ChildSocial Learning

    Grade 7 Maths Revision

    Practise advanced number skills, algebra, geometry, probability, and problem-solving. Enter an answer for each question, then check your work.

    60 questionsSuggested time: 90 minCalculator-free practice
    Your progress0 of 60 answered

    Section A: Integers, factors and powers

    Apply order of operations, prime factors, HCF, LCM and integer rules.

    1
    Evaluate: -18 + 4 × (-3) - (-10).
    2
    Express 360 as a product of prime factors.
    3
    Find the HCF of 84 and 126.
    4
    Find the LCM of 18, 24 and 30.
    5
    Evaluate: 3^4 - 2^5 + 7.
    6
    A number is divisible by both 6 and 15. What is the smallest positive number it could be?
    7
    Find the smallest integer n such that 2^n > 500.
    8
    Evaluate: (-7)^2 - 3 × 8.
    9
    Find the missing digit in 4□2 so that the number is divisible by 9. Give all possible digits.
    10
    Three bells ring every 12, 18 and 30 minutes. They ring together at 9:00 a.m. When will they next ring together?

    Section B: Fractions, decimals and percentages

    Simplify fractions and solve percentage change problems.

    11
    Calculate: 5/6 - 7/15.
    12
    Calculate: 3/4 ÷ 5/8.
    13
    Express 0.045 as a fraction in its simplest form.
    14
    A price of $320 is increased by 12.5%. Find the new price.
    15
    After a 20% discount, a bag costs $144. Find its original price.
    16
    Express 7/16 as a percentage.
    17
    Evaluate: 2.4 × 0.35.
    18
    A student answers 42 questions correctly out of 56. What percentage is correct?
    19
    A value decreases from 250 to 190. Find the percentage decrease.
    20
    Calculate: 2 1/3 + 1 5/6.

    Section C: Ratio, proportion and rates

    Use proportional reasoning, unit rates and scale factors.

    21
    Simplify the ratio 84:126:210.
    22
    Divide $540 in the ratio 2:3:4. Find the largest share.
    23
    The ratio of boys to girls is 5:7. There are 144 students. How many are girls?
    24
    Four machines produce 360 items in 6 hours. How many items will 7 identical machines produce in 5 hours?
    25
    A map has scale 1:50,000. Two places are 7.2 cm apart on the map. Find their actual distance in kilometres.
    26
    A car travels 225 km in 2 hours 30 minutes. Find its average speed.
    27
    If 8 workers finish a task in 15 days, how many days will 12 workers take at the same rate?
    28
    Flour and sugar are mixed in the ratio 7:3. If the mixture weighs 800 g, how much sugar is used?
    29
    y is directly proportional to x. If y = 42 when x = 12, find y when x = 20.
    30
    A cyclist travels 18 km in 45 minutes. Find the average speed in km/h.

    Section D: Algebra and sequences

    Expand, simplify, solve equations and identify sequence rules.

    31
    Simplify: 5a - 3(2a - 4) + 7.
    32
    Expand and simplify: 4(2x - 3) - 2(x + 5).
    33
    Solve: 7x - 9 = 4x + 24.
    34
    Solve: 3(2y + 1) = 5y + 14.
    35
    Make x the subject of y = 3x - 8.
    36
    Find the next two terms: 2, 6, 12, 20, 30, ...
    37
    Find the nth term of the sequence 5, 9, 13, 17, ...
    38
    The nth term of a sequence is 3n + 7. Find the 25th term.
    39
    A rectangle has length 2x + 3 and width x - 1. Write and simplify an expression for its perimeter.
    40
    Solve: (x - 3)/4 = 5.

    Section E: Geometry, angles and mensuration

    Apply angle properties, area formulae and properties of polygons.

    41
    The angles of a triangle are in the ratio 2:3:4. Find the largest angle.
    42
    An exterior angle of a triangle is 132°. One opposite interior angle is 57°. Find the other opposite interior angle.
    43
    Find each interior angle of a regular hexagon.
    44
    Find the sum of the interior angles of a 12-sided polygon.
    45
    A parallelogram has base 18 cm and perpendicular height 7.5 cm. Find its area.
    46
    A trapezium has parallel sides of 11 cm and 17 cm, and height 8 cm. Find its area.
    47
    A circle has diameter 14 cm. Find its circumference using π = 22/7.
    48
    Find the area of a circle with radius 5 cm. Give your answer in terms of π.
    49
    A cuboid measures 8 cm by 5 cm by 3 cm. Find its total surface area.
    50
    Point P is at (-4, 6). It is reflected in the y-axis. Give the new coordinates.

    Section F: Statistics, probability and problem solving

    Interpret data, calculate probability and solve multi-step problems.

    51
    Find the mean of 14, 17, 19, 22, 28.
    52
    Find the median of 13, 7, 21, 16, 9, 25, 11.
    53
    The mean of 6 numbers is 14. Five numbers sum to 61. Find the sixth number.
    54
    A bag contains 5 red, 4 blue and 3 green counters. Find the probability of not selecting a blue counter.
    55
    A fair die is rolled. Find the probability of getting a prime number.
    56
    Two fair coins are tossed. Find the probability of getting exactly one head.
    57
    A shop sells 240 items in a week. Sales increase by 15% the following week. How many items are sold?
    58
    A tank is 3/5 full and contains 420 litres. Find its full capacity.
    59
    A number is multiplied by 5, then 12 is subtracted. The result is 83. Find the number.
    60
    A rectangular garden is 24 m long and 15 m wide. A path 1 m wide runs all around the outside. Find the area of the path.

    Made for learning and practice on ChildSocial.com · Cambridge-style primary maths revision (not an official exam paper).