Printable · GCSE Higher · ages 14-16
Geometry and measures worksheet — GCSE Higher
Fifteen questions across the geometry and measures statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
Geometry and measures worksheet — GCSE Higher
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- 1.Point Q has coordinates (3, 5). It is translated by the vector (1, −2), and the image is then enlarged by scale factor 3, centre the origin. Work out the coordinates of the final image of Q.
- 2.In a construction, a point P is marked at the foot of the perpendicular drawn from point X to a straight line. Which statement correctly compares the distance XP with the distance from X to any other point on the line?
- 3.Which of these correctly compares a 'line' with a 'line segment'?
- 4.A circle has a radius of 1 cm. Work out the circumference of the circle. Give your answer in terms of π.
- 5.Triangle ABC and triangle DEF both contain a right angle, at B and E respectively, and the hypotenuses AC and DF are equal in length. Which extra fact would prove the triangles are congruent by RHS?
- 6.Each of these has an exact value. Write down the one whose value is the greatest.
- 7.Lines JK and LM are parallel. A straight line crosses JK at point P and crosses LM at point Q. Angle KPQ = 118°. Angle KPQ and angle MQP are co-interior (allied) angles. Work out angle MQP.
- 8.A rotation of 180° about the point (3, 2) can be written as a reflection in the line x = 3, followed by a reflection in a second line, for every point in the plane. Which line is the second line?
- 9.A shop sells rice in packs of 250 g. Aisha buys 4 packs. Work out the total mass of rice she buys, in kilograms.
- 10.A sector of a circle has an angle of 90° and an area of 78.5 cm². Using π = 3.14, work out the radius of the circle.
- 11.Point P(2, 5) is enlarged with centre (2, 1) to give image point P′(2, −7). Work out the scale factor of the enlargement.
- 12.In triangle ABC, AB = 6 cm, AC = 8 cm and angle BAC = 60°. Work out the exact area of triangle ABC, giving your answer in the form .
- 13.Point P has coordinates (2, 1). Transformation A reflects a point in the x-axis. Transformation B translates a point by the vector (0, 4). Work out the coordinates of the image of P when A is applied first, followed by B.
- 14.A round cake has a radius of 10 cm. Icing costs £0.02 per square centimetre. One slice of the cake is a sector with an angle of 90°. Using π = 3.14, work out the cost of icing the top of that slice, to the nearest penny.
- 15.In triangle ABC, angle BAC = 42°, angle ABC = 63° and BC = 8.4 cm. Work out the length of AC. Give your answer to 1 decimal place.
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