Geometry and measures worksheet — GCSE Foundation

1.Write down the exact value of tan 45°.

2.A scale drawing of a rectangular lawn uses a scale of 1 : 125. On the drawing, the lawn measures 4 cm by 2.4 cm. Work out the perimeter of the real lawn, in metres.

3.A tangent to a circle with centre O touches the circle at point P, where OP = 5 cm. Point Q lies on the tangent so that PQ = 12 cm. Using the fact that a tangent is perpendicular to the radius at the point of contact, work out the length OQ.

4.In this question, a curved surface counts as a face. How many faces does a sphere have?

5.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

6.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

7.A bearing is described as being exactly halfway between north and east, measured clockwise. What is the three-figure bearing?

8.p is the column vector with top number 2 and bottom number 3. q is the column vector with top number −1 and bottom number 4. Work out 2p + q, giving your answer as a column vector in the form (top, bottom).

9.A cable supporting a flagpole is anchored to the ground 5 m from the base of the pole. The cable makes an angle of 60° with the ground. Using the exact value of tan 60°, work out the exact height of the flagpole.

10.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

11.p is the column vector with top number 4 and bottom number −3. Work out 2p, giving your answer as a column vector in the form (top, bottom).

12.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.

13.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?

14.Point E is at (4, 2). It is rotated 180° about the point (1, 1). Work out the coordinates of the image of point E.

15.A parallelogram has a base of 20 cm and a sloping side of 13 cm. The perpendicular drawn from the top of that sloping side down to the base meets the base 5 cm from the foot of the sloping side, so the perpendicular, the 5 cm and the 13 cm sloping side form a right-angled triangle. Work out the area of the parallelogram.