Cambridge Lower Secondary Maths: Stage 7

Estimate, add and subtract integers

33 − 51 = ?

1. 18
2. −84
3. 84
4. −18

The order of brackets, positive indices and operations

(2 + 8) × 3 = ?

1. 30
2. 13
3. 26
4. 14

Multiply and divide integers, one of them negative

16 ÷ (−4) = ?

1. 8
2. 12
3. 4
4. −4

Lowest common multiple and highest common factor, numbers under 100

Find the LCM of 12 and 15.

1. 180
2. 60
3. 27
4. 30

Use tests of divisibility to find factors of numbers above 100

Which of these is a factor of 616?

1. 11
2. 10
3. 6
4. 9

Squares and square roots, cubes and cube roots, as inverses

15² = 225.
So what is √225?

1. 15
2. 112.5
3. 16
4. 225

Multiply and divide whole numbers and decimals by any positive power of 10

0.31 × 1,000 = ?

1. 310
2. 31000
3. 3.1
4. 31

Round to a given number of decimal places

Round 17.717 to 2 decimal places.

1. 17.71
2. 17.74
3. 17.72
4. 18.72

Fractions, terminating decimals and percentages can be equal

Write 7/10 as a percentage.

1. 7%
2. 30%
3. 70%
4. 80%

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

1/6 + 3/4 = ?
(simplest form)

1. 1/6
2. 1/8
3. 2/5
4. 11/12

Multiply and divide proper fractions

1/3 ÷ 5/6 = ?

1. 5/18
2. 2/5
3. 5/2
4. 2/3

Simplify calculations with decimals or fractions using factors, laws and order of operations

Work out 5 × 20 × 20 the easy way.

1. 2010
2. 2000
3. 120
4. 1990

Percentages of shapes and numbers, including below 1% and above 100%

What is 15% of 1160?

1. 116
2. 232
3. 1145
4. 174

Compare and order decimals and fractions with =, ≠, > and <

Which statement is true?

1. 7.5 < 7.44
2. 7.44 > 7.5
3. 7.5 > 7.44
4. 7.44 = 7.5

Add and subtract positive and negative decimals

8.9 − −1.7 = ?

1. 7.2
2. 10.6
3. −7.2
4. −10.6

Multiply and divide decimals by whole numbers

0.4 × 0.7 = ?

1. 2.8
2. 0.28
3. 0.028
4. 1.1

The unitary method for ratio and direct proportion

y is inversely proportional to x.
When x = 3, y = 8.
Find y when x = 8.

1. 8
2. 3
3. 21.3
4. 4

Simplify and compare ratios in the same units

Drink A mixes juice and water 3:5. Drink B mixes them 4:2.
Which drink is MORE juicy?

1. They are the same
2. You cannot compare different ratios
3. Drink B
4. Drink A

Divide an amount in a ratio with two parts

$30 is shared in the ratio 1 : 4.
How much is the larger share?

1. $26
2. $6
3. $24
4. $7.5

Letters can stand for unknowns, variables or constants

In y = 2x + 1, what is the letter x?

1. Always the number 1
2. A variable: it can take many values
3. An unknown: one value makes it true
4. A label for a unit, like cm

The laws of arithmetic and the order of operations apply to algebra

Which is the same as x × 7 × y?

1. 7x + 7y
2. 7xy
3. 7 + xy
4. 7x + y

Collect like terms; multiply a bracket by a constant

Expand
2n(2n − 2)

1. 4n² − 4n
2. 4n − 4n
3. 4n² − 4
4. 4n² − 2

A situation in words or as a linear expression

Aisha has p stickers.
They are shared equally between 3 friends, and then each friend gets 4 more.
Which expression is one friend's number?

1. (p + 4)/3
2. p/3 + 4
3. p/7
4. 3p + 4

A situation in words or as a one-step formula

A regular shape has 6 equal sides, each s cm long.
Which formula gives its perimeter P?

1. P = s⁶
2. s = 6P
3. P = 6s
4. P = s + 6

A situation in words or as an equation; solve it (unknown on one side)

I think of a number.
I multiply it by 5 and then add 4.
The answer is 14. What was my number?

1. 4
2. 10
3. 2
4. 50

A letter can stand for an open interval (one term)

How many integers satisfy
−2 < x ≤ 1 ?

1. 3
2. 2
3. 4
4. 8

Term-to-term rules; generate linear sequences from numbers and patterns

3, 10, 17, 24, …
Which is the term-to-term rule?

1. add 7
2. multiply by 3
3. add 3
4. add 8

nth term rules of the form n ± a and a × n

Find the nth term.
1, 6, 11, 16, …

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

A function gives one output for each input; find outputs, and inputs by inverse operations

A function machine: input → × 6 → + 2 → output.
The OUTPUT is 20. What was the input?

1. 3.666667
2. 1.333333
3. 3
4. 122

A situation in words or as a linear function (y = x + c, y = mx)

A plumber charges C = 8h + 9, where h is the number of hours.
What does the formula say in words?

1. $8 to come out, plus $9 for every hour
2. $17 for every hour
3. $9 to come out, plus $8 for every hour
4. $72 for the job

Tables of values and graphs of y = x + c and y = mx

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

1. (3, 1)
2. (3, 6)
3. (3, 5)
4. (5, 3)

Straight lines parallel to the x- or y-axis

Which point lies on the line x = 1?

1. (0, 0)
2. (−1, 1)
3. (2, 2)
4. (1, −1)

Read and interpret graphs of rates of change, and explain their shape

On a graph of water in a bath against time, the line goes DOWN.
What does that show?

1. Water is going out: the bath is emptying
2. The water is getting hotter
3. The bath is filling
4. Nothing is happening

Regular polygons: sides, angles and symmetry

A regular polygon has rotational symmetry of order 8.
How many sides does it have?

1. 16
2. 45
3. 8
4. 10

Congruent shapes have equal corresponding sides and angles

Triangles ABC and PQR are congruent:
A matches P, B matches Q and C matches R.
AB = 6 cm, BC = 7 cm and AC = 8 cm. How long is QR?

1. 8 cm
2. 7 cm
3. 5 cm
4. 6 cm

Parts of a circle, including chord and tangent

The radius of a circle is 12 cm.
How long is its diameter?

1. 24 cm
2. 144 cm
3. 14 cm
4. 6 cm

Convert between metric units of area, including hectares

Convert 5 litres to cm³.

1. 500
2. 50,000
3. 5,000
4. 500,000

Area of a triangle, and of compound shapes made of rectangles and triangles

A triangle has base 40 cm and height 22 cm.
What is its area?

1. 880 cm²
2. 440 cm²
3. 124 cm²
4. 62 cm²

The properties that fix a particular 3D shape

A solid has 6 faces, 10 edges and 6 vertices.
Which solid could it be?

1. pentagonal pyramid
2. pentagonal prism
3. cube
4. square-based pyramid

Volume of cubes and cuboids, and of compound shapes made from them

A cuboid measures 3 cm by 4 cm by 11 cm.
Find its volume.

1. 132 cm³
2. 18 cm³
3. 178 cm³
4. 12 cm³

Front, side and top views of 3D shapes

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 and cuboids

Find the total surface area of a 9 cm by 2 cm by 2 cm cuboid.

1. 80 cm²
2. 40 cm²
3. 36 cm²
4. 52 cm²

Reflective symmetry and order of rotational symmetry

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

Angles in a quadrilateral add to 360°; find the missing one

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

Angles around a point add to 360°; find the missing one

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

Angles on parallel lines and transversals, perpendicular and intersecting lines

Two parallel lines are crossed by a third line.
One angle is 115°. What is its alternate angle?

1. 245°
2. 115°
3. 25°
4. 65°

Use scale to interpret maps and plans

A map has a scale of 1 : 100,000.
A road is 4 km long. How long is it on the map?

1. 40 cm
2. 4 cm
3. 5 cm
4. 0.4 cm

Distance between two coordinates that share an x or a y

Find the distance between (−6, −3) and (7, −3).

1. 7
2. 12
3. 13
4. 1

Corresponding points under a translation, without a grid

A translation takes P (8, 4) to (10, 9).
Where does the same translation take Q (9, 5)?

1. (19, 14)
2. (11, 10)
3. (7, 0)
4. (14, 7)

Reflect shapes in the x- or y-axis; the image is congruent

The point (3, 5) is
reflected in the line y = x.
Where is its image?

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

Rotate shapes 90° and 180° about a centre; the image is congruent

The point (4, −1) is
rotated 180° about the origin.
Where is its image?

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

Enlarge by a positive whole-number scale factor; the image is similar

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

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

The effect of sample size

Which statement about samples is true?

1. A sample can tell you nothing about the population.
2. A larger sample gives results closer to the whole population, but costs more time and money.
3. A sample of 10 is always as good as a sample of 1,000.
4. Doubling a sample makes its results twice as accurate.

Record and show data: Venn, Carroll, two-way tables, dual and compound bar charts, waffle and pie charts, frequency diagrams, line and scatter graphs, infographics

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

Use mode, median, mean and range on large data sets, and choose the most suitable

A shop wants to know which shoe size to stock most of.
Which average is most suitable?

1. The range
2. The mean
3. The median
4. The mode

Interpret patterns within and between data sets; check predictions

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

Describe, compare and order likelihoods in the language of probability

An event has probability 0.9.
In words, it is…

1. unlikely
2. an even chance
3. impossible
4. likely

Probabilities run from 0 to 1, as fractions, decimals or percentages

Where on the probability scale from 0 to 1 is an event that is likely?

1. 0.8
2. 0
3. 1
4. 0.5

List all the mutually exclusive outcomes of one event; are they equally likely?

A fair dice is rolled once.
Which list shows ALL the possible outcomes?

1. 1, 2, 3, 4, 5, 6
2. odd, even, 6
3. 6
4. 1, 2, 3

Theoretical probability of equally likely outcomes

A bag holds 3 red and 1 blue balls.
One is picked at random.
What is the probability it is red?

1. 4/5
2. 1/4
3. 3/4
4. 1/3