Year 8 Exam Booklet:
Algebra
Year 8 Mathematics
Algebra
Name: …………………………
Easy
1.
Which of the following algebraic expression represents 2 less than 3 lots of n?
(A)
(B)
(C)
(D)
2.
12ab
Which of the following is the correct simplification of 24a2 ?
(A)
2ab
(B)
2a
(C)
(D)
3.
3(n − 2)
2 − 3n
3+n−2
3n − 2
b
b
2a
ab
2
Simplify the following expression:
5x − 3y 2 − 8x − 4y 2
4.
Simplify:
5s + 2m − 7s + 8m =
(A)
(B)
(C)
(D)
−2s + 10m
2s + 10m
2s − 10m
−2s + 6m
Page 2
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
5.
Name: …………………………
Simplify:
6d × dw
(A)
(B)
(C)
(D)
6.
6dw
6d2 w
6d2 w 2
6d
Which expression does this simplify to?
ab 18
×
=
15 a
(A)
(B)
(C)
(D)
7.
a2 b
15
18a2
15
18ab
15
6b
5
Expand and fully simplify:
(i)
2(x − 8)
(ii)
4(x − 4) − 2(x + 1)
Page 3
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
8.
9.
Name: …………………………
Fully simplify:
(i)
3s
(ii)
w
6
3
5s
+6
2w
− 7
Expand and simplify the following:
(i)
3(x − 6)
Page 4
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
10.
Name: …………………………
(ii)
2x(3 − 4x)
(iii)
7 − 4(5 + 2x)
Full factorise the following:
3g + 12
11.
What is −2x(x − 3) simplified? (Circle the correct answer)
(A)
(B)
(C)
(D)
−2x − 3
−2x 2 − 6x
−2x 2 + 6x
−2x + 6x
Page 5
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
12.
Which answer is a fully simplified form of 7p + 5p2 − 39 ? (Circle the correct
answer)
(A)
(B)
(C)
(D)
13.
Name: …………………………
9p2
4p + 5p2
10p + 5p2
10p − 5p2
Fully simplify:
(i)
5mp + 2m − 7pm =
(ii)
4ab × 3a =
(iii)
10bc
15c
=
Page 6
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
(iv)
14.
15.
Name: …………………………
2m
3
m
−4=
Simplify each expression.
(i)
(m6 )3 =
(ii)
(2p7 )4 =
Factorise fully:
4x + 8 =
Page 7
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
16.
17.
Name: …………………………
Simplify:
(i)
4a × 3a2
(ii)
(m4 )5
Simplify
(i)
a3 × a4
(ii)
−4y 3 ÷ 12y
Page 8
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
18.
Name: …………………………
Factorise:
3m + 18
19.
Which expression does this simplify to?
2m m
+ =
5
3
Page 9
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
20.
21.
Name: …………………………
Expand and simplify:
(i)
−3(2x − y)
(ii)
5 − 2(x − 3)
Write down the expression for the number of weeks in m days.
Page 10
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
Name: …………………………
Medium
22.
Simplify:
4k + 6k ÷ 2
23.
Simplify the following
(i)
3y × 4y 2
(ii)
a2 b × ab2
(iii)
(3x 2 )3
Page 11
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
24.
Name: …………………………
Fully simplify:
(−5mn) × (−7mp) × (2np) =
25.
Full simplify:
40a 36a2
÷
77b 35b 2
26.
Fully factorise:
12x 2 y − 18xy
Page 12
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
Name: …………………………
27.
What is the fully factorised form of 14bm2 − 7b2 m ? (Circle the correct answer)
28.
Which expression represents the total area of the following rectangle?
(Circle the correct answer)
(A)
(B)
(C)
(D)
29.
2(x + 3) + 2 × 7
2(x + 10)
2x + 20
All of the above
Fully simplify each expression.
(i)
ab
12c
6a
×b =
Page 13
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
(ii)
30.
Name: …………………………
vw
21
tv
÷ 49 =
Factorise fully:
9xy 2 − 12x 2 y =
31.
Simplify:
(i)
x
2x
− 3a
y
Page 14
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
(ii)
32.
Name: …………………………
3x+7
4
x−1
− 3
Factorise:
2a2 b − 4ab
33.
Simplify:
(i)
2t
t
−6
7
Page 15
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
(ii)
34.
Name: …………………………
x
5x2
÷ 6
3
Simplify:
x+1 2−x
+
6
5
35.
Fully factorise:
re2 r 2 e3
−
11
11
Page 16
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
36.
Name: …………………………
Expand, and simplify if possible
(i)
5(a + 4) =
(ii)
2m(3m − 4) + 3m =
(iii)
a(b − a) − b(a − b) =
Page 17
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
37.
Name: …………………………
Expand and simplify:
(x + 7)(x + 3).
Page 18
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
Name: …………………………
Hard
38.
The following is a magic square.
Fill in the empty squares in the box so that all rows and columns add or subtract
to the magic sum of 3 − 3.
39.
Fully simplify:
b3 108 27a
×
÷
=
22 ab 4 55b
40.
Fully simplify:
1−
a
a−b
−
a−b a+b
Page 19
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
41.
Name: …………………………
Simplify:
1
x
3
2+x
42.
Expand and simplify
(x + 4y)2 − (x + 6y)(x − 6y) .
43.
Expand and simplify:
(i)
(4x + 2)(5x − 7)
Page 20
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
44.
Name: …………………………
(ii)
(5x − 3)(2x 2 − 3x + 2)
(iii)
(4𝑥 − 1)2 − (−𝑥 + 2)2
Factorise fully:
(i)
6x 2 y 2 − 8xy 3
Page 21
© 2020 Capra Coaching Pty Ltd
Year 8 Mathematics
Algebra
(ii)
Name: …………………………
p4 − 16y 4
Page 22
© 2020 Capra Coaching Pty Ltd