Printable · GCSE Foundation · ages 14-16

Geometry and measures worksheet — GCSE Foundation

Fifteen questions across the geometry and measures statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Geometry and measures worksheet — GCSE Foundation

Maths · GCSE Foundation · Geometry and measures · 15 questions

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1.In the RHS congruence condition, which three facts must be true about two triangles for RHS to prove they are congruent?
(a)Two sides and the angle between them
(b)Right angle, equal hypotenuse, one more side
(c)Right angle and all three sides equal
(d)Right angle, hypotenuse, one more angle
2.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.
(a)125 g
(b)1025 g
(c)1000 g
(d)1250 g
3.A quadrilateral has both pairs of opposite sides parallel and equal in length, but none of its angles are right angles. Which statement about this quadrilateral is correct?
(a)It is a trapezium
(b)It must be a rhombus
(c)It is a parallelogram but not a rectangle
(d)It must be a rectangle
4.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.
(a)tan θ = adjacent/opposite
(b)cos θ = opposite/adjacent
(c)tan θ = opposite/adjacent
(d)sin θ = opposite/adjacent
5.Line 1 passes through (0, 1) and (2, 5). Line 2 passes through (3, 2) and (5, 6). Work out the gradient of each line. Then write down whether the two lines are parallel.
(a)Parallel, since both gradients are 2
(b)Not parallel, since the gradients are 2 and 4
(c)Parallel, since both lines pass through positive coordinates
(d)Not parallel, since the two lines cross the y-axis at different points
6.A footpath is 3750 m long. Work out this distance in kilometres.
(a)3.75 km
(b)0.375 km
(c)37.5 km
(d)375 km
7.A circular clock face has a radius of 9 cm. Work out the circumference of the clock face. Use π = 3.14. Give your answer to 1 decimal place.
(a)28.3 cm
(b)254.3 cm
(c)113.0 cm
(d)56.5 cm
8.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?
(a)080°
(b)100°
(c)180°
(d)440°
9.Vector A is $(- 5 2)$ and vector B is $(5 - 2)$ . Write down how vector B compares to vector A.
(a)B is the same as A
(b)B is unrelated to A in direction
(c)B is twice A
(d)B is the reverse of A
10.A flagpole is 12 m tall. Freya stands 9 m from the base of the flagpole on level ground. Work out the angle of elevation of the top of the flagpole from where Freya stands. Give your answer correct to 1 decimal place.
(a)41.4°
(b)53.1°
(c)48.6°
(d)36.9°
11.A wooden block is a cuboid measuring 2 cm by 10 cm by 15 cm. Work out the volume of the block.
(a)27 cm³
(b)400 cm²
(c)150 cm³
(d)300 cm³
12.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?
(a)No — hexagons can't be regular
(b)Yes — six equal sides means regular
(c)Yes — all sides are equal
(d)No — angles must be equal too
13.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.
(a)49°
(b)41°
(c)82°
(d)98°
14.A circle has centre O. PQ, RS and TU are three chords of the circle, and only one of them passes through O. Write down what this tells you about that chord.
(a)It is the same length as the other two chords
(b)It is the longest of the three chords
(c)It is the shortest of the three chords
(d)It is half the length of each of the other two chords
15.The diagram shows the plan, front elevation and side elevation of a solid. Which of these solids matches all three views?
(a)A triangle-based pyramid standing on its triangular base
(b)A triangular prism standing on its triangular end
(c)A cuboid standing on a rectangular face
(d)A triangular prism lying on one of its rectangular faces

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