Algebra Test A: Worked Solutions

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Algebra Test A (Standard) – Worked Solutions
Multiple choice section

Question Number
1
2
3
4
5
6
7
8
9
10
Answer
D
D
C
A
B
D
C
B
D
A

Question 1
D

Question 2
D
(b – 5)2
= b2 – 2 × 5 × b + (-5)2
= b2 – 10b + 25

Question 3
C
-3(2x – 1)
= -6x + 3

Question 4
A
3p2 – 15p + 27ap3 = 3p(p – 5 + 9ap2)

Question 5
B
6 significant figures
Zeroes before the 3 do not count
The rest of the zeroes do count

Question 6
D
k2 + 2k + 6k + 12
= k(k + 2) + 6k + 12
= k(k + 2) + 6(k + 2)
= (k + 6)(k + 2)

Question 7
C

Question 8
B

Question 9
D

Question 10
A

Short answer section

Question 11
Scientific notation is used by scientists who wish to write very large or very small numbers in a convenient way. When writing index numbers, the index indicates the number of times that the base is multiplied by itself.

Question 12
Factorise and expand are opposite instructions. Factorising involves expressing something as a product of its factors (often using brackets) whereas expanding involves the multiplication of these factors (removing brackets by multiplying the factors inside by those outside).
e.g. 4x + 10xy.
The common factor is 2x, so place it outside of a pair of brackets and place the other factors inside:
2x(2 + 5y)
Expanding these brackets gives the original expression back again:
2x × 2 + 2x × 5y = 4x + 10xy

Question 13
(a) 3t2 × 5t8
= 15t10
(b) -4z8y2 × z5y6
= -4z13y8
(c) bgh × -11bg2
= -11b2g3h

Question 14
(a) 12n3 ÷ 4n (b) -42jk10 ÷ 6k3
= 3n2 = -7jk7

(c) =

Question 15
(a) (22)3
= 26
= 64
(b) (d5)2 × (d2)8
= d10 × d16
= d26
(c) (f 5)6 ÷ (f 2)3
= f 30 ÷ f 6
= f 24

Question 16
(a) (3p2)4
= 34p8
= 81p8
(b)
(c) (2xy2)3 × (x2y)5
= 23x3y6 × x10y5
= 8x13y11

Question 17
(a) 55 × 35
= (5 × 3)5
= 155
(b) v-6
=

(c) q7 ÷ q11
= q-4
=

Question 18
(a) 100
= 1

(b) 4r0
= 4 × 1
= 4

(c) (13s)0
= 130s0
= 1 × 1
= 1

Question 19
(a)
(b)

(c)

Question 20
(a) 92 017 000 = 9.2017 × 107
(b) 3.2 × 104 = 32 000

(c) 5.62 × 10-5
(d) 0.007 23

Question 21
3.42 × 10-3 × 3.8 × 107 – 8.706 × 10-1
= 129 959
= 1.299 59 × 105

Question 22
(a) Non-zero significant figures = 5
Zero significant figures = 1
In total, six significant figures

(b) Non-zero significant figures = 1
Zero significant figures = 0
In total, one significant figure

(c) 1.400 × 101

Question 23
(a)
(b) km – n = d km = d + n km – d = n n = km – d

Question 24
(a) = w + v a + b = p(w + v) b = p(w + v) – a (b) b = 5 × 0 + 5 × 8 – 1 b = 39

b = pw + pv – a

Question 25
(a) A = × (3 + 4) × 6
A = 21 cm2

(b) Substituting in A = 21, h = 6, b = 4:

Question 26
(a) 5(x – 8z)
= 5x – 40z

(b) -3p2(1 – 5mp)
= -3p2 + 15mp3

(c) 2(a + 1) + 4(a + b)
= 2a + 2 + 4a + 4b
= 6a + 4b + 2

Question 27
(a) (q + 7)(q + 2)
= q2 + 2q + 7q + 14
= q2 + 9q + 14

(b) (w – 6)(w + 4)
= w2 + 4w – 6w – 24
= w2 – 2w – 24

(c) 2(11 – a)(a + 3)
= 2(11a + 33 – a2 – 3a)
= 22a + 66 – 2a2 – 6a = -2a2 + 16a + 66

Question 28
(a) P = 2 × 18 + 2 × 16
P = 36 + 32 68 m

A = 16 × 18
A = 288 m2

(b) P = 2(18
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