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.
Non-calculator
Geometry and measures worksheet — GCSE Foundation
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- 1.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.
- 2.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?
- 3.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.
- 4.A circle has centre O. Radii OA and OB are drawn, together with the arc AB, enclosing a sector. The straight chord AB is also drawn. Write down the name of the region enclosed between the chord AB and the arc AB.
- 5.A circular coin has a diameter of 3 cm. Work out the circumference of the coin. Give your answer in terms of π.
- 6.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?
- 7.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?
- 8.u is the column vector with top number 5 and bottom number 1. v is the column vector with top number 2 and bottom number 4. Work out u − v, giving your answer as a column vector in the form (top, bottom).
- 9.After a translation by the vector , a point lands on (4, 1). Write down the coordinates of the point before the translation.
- 10.A solid cylinder is lying on its curved side on a table, with its circular ends facing left and right. What shape is its plan view, looking down from above?
- 11.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.
- 12.Work out the exact value of sin 30° + cos 60°.
- 13.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.
- 14.The column vector r has top number 2 and bottom number 6. Which of these column vectors is parallel to r?
- 15.Triangle LMN has a right angle at M, with hypotenuse LN = 15 cm and LM = 9 cm. Triangle PQR has a right angle at Q, with hypotenuse PR = 15 cm and PQ = 9 cm. Which condition proves the two triangles are congruent?
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