algebra 71
3
Algebra
Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

AAlglgeberabra EXCEL STEP-BY-STEP MATHS
YEAR 7
Topic 4: Algebraic abbrevUiaNtiIoTn4s : Algebraic abbreviations
Pages 186, 252–254

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 × m × 5 = _____________ c x + 4 × y = _______________

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

g 3 × b × 9 = ______________ h 2p × q × q = ____________ i 5 × a × 6 × b = ____________
j 3 × m − 6 = ______________ k 5 + 8 × x = _____________ l 8 × x + 5 × y = ____________
m 15 ÷ x = ________________ n 5x ÷ 17 = _____________ o k ÷ 15 = _________________

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

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

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

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

g xy − 5 = ________________ h 8k − 3l = ______________ i x2 yz = __________________

j 15xyz = _________________ k 7a2 + 3 = ______________ l m3 − n3 = ________________

QUESTION 4 Write the following in a shortened form.

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

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

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

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

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

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

m a × 5 × a × a = ___________________________ n 9 × b × b × b × 7 = __________________________
o y × y × y × y × a × a = _____________________
p (2 × x + 1) × (3 × x − 2) = ____________________

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

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

Algebra 4
Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

AAlglgeberabra UNIT 5: Substitution EXCEL STEP-BY-STEP MATHS
YEAR 7
Topic 5: Substitution Pages 187, 264–265

QUESTION 1 If a = 5, find the value of each expression. c 9a – 1 = __________________
f (a + 1)(a – 1) = ____________
a 7a = ____________________ b 9a + 1 = _______________ i (2a + 7) × 3a = ____________
l (a – 2) ÷ 15 = _____________
d a2 = ____________________ e 5a2 = __________________

g a3 = ____________________ h a2 – 2a = _______________

j 7a – 12 = ________________ k 180 ÷ 6a = _____________

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 = 2a + 1 b y = 3x −2 c m = 15 − 2l
l 01234
a01234 x 12 3 4 m
b y

d y = 4x −2 e p = 5q + 7 f v = 30 − 7u

x 12 3 456 q01234 u123456

y pv

QUESTION 4 Complete the table.

x y x+y x–y xy x2 y2 4x + 5y
a5 2
b6 1 73
c9 3 5
d8 1
e 10 2
f4 1
g7 3
h9 6
i3 5

Chapter 6: Algebra

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

AAlglgeberabra UNIT 6: Index notation EXCEL STEP-BY-STEP MATHS
YEAR 7
Topic 6: Index notation
Pages 253–254, 265

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 = ___________________________________
e e3 = ___________________________________ d n8 = ____________________________________
f p10 = ____________________________________

g y 4 = ___________________________________ h l9 = ____________________________________

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 x2 y5 = __________________

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

j x5 = ___________________ k x2 y2 = ________________ l 6xy 4 = ___________________

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

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

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

e 16 × x × x × x × x = _______________________ f h × 3 × h × 5 × h = __________________________
g 4 × y × 3 × y × y = ________________________ h 8 × b × b × 2 × b = __________________________

QUESTION 5 Expand each of the following. b 8x3 = ___________________________________
d 5m7 = ___________________________________
a 6a2 = __________________________________ f 16 y5 = __________________________________
c 9 y3 = __________________________________ h 3a2b3 = __________________________________
e 15b2 = _________________________________
g 7a 4 = __________________________________

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

a a2 + b = _________________________________ b a3b = ____________________________________
c a2 + b2 = ________________________________ d ab3 = ____________________________________
e a3 + b2 = ________________________________ f a2b2 = ___________________________________

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

Algebra 6
Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

AAlglgeberabra UNIT 7: Index laws EXCEL STEP-BY-STEP MATHS
YEAR 7
Topic 7: Index laws
Pages 253–258

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

a x2 × x3 = _______________ b y3 × y3 = ______________ c a3 × a 4 = ________________

d m3 × m4 = ______________ e p3 × p7 = ______________ f n10 × n3 = ________________

g a2 × a3 × a 4 = ____________ h x5 × x2 × x = __________ i y5 × y9 = ________________

QUESTION 2 Simplify the following.

a x9 ÷ x3 = _______________ b x12 ÷ x 4 = ______________ c x7 ÷ x = _________________
d y7 ÷ y 4 = _______________ e y9 ÷ y2 = _____________ f a9 ÷ a = __________________
i m15 ÷ m11 = _______________
g m25 ÷ m14 = ______________ h m12 ÷ m10 = ____________

QUESTION 3 Simplify the following.

( )a a2 3 = __________________ b ( )b5 4 = ________________ ( )c a5 6 = ___________________
( )b2 7 = ________________ ( )f x7 8 = __________________
( )d x3 7 =__________________ e ( )3x2 4 = _______________ ( )i 3b4 3 = __________________

( )g 3x3 2 = _________________ h

QUESTION 4 Simplify the following.

a 5x 4 × x5 = _______________ b 9x5 × x2 = _____________ c a11 × 3a5 = _______________
d m7 × 5m2 = ______________ e 8k3 × 7k5 = _____________ f 5a7 × 8a6 = _______________
g m3n2 × m5n7 = ____________ h x 2 y 4 × x 5 y7 = __________ i x2 y2 × x 4 y2 = _____________

QUESTION 5 Simplify the following.

( )a a2b3 3 = ________________ ( )b x5 y 6 = _______________ ( )c m5n6 3 = _________________

d x5 × x6 × x7 = ____________ e x8 ÷ x 4 ÷ x3 = __________ f a6 × a7 ÷ a5 = _____________

g a9 × a9 = _______________ h a15 × a5 = _____________ i b12 × b12 = ________________
a3 a7 b10

QUESTION 6 Simplify the following.

a x8 ÷ x6 = _______________ b x13 ÷ x8 = _____________ c x17 ÷ x13 × x 4 = ___________
x x6 × x 4 ÷ x3 = __________ f x9 × x 4 ÷ x7 = ____________
i a7 × a8 ÷ a2 = _____________
( )d 2x7 3 = _________________ e

g a 4 × a5 ÷ a2 = ____________ h x9 ÷ x2 = ______________

Chapter 6: Algebra 75
7
Algebra
Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

AAlglgeberabra EXCEL STEP-BY-STEP MATHS
YEAR 7
Topic 8: Grouping symbols UNIT 8: Grouping symbols
Page 256

QUESTION 1 Expand the following expressions.

a 2(a + 3b) = ______________ b 8(2a + b) = _____________ c 3(5a + b) = _______________
f 5(3x + 8 y) = ______________
d 5(2m + 5n) = ______________ e 7(5m − n) = _____________ i 6(4a − 2b) = ______________

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

QUESTION 2 Expand. b y( y + 7) = _____________ c 10(3x − 8 y) = _____________
e 9(5x − y) = _____________ f 2a(a + b) = ______________
a 6(2a + 7) = ______________ h x(x + 15) = _____________ i 3p(p − 7) = ______________
d m(2m + 3) = ______________
g k(3k − 2) = ______________

QUESTION 3 Remove the grouping symbols.

a a(3a + 5) = ______________ b 3m(2m − 9) = ___________ c p(3p + 7) = _______________
f 6p(4p − 1) = ______________
d x(5x − 3) = ______________ e 8 y(3 y − 10) = ___________ i 6a(3a − 9) = ______________

g m(4m − 7) = _____________ h 5x(3x + 7) = ____________ c 9(x − 2 y) = ______________
f 3(3a − 5b) = ______________
QUESTION 4 Expand. b 3(7a − 2b) =_____________ i 19(a + 2b) = ______________
e 5(5a − 3b) =_____________
a 7(4 y + 5) = ______________ h p(4p − 9) = _____________
d 9(8 y − 2) = ______________
g 6(3x − 4 y) =______________

QUESTION 5 Expand the following expressions.

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

d q(8q + 3p) = _____________ e 3m(4m − 3n) = __________ f 9(5p − 6) = _______________
i 10(5a − 9b) = _____________
g 7(6x − 10 y) =_____________ h 7p(3p − 4) = ___________

QUESTION 6 Expand. ( )b x3 x 4 − x2 = ___________ c 5a(6a − 7b) = _____________

a 2x(10x − 3 y) = ___________ e x5(x − 3) = _____________ ( )f 6a2 a3 + 5 = _____________
( )i 7a3b2 a3 + b = ____________
( )d x2 x 4 − 7 = _____________ ( )h x7 x2 − x = ___________
( )g a3 a2 − a = _____________ ( )k xy x2 − y2 = ___________ l 8a2b(a + b) = _____________

j m(4m − 5n) = ____________ n mn(m − n) = ____________ ( )o 9a a2 + b2 = _____________
m 6mn(3m − 2n) = ___________

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

Algebra 8
Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

AAlglgeberabra UNIT 9: Equations EXCEL STEP-BY-STEP MATHS
YEAR 7
Topic 9: Equations
Pages 272–273

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

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

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

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

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

QUESTION 2 Solve the following equations. b m + 5 = 16 ___________________________
___________________________ d n + 9 = 27 ___________________________
a x + 3 = 10 ___________________________ f q +7=7 ___________________________
c y + 9 = 15 ___________________________ h b + 8 = 24 ___________________________
e p + 7 = 21 ___________________________
g a + 5 = 13

QUESTION 3 Solve the following. b x − 5 = 17 ________________________________
d t − 7 = 15 ________________________________
a a − 9 = 11 _______________________________ f x − 6 = 36 ________________________________
c b − 3 = 7 ________________________________
e y − 1 = 8 ________________________________ h n − 3 = 25 ________________________________
g m − 2 = 13 _______________________________

QUESTION 4 Find the solutions to the following. b 2x = 20 __________________________________
d 5x = 55 __________________________________
a 3a = 21 _________________________________ f 8x = 64 __________________________________
c 5a = 35 _________________________________ h 6y = 42 __________________________________
e 4y = 32 _________________________________
g 8a = 48 _________________________________

QUESTION 5 Solve.

a x = 9 __________________________________ b x = 3 ___________________________________
3 8

c x =7 __________________________________ d x = 15 __________________________________
5 5

e m =3 __________________________________ f a = 20 __________________________________
7 3

g x =4 __________________________________ h m = 16 __________________________________
6 5

i x =2 __________________________________ j n = 9 ___________________________________
7 7

Chapter 6: Algebra 77
9
Algebra
Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

AAlglgeberabra EXCEL STEP-BY-STEP MATHS
YEAR 7
Topic 10: Problem solUviNnIgTw1i0th: aPlrgoebbrlaem solving with algebra
Pages 186, 274–275

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.

_______________________________________________________________________________________

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

Algebra 10
Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

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11
Algebra
Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

Algebra PART A continued

Topic Test

Algebra B 4x66 C 16x55 D 16x66 MMaarrkkss
C 6b 6 1
11 (4x33)22 = C 4ab – b
C x1122 Db 1
A 4x55 C m88 D 4ab – 3b 1
D x2222
12 6a 22 equals D m99 1
2ab
1
A 3ab 3a
Bb

13 3ab – b + ab – 2b = B 2ab – 3b

A 2ab – b

14 x 44 × x 66 =
x 22

A x55 B x88

 m66  22
 m22 
15 equals

A m55 B m66

Total mToatrakl ms aarckhsiaecvheiedvfeodrfoPrAPRATRTAA 1155

Algebra 12
Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

bCrTaESTTAoATTAlOplgOglgPicePeeIIbCbTbCreTrraTasaEEtS STT PPAPPAARARTRRTBTTBBB
Instructions This part consists of 15 questions
••• TIiInEWTmnshaerstciitrstahrueluplcqocaatwutinroieteosnsdwncst:osieo2n r•••0nssWE•••imasirWETicsinTEWtthaihershnaciiwrsqattcihuisethounhpoeteqspfeeaarqwsuaanrstt1ueetinr‘hso Aetrs5swcnsstwnco1ietiiooqnsniseronnssurmwwtnhsissioeieisensitarissnsttarwhrtstnswhoktio1shoofeorwomfetnr1‘ehntA1a5s‘hrA5snrl1kyqn-s1osqu’smwnumwecleayeseorarstcsrkriltosokuioolnuomnnsmnlsylnny’ ’ccoolulummnn Total marks = 15
tions

lowed: TT1imi5meemaalilonlowuweteded:s:1155mQmiunienusutiteoesnss TotaTATlonomtstawalaelmrrmskaaorsnrkkls=ys==115155Marks

Questions QQuueesstitoionnss AnswAAnensrswsweoersrnsolyonnlyly MMMaaarrkrkksss
fy 5 × m ×191 ×SSipmimpplilfiyfy55××mm××99××pp
_______________________________________ 111

fy 12x + 7y22– 3SSixmim–ppliylfiyfy1122xx++77yy––33xx––yy _______________________________________ 111

n a shorte3r3waWyWr:irtie8tei×nina7as(hs5hoor×treterarww–aay3:y:)88××77(5(5××aa––33)) _______________________________________ 111

7, find 3a244 IfIfaa==77, ,fifnindd33aa2 2 _______________________________________ 111

5 and y = 75,5fiInfIdfxx=5=x55+aann7ddyyy==77, ,fifnindd55xx++77yy _______________________________________ 111

he sum of 866x +FiF9ninyddtahtnhedesus5um6moof f88xx++99yyaanndd5566 _______________________________________ 111

sum of 9x7a7ndToTyot,htaheedsdusum6moyof f99xxaannddy,y,aaddd66yy _______________________________________ 111

6a by 5b a8n8d DtDihvieivdindee6a6adadbbyy1505bbatanonddtthhtheeennraeadsdudl1t10.0totoththeereresusultl.t. _______________________________________ 111

n a shorte9r9waWyWr:irti2ete3ininpalaushsshoorytr,eterarwlwlaayd:yi:2v23id3pepludlussby,yy,a9allllddiviivdideeddbbyy99 _______________________________________ 111

the differe1n10c0eDDiovifivdideaetahthneedddifbiffefbereryennctecheoeof fsauaamannddobfbbabyytahtnheedsusbummoof faaaannddbb _______________________________________ 111

s the produ11c11t WoWfhha6at,tisixsthathenedppror9od?duuctctoof f66, ,xxaanndd99?? _______________________________________ 111

s 8m subtr1a12c2teWWdhhafatrtoisims88mtmhseusubpbtrtraroactcdetuedcdftrforoommf t2hthmeeppraornoddduuct3ctnoof?f22mmaanndd33nn?? _______________________________________ 111

fy 9x3 × 5x12133SSimimpplilfiyfy99x3x3××55x2x2 _______________________________________ 111

a 6 × a 4 1144SSimimpplilfiyfy aa6 6××aa4 4 _______________________________________ 111
a3 aa3 3 _______________________________________ 111
fy

d 8(5x – 121)155EExpxpaanndd88(5(5xx––1122))

ChCahpateprte6r: 6A:lgAelgberabra Total mTaTorotktaasl lmamacarhrkkisesavacechhdieievfveoedrdfPoforArPRPATARRTBTBB 111555
Total marks achieved for PART B
15
Algebra 81881311
Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

Algebra

TAolpgiecbTreast PART C
PART C
TOPIC TESTInstructions This part consists of 4 questions
Total marks = 20
Instructions • Each question is worth 5 marks
• ShTEohawcishaplqlanureetcscetosionsnasriysistswoofrt4hq5uemsatiroknss

Time allowed: 2•0 mShinowutaelsl necessary working

Time allowed: 20 mQiuneustteiosns Total marks = 20 Marks

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

a 3x + 5y __________________________ b y22 ÷ z _____________________________

c y − z ___________________________ d –y33 _______________________________
x

e x22 + y22 – 4xz _______________________________________________________________ 5

2 Solve the following equations. 5

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 m44 x m77 = _______________________ b (3x33)22 = ___________________________
d 24x1122y1188 ÷ 3x88y99 = __________________
c 9m77 x 3m55 = ____________________

( )ep99 × p55 = _______________________ 5
p22 33

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 ____________________________

e x >6 _________________________ 5
7

Total marks achieved for PART C 20
Total marks achieved for PART C 20

82 Algebra

EEXXCCEELL EESSSSEENNTTIIAALL SSKKIILLLLSS:: YYEEAARR 77 MMAATTHHEEMMAATTIICCSS RREEVVIISSIIOONN AANNDD EEXXAAMM WWOORRKKBBOOOOKK 22 –– EEXXTTEENNSSIIOONN

14Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning