Geometry and measures worksheet — GCSE Higher

1.A tangent touches a circle with centre O at the point P. Q is a point on the tangent. Write down the circle fact that tells you the size of angle OPQ.

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.From an external point P, two tangents PA and PB touch a circle with centre O at the points A and B. Angle APB = 50°. Work out the size of angle OAB.

4.A vertical line passes through the point (5, 2). Write down the equation of this line.

5.A, B, C and D are points on a circle with centre O, in that order around the circle. B lies on the major arc AC, and angle AOC = 152°. In triangle ACD, angle ACD = 30°. Work out the size of angle DAC.

7.A quadrilateral has two pairs of parallel sides. All four of its interior angles are right angles, but its sides are not all the same length. Which quadrilateral is this?

8.To prove that the angle at the centre is twice the angle at the circumference, a student draws radii OA and OC, where A and C are points on the circle and O is the centre. The student's first step is: 'Since OA = OC, both being radii of the circle, triangle OAC is isosceles, so angle OAC = angle OCA.' Is this first step correct?

9.Two similar ponds have perimeters in the ratio 4 : 11. The perimeter of the larger pond is 88 m. Work out the perimeter of the smaller pond.

10.A quadrilateral has vertices A(1, 1), B(5, 1), C(6, 4) and D(2, 4). By comparing the y-coordinates of A, B and of D, C, write down whether the sides AB and DC are parallel, and give a reason for your answer.

11.Two triangles are proved congruent using the ASA condition. What can be concluded about the two remaining pairs of corresponding sides that were not part of the original ASA facts?

12.A, B and C are points on a circle with centre O, and AC is a diameter of the circle. Work out the size of angle ABC.

13.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?

14.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

15.A shopkeeper builds a display from two cuboid boxes, shown in the diagram. She wants to cover the front of the display with coloured paper. Work out the total area of the front elevation, in square centimetres.