C2L3
100 marks from 100 questions
Question 1 Question 2
The difference between t and 15 is tripled. Start with r, double it and then add 11.
Choose all the expressions that could Then you will have:
represent this sentence.
a) r + 2 + 11
a) 3(3t − 15)
b) 2r − 11
b) 3t − 15
c) 2r + 11
c) 3t − 45
d) 2(r + 11)
d) 3(t − 15)
Question 3 Question 4
The sum of q and 7 is multiplied by 2 and ‘Triple a number and then halve your
then divided by 5. answer’ could be written in different ways
The algebraic expression for this sentence using algebra.
is: Pick the correct expressions:
a) 3m ÷ 2
a.
b)
b.
c)
c. 2q + 7 ÷ 5
d)
d. 2q +
Question 5 Question 6
Halve an unknown number and then add
this answer to q.
Using algebra you could write this as:
a) p+
There are m counters in each mug.
b)
Write an algebraic expression for twice the
number of counters in the diagram. c) +q
m+
d) 3p + q
Question 7 Question 8
If the number that is 5 less than 30 is 25,
what is the number that is 5 less than p?
−
Jane has k + 3 counters.
If she doubled her number of counters she
would have:
k+ counters
Question 9 Question 10
Triple the number of pens in the diagram. If r = 0.5 and m = 6, then:
rm =
z+
Question 11 Question 12
If y + z = 20 and z = 9, then y = If r = 5 and p = 2, evaluate (r − p)2.
(r − p)2 = ( − )2
2
=
=
Question 13 Question 14
There are 2p + 5 counters in the picture.
There are b books in each box.
If p = 17, how many counters are there
And so there are (2b + 6) books to be
altogether?
placed on shelves in the shop.
Total number of counters =
There are 102 books in total. What is the
value of b, the number of books in one box?
b=
Question 15 Question 16
If r = 5 and p = 3 , evaluate r2 − 2p.
r2 − 2 p = 2
–2×
= –
=
There are 2p + 5 counters in the picture.
If p = 25, how many counters are there?
Question 17 Question 18
If k = , evaluate:
8k =
There are 2p + 5 counters in the picture.
If there are 25 counters altogether, what is
the value of p?
p=
Question 19 Question 20
This is Jane’s working for simplifying 7 m Fill in the missing term:
+ 3 a − 2 ab + 4 m :
m2 + 2
= 5m 2
7 m + 3 a − 2 ab + 4 m ... line 1
= 7 m + 4 m + 3 a − 2 ab ... line 2
= 11 m + ab ... line 3
= 12 abm ... line 4
Jane made mistakes in:
a. line 1
b. line 2
c. line 3
d. line 4
Question 21 Question 22
Fill in the missing term: Fill in the missing term:
7a − =a + 5n = 21n
Question 23 Question 24
Simplify this expression by collecting like
terms:
2m2 − 3mn + m2 m2
mn
15 ab + 5 bc − 6 ac + 9 + 14 ac − 5 − 5 bc − 4mn = −
= ab + ac +
Question 25 Question 26
Fill in the missing term: 3z + 7 y − z − 5 y = z+ y
3a + + 4b = 7 a + 4 b
Question 27 Question 28
Enter the missing term. Insert the missing term to make this equation
y3 × y × = 3 y5 true. (Enter any variables in alphabetical
order.)
7ab
= 1
Question 29 Question 30
What is the missing term? (Enter any variables Enter the missing coefficient and the two
alphabetically.) missing indices (powers).
5ab × = 25a2b2 2m × m × 3 m
n
× 5n × n = m
Question 31 Question 32
What is the missing term that makes this
= 2
equation true? (Enter any variables in 15a
alphabetical order.)
6d
=
11ef e
Question 33 Question 34
Insert the missing term to make this equation Insert the missing variables (in alphabetical
true. (Enter any variables in alphabetical order) to make this equation true.
order.)
mr × = mr2w
15pq2 ÷ = 3q
Question 35 Question 36
Complete both expansions and collect the
like terms.
9(b − 1) + 6(4 − b) = 9b − + 24 − b
= b+
You can write ‘five groups of (m + 3) lollies,
plus 4 more lollies’ as:
(m + )+ lollies
Question 37 Question 38
Select all correct answers. Expand this expression and then collect like
3(x + 2) means: terms:
a) 3 groups of x + 2 n (3n − 5) + n2 − n+
=
10n 10n
b) 3 × (x + 2)
= n2 + n
c) 3x + 2
d) x+2+x+2+x+2
Question 39 Question 40
Expand this expression and then collect like 7b(3b + 11) = b2 + b
terms:
4(2a + 5) + 10 = a+ + 10
= a+
Question 41 Question 42
(6d + 9) Expand this expression and then collect like
d+ terms:
=
7(m + 3) − 5 = m+ −5
= m+
Question 43 Question 44
In the table of powers, an index has been Using your calculator, experiment with
replaced with a heart. values to find the missing power.
Index notation Basic numeral 4 = 1 048 576
31 3
32 9
33 27
34 81
3 243
What number does the heart represent?
Question 45 Question 46
In the table of powers, the base has been In the table, the same number is replaced
replaced with a star.
with .
Index notation Basic numeral
Index notation Basic numeral
1 1000
× 101 70
2 1 000 000
× 102 700
3 1 000 000 000
× 103 7000
4 1 000 000 000 000
× 104 70 000
5 1 000 000 000 000 000
× 105 700 000
What number does the star represent?
What number is represented by ?
Question 47 Question 48
In the table of powers, the base has been In the table of powers, the base has been
replaced with a star. replaced with a heart.
Index notation Basic numeral Index notation Basic numeral
1 5 2 4
2 25 3 8
3 125
4 16
5 32
4 625
6 64
5 3125
What number does the heart represent?
What number does the star represent?
Question 49 Question 50
Write the basic numeral for 3 × 52 × 2. 96 can be written as:
3 × 52 × 2 =
a. 25 + 3 1
b. 25 × 3 1
c. 25 – 3 1
d. 25 ÷ 3 1
Question 51 Question 52
12p 0 ÷ 120 = Simplify:
k7 × k5 ÷ k = k
Question 53 Question 54
k0 Simplify the following expression.
=
k0
24f 5g 6 ÷ 6f 3g 2 = f g
Question 55 Question 56
× =
a.
b.
c.
d.
Question 57 Question 58
Evaluate: Write 256 in index form using three
(5r 0 + 3)2 = different bases.
256 = 16 =4 =2
Question 59 Question 60
What is the value of m ?
(5p 6q 4)3 = 125p q
4 m 12
(g ) = g
m=
Question 61 Question 62
(m4)6 ÷ m10 = m (2k 5)2 × (2k 5)2 = k
Question 63 Question 64
(2q 8)3 ÷ (2q 8)2 = q (3b 2)3 × (b 3)0 = b
Question 65 Question 66
(y 2)5 × (y 4)2 ÷ (y 4)3 = y (2xy 4)5 = x y
Question 67 Question 68
The reciprocal of is:
The reciprocal of is:
a.
a.
b.
b.
c.
c.
d. d.
Choose all correct answers. Choose all correct answers.
Question 69 Question 70
The reciprocal of is: Select all the correct answers.
can be written as:
a.
a.
b.
b.
c. c.
d. d.
(Choose all correct answers.)
Question 71 Question 72
Written as an improper fraction: Enter the missing coefficient and the
missing index.
16y 5 ÷ 8y –3 = y
Question 73 Question 74
0.000027 = 2.7 ÷ 100 000
2.4 × 10–2 × 2 × 10–3 = × 10
= 2.7 × 10
Question 75 Question 76
95 can be written as (32)5. Evaluate (2–4)0.
Use your index laws to simplify 3–4 × 95. (2–4)0 =
3–4 × 95 = 3
Question 77 Question 78
Simplify: Evaluate each term.
=p
Question 79 Question 80
= (p ) in index form = .
=p
A=
Question 81 Question 82
Evaluate .
Question 83 Question 84
Simplify this expression. Calculate the value of m.
m=
Question 85 Question 86
is equal to:
Question 87 Question 88
Simplify by entering the missing index.
9 ×3 =3 ?
Missing index =
You can write ‘five groups of (m + 3) lollies,
plus 4 more lollies’ as:
(m + )+ lollies
Question 89 Question 90
Complete both expansions and collect the
like terms.
9(b − 1) + 6(4 − b) = 9b − + 24 − b
= b+
There are b books in each box.
And so there are (2b + 6) books to be
placed on shelves in the shop.
There are 102 books in total. What is the
value of b, the number of books in one box?
b=
Question 91 Question 92
7b (3b + 11) = b2 + b
There are 2p + 5 counters in the picture.
If p = 17, how many counters are there
altogether?
Total number of counters =
Question 93 Question 94
If the number that is 5 less than 30 is 25, Insert the missing term to make this
what is the number that is 5 less than p? equation true. (Enter any variables in
− alphabetical order.)
15pq 2 ÷ = 3q
Question 95 Question 96
If y + z = 20 and z = 9, then y = .
(6d + 9) = d+
Question 97 Question 98
Halve an unknown number and then add Enter the missing term.
this answer to q. 7a − =a
Using algebra you could write this as:
a.
b.
c.
d.
Question 99 Question 100
Insert the missing term to make this If r = 5 and p = 2, evaluate (r − p)2.
equation true. (Enter any variables in (r − p)2 = ( − )2
alphabetical order.) 2
=
7ab
=1 =
