Mathematics

Geometry and measures, Year 8: more practice

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AQAEdexcelKS3 groundwork for geometry and measures — what GCSE builds on at AQA and Edexcel.

Answer in your head, then tap to check. Slide or use the buttons to grade.

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

Answer in your head…A translation moves every point 4 left and 1 up. Point B ends at (0, 6). Where was B before the translation?

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★ KS3-MATH-GEO-0104Front

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

(4, 5)

HintReverse the movement: go back 4 right and 1 down.

The whyBefore the move B was 4 to the right and 1 lower: (0 + 4, 6 − 1) = (4, 5). Check: 4 left and 1 up from (4, 5) lands on (0, 6).

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Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

Answer in your head…What is the area of a parallelogram with base 3.5 m and perpendicular height 4 m?

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★ KS3-MATH-GEO-0105Front

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

14 m²

HintMultiply the base by the perpendicular height.

The why3.5 × 4 = 14, in square metres.

★ KS3-MATH-GEO-0105Back

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

Answer in your head…A trapezium has parallel sides of 6 cm and 10 cm, and the distance between them is 4 cm. What is its area?

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★ KS3-MATH-GEO-0106Front

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

32 cm²

HintFind the mean of the parallel sides, then multiply by the height.

The whyMean of the parallel sides is (6 + 10) ÷ 2 = 8, and 8 × 4 = 32 cm².

★ KS3-MATH-GEO-0106Back

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

Answer in your head…A trapezium has area 45 cm² and parallel sides of 7 cm and 11 cm. What is the height between them?

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★ KS3-MATH-GEO-0107Front

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

5 cm

HintWrite the area formula with h as the unknown, then solve.

The why45 = ½ × (7 + 11) × h = 9h, so h = 5. Check: ½ × 18 × 5 = 45.

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Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

Answer in your head…A circle has radius 4 cm. Find its circumference to 1 decimal place, using the π button.

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★ KS3-MATH-GEO-0108Front

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

25.1 cm

HintCircumference is π times the diameter, and the diameter is twice the radius.

The whyd = 8 cm, so C = π × 8 = 25.13… ≈ 25.1 cm.

★ KS3-MATH-GEO-0108Back

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

Answer in your head…Point (2, 1) is rotated 90° clockwise about the origin. Where does it land?

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★ KS3-MATH-GEO-0109Front

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

(1, −2)

HintPicture the point turning like a clock hand. It starts to the right of and above the origin and ends below.

The whyA 90° clockwise turn sends (x, y) to (y, −x). The point lands 1 right and 2 down, at (1, −2).

★ KS3-MATH-GEO-0109Back

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

Answer in your head…A 2 cm by 5 cm rectangle is enlarged by scale factor 4. What is the perimeter of the image?

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★ KS3-MATH-GEO-0110Front

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

56 cm

HintFind the new side lengths first.

The whyThe sides become 8 cm and 20 cm, so the perimeter is 2 × (8 + 20) = 56 cm. The original perimeter, 14 cm, is also multiplied by 4.

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Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

Answer in your head…A prism has a cross-section area of 12 cm² and is 9 cm long. What is its volume?

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★ KS3-MATH-GEO-0111Front

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

108 cm³

HintVolume of a prism = area of cross-section × length.

The why12 × 9 = 108, and the units are cubic because three lengths are multiplied.

★ KS3-MATH-GEO-0111Back

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

⌨ Type the answerAnswer in your head…A prism has volume 150 cm³ and length 6 cm. What is the area of its cross-section in cm²? (number only)

★ KS3-MATH-GEO-0112Front

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

25

HintWork backwards: volume = cross-section area × length.

The why150 ÷ 6 = 25. Check: 25 × 6 = 150.

★ KS3-MATH-GEO-0112Back

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

Answer in your head…Find the total surface area of a cuboid that is 2 cm by 3 cm by 4 cm.

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★ KS3-MATH-GEO-0113Front

Mathematics · Geometry and measures, Year 8: more practiceProfessor Pi

52 cm²

HintA cuboid has three pairs of identical faces.

The whyThe faces are 2 × 3 = 6, 2 × 4 = 8 and 3 × 4 = 12. The total is 2 × (6 + 8 + 12) = 52 cm².

★ KS3-MATH-GEO-0113Back

Geometry and measures, Year 8: more practice

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