Geometry and measures worksheet — GCSE Foundation

1.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?

2.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.

3.A designer enlarges a drawing of a model car for a poster. She first enlarges the drawing by a scale factor of 1.5, and then enlarges that result by a further scale factor of 2. On the original drawing, the position of a wheel relative to the front bumper is given by the column vector with top number 4 and bottom number −3, in centimetres. What is the corresponding column vector on the poster, in centimetres?

4.A builder lays a low wall made from identical bricks. The diagram shows the plan of the wall's footprint on a grid, where each square is one brick. The wall is built up to a height of 4 bricks everywhere. Work out the total number of bricks used.

5.Every point on a circle is exactly the same distance from one particular point. Write down the name of that point.

6.A sector of a circle has an angle of 150°. Work out what fraction of the circle's area the sector is.

7.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.

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

9.In a kite, one pair of opposite angles are equal in size. In kite WXYZ, angle X = 40° and angle Z = 100° are the two angles that are NOT equal to each other. The other two angles, W and Y, are equal to each other. Work out the size of angle W.

10.P is the point (3, 4) and Q is the point (6, 0). Work out the distance of each point from the origin, and write down which point is closer to the origin.

11.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.

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

13.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.

14.A square-based pyramid has a square base and four identical triangular sloping faces, with its apex directly above the centre of the base. How many planes of symmetry does it have?

15.Triangle ABC is right-angled at B. Triangle DEF is right-angled at E. AB = DE = 6 cm and AC = DF = 10 cm (AC and DF are the hypotenuses of their triangles). A student says this is not enough information to prove the triangles are congruent, because only two sides are given. Which reason shows the student is wrong?