Cambridge Lower Secondary Maths: Stage 8

The order of brackets, indices (square and cube roots) and operations

Work out
7 × (3 + 2)

1. 42
2. 23
3. 35
4. 12

Multiply and divide integers

−30 ÷ (−6) = ?

1. −5
2. 5
3. −36
4. 11

Factors, multiples, prime factors, HCF and LCM

Write 12 as a product of prime factors.

1. 2² × 3
2. 2² × 3²
3. 2³ × 3
4. 4 × 3

Natural numbers, integers and rational numbers

Which of these is a natural number?

1. −3
2. 1/2
3. 2.5
4. 1

Positive and zero indices; index laws for multiplying and dividing

Simplify x⁹ × x³

1. x²⁷
2. 2x¹²
3. x⁶
4. x¹²

Squares of negative and positive numbers, and the matching square roots

Which numbers, squared, give 9?

1. −3 only
2. 3 only
3. 9 and −9
4. 3 and −3

Positive and negative cube numbers, and the matching cube roots

What is ∛(−216)?

1. −72
2. 6
3. −6
4. −7

Multiply and divide by 0.1 and 0.01

6 ÷ 0.01 = ?

1. 6000
2. 0.06
3. 60
4. 600

Round to a given number of significant figures

Round 0.02276 to 3 significant figures.

1. 0.0231
2. 0.0227
3. 0.0230
4. 0.0228

Fractions that equal recurring decimals

Which fraction is equal to a RECURRING decimal?

1. 7/20
2. 5/12
3. 1/4
4. 1/5

Subtract mixed numbers; answer as a mixed number in simplest form

5 5/6 − 3 1/6 = ?
(simplest form)

1. 2 2/3
2. 8 2/3
3. 2 5/6
4. 1 2/3

Multiply an integer by a mixed number; divide an integer by a proper fraction

1/6 ÷ 1/7 = ?

1. 1/42
2. 2/13
3. 6/7
4. 7/6

Simplify calculations with decimals or fractions, including brackets

Which is the same as 7 × (24 + 4)?

1. 7 × 24 × 4
2. 7 + 24 × 4
3. 7 × 24 + 7 × 4
4. 7 × 24 + 4

Percentage increase and decrease; absolute change

Decrease $60 by 10%.

1. $6
2. $66
3. $54
4. $50

Compare and order positive and negative decimals and fractions

Which is the SMALLEST?
⅖ 0.3 −1.2 −0.5

1. −0.5
2. 0.3
3. −1.2
4. ⅖

Multiply decimals by integers and by decimals

0.9 × 0.3 = ?

1. 2.7
2. 0.27
3. 1.2
4. 0.027

Divide decimals by numbers with one decimal place

0.9 ÷ 0.3 = ?

1. 30
2. 3
3. 0.3
4. 2.8

How ratio and direct proportion relate

Boys and girls in a club are in the ratio 4:3.
What PROPORTION of the club are boys?

1. 4%
2. 4/7
3. 4/3
4. 3/7

Simplify and compare ratios in different units

Write the ratio 15 minutes : 2 hours in its simplest form.

1. 15 : 2
2. 8 : 1
3. 1 : 8
4. 1 : 80

Divide an amount in a ratio with two or more parts

$170 is shared in the ratio 2 : 3.
How much is the smaller share?

1. $102
2. $68
3. $85
4. $34

Letters mean different things in expressions, formulae and equations

Which of these is an EQUATION, where the letter is an unknown to be found?

1. y = 2x + 1
2. 3x + 2 = 11
3. A = lw
4. 3x + 2

The laws and the order of operations in algebra, with squares and cubes

Which is the same as x × 6 × y?

1. 6 + xy
2. 6x + y
3. 6xy
4. 6x + 6y

Multiply a bracket by a single term; factorise by the highest common factor

Factorise fully
8y + 28

1. 8(y + 7)
2. 2(4y + 7)
3. 4(2y + 7)
4. 4(2y + 28)

A situation in words or as an expression with integer or fractional coefficients

A third of a number t, and then 9 is taken away.
Which expression is this?

1. t/3 − 9
2. 3t − 9
3. (t − 9)/3
4. 9 − t/3

A situation in words or as a formula; change the subject

A phone plan costs $40 a month plus $45 for every gigabyte used.
h is the number of gigabytes and C is the bill in dollars.
Which formula is right?

1. C = 45h + 40
2. C = 85h
3. C = 45(h + 40)
4. C = 40h + 45

A situation in words or as an equation; solve it (unknown on either or both sides)

Ben has 8 full boxes of pens and 6 loose pens.
Tom has 2 full boxes and 60 loose pens.
They have the SAME number of pens. How many pens are in a full box?

1. 7
2. 9
3. 5
4. 54

Letters can stand for open and closed intervals (two terms)

Solve
3x − 3 > −6

1. x < 1
2. x > 1
3. x < −1
4. x > −1

Term-to-term rules and sequences, including fractions

A sequence starts at 2 and the rule is "add 2/3".
What is the 4th term?

1. 10/3
2. 3
3. 4
4. 14/3

nth term rules of the form an ± b

Find the nth term.
4, 13, 22, 31, …

1. 9n + 4
2. 9n − 5
3. 4n + 9
4. n + 9

Functions: outputs, and inputs by inverse operations, including fractions

A function machine: input → × 3 → + 4 → output.
The INPUT is 8. What comes out?

1. 24
2. 36
3. 28
4. 15

A situation in words or as y = mx + c

A phone plan costs $27 a month plus $35 for every gigabyte used.
x is the number of gigabytes and y is the bill in dollars.
Which equation is right?

1. y = 27x + 35
2. y = 62x
3. y = 35x + 27
4. y = 35(x + 27)

Tables of values and graphs of y = mx + c

A point on the line y = 2x − 3 has x = −1.
What are its coordinates?

1. (−1, −5)
2. (−5, −1)
3. (−1, 1)
4. (−1, −2)

y = mx + c is a straight line with gradient m and y-intercept c

What is the gradient of
y = x + 6?

1. −1
2. 6
3. 7
4. 1

Graphs with more than one component; what their intersections mean

Gym A costs $30 to join plus $4 a visit. Gym B costs $5 a visit.
Their cost graphs cross at 30 visits. What does the crossing mean?

1. At 30 visits both gyms cost the same
2. You must go 30 times
3. Gym A costs $30
4. Gym B is cheaper after 30 visits

The hierarchy of quadrilaterals

Which quadrilateral has two pairs of equal sides next to each other, and no parallel sides?

1. kite
2. square
3. parallelogram
4. rhombus

π as circumference over diameter; the circumference formula

A circle has diameter 12 cm.
Find its circumference, in terms of π.

1. 24π cm
2. 36π cm
3. 6π cm
4. 12π cm

Miles and kilometres

5 miles is about 8 km.
About how many km is 5 miles?

1. 8 km
2. 10 km
3. 3.125 km
4. 6 km

Area of parallelograms and trapezia

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Euler's formula for vertices, faces and edges

A solid has 8 faces and 18 edges.
Use Euler's formula to find how many vertices it has.

1. 10
2. 12
3. 26
4. 14

Volume of a triangular prism

A prism has a triangular cross-section with
base 6 cm and height 7 cm. It is 3 cm long.
Find its volume.

1. 16 cm³
2. 63 cm³
3. 21 cm³
4. 126 cm³

Front, side and top views to scale

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Surface area of cubes, cuboids, triangular prisms and pyramids

A square-based pyramid has base edges of 8 cm.
Each triangular face has a slant height of 9 cm.
Find its total surface area.

1. 352 cm²
2. 208 cm²
3. 136 cm²
4. 144 cm²

A regular polygon has as many lines of symmetry, and the same order of rotation, as sides

A regular polygon has rotational symmetry of order 10.
How many sides does it have?

1. 20
2. 12
3. 10
4. 36

The exterior angle of a triangle equals the two opposite interior angles

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Alternate, corresponding and vertically opposite angles

Two parallel lines are crossed by a third line.
One angle is 70°. What is its alternate angle?

1. 110°
2. 70°
3. 20°
4. 290°

Bearings as a measure of direction

The bearing of B from A is 265°.
What is the bearing of A from B?

1. 265°
2. 095°
3. 085°
4. 090°

Midpoint of a line segment from coordinates

Find the midpoint of
(−4, 3) and (2, 11).

1. (7, −1)
2. (3, 4)
3. (−2, 14)
4. (−1, 7)

Translate points and shapes by a vector

a = (5, 1) b = (5, −1)
Find a + b.

1. (25, −1)
2. (4, 6)
3. (0, 2)
4. (10, 0)

Reflect in lines on or parallel to the axes and in y = ±x; identify a reflection and its line

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

A rotation needs a centre, a direction and an angle

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Enlarge from a centre outside or on the shape; identify an enlargement and its scale factor

The point (−6, −4) is enlarged with centre (0, 0)
and scale factor 2. Where does it go?

1. (−6, −8)
2. (−12, −8)
3. (−12, −4)
4. (−4, −2)

Advantages and disadvantages of sampling methods

50 pupils are chosen so that each year group has the same share of the sample as it has of the school.
Which sampling method is this?

1. systematic
2. convenience
3. random
4. stratified

Record and show data, now including time series and stem-and-leaf diagrams

Score: 1, 2, 3, 4
Frequency: 2, 2, 4, 6
Find the mean score.

1. 42
2. 10.5
3. 3
4. 2.5

Compare two distributions with an average and the range

Test scores.
Class A: mean 61, range 15.
Class B: mean 64, range 8.
Which class did better on average?

1. It is impossible to tell
2. Class A
3. They are the same
4. Class B

Interpret patterns, trends and relationships within and between data sets

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Complementary events have probabilities that total 1

The probability that it rains is 0.45.
What is the probability that it does not rain?

1. 0.55
2. 1.45
3. 0.65
4. 0.45

Tables, diagrams and lists of the outcomes of combined independent events

Two fair coins are tossed.
How many possible outcomes are there?

1. 6
2. 4
3. 2
4. 3

Theoretical probability of equally likely combined events

Two fair coins are tossed.
What is the probability of one head and one tail?

1. 1/2
2. 1/4
3. 3/4
4. 1/3