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Grade 8 · Mathematics

Grade 8 Mathematics diagnostic

16 questions on arithmetic, percentages, algebra, powers & roots, coordinate geometry, geometry and statistics & probability, plus 2 from Grade 7. Answer what you can, then check your answers to see which topics are secure and what to practise next.

16 questions7 topicsAbout 20 minutesSet 4 of 5

Skip a question if you do not know the answer. It is better than guessing, because it shows what to practise.

1Arithmetic(-99) + 188 = ?
2Arithmetic4 + 4 × 2 = ?
3PercentagesA value increases from 550 to 632.5. What is the percentage increase?
%
4PercentagesA quantity starts at 6700, increases by 20%, then decreases by 10%. Find the final quantity.
5AlgebraFind the coefficient of x after simplifying 6x + 21x.
6Algebray = kx. When x = 8, y = 96. Find y when x = 81.
7Powers & rootsFind n: 8^8 × 8^8 = 8^n.
8Powers & roots3^5 = ?
9Coordinate geometryReflect (-17, -5) in x = 8. What is the new x-coordinate?
10Coordinate geometryRotate (-29, 14) 90° counterclockwise about the origin. Give the new x-coordinate.
11GeometryA trapezoid has parallel sides 30 cm and 15 cm and height 21 cm. Find its area in cm².
cm²
12GeometryA cylinder has radius 15 cm and height 31 cm. Its volume is kπ cm³. Find k.
13Statistics & probabilityA bag has 6 red and 13 blue counters. Draw twice, replacing the first counter. What is the probability both are red? Give a simplified fraction.

Give your answer as a fraction, for example 3/4.

14Statistics & probabilityData: 2, 9, 16, 23, 30, 37, 44, 51. Using medians of the lower four and upper four values, find the interquartile range.

From Grade 7

These questions check skills from the grade below, so gaps can be spotted early.

15Statistics & probability (Grade 7)Find the range of 5, 9, 9, 12.
16Fractions (Grade 7)7/39 − 3/39 = ?