Geometry and measures worksheet — GCSE Foundation

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

2.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.

3.Write down the term for the distance all the way around the edge of a circle.

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

5.Write down which one of these statements about quadrilaterals is true.

6.A dog is tied by a lead 4 m long to a fixed ring on a straight garden wall. The wall extends much further than the lead can reach in both directions, and the dog cannot cross through it. Describe the region the dog can reach.

7.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.

8.A cuboid measures 5 cm long (left to right), 3 cm deep (front to back) and 2 cm tall. Its front elevation is 5 cm wide by 2 cm high. Its side elevation is 3 cm wide by 2 cm high. What are the dimensions of its plan view, looking down from above?

9.A gardener wants to plant a tree so that it is the same distance from two straight garden walls that meet at a corner, and also the same distance from two ornamental posts standing 4 m apart. Which construction locates this point?

10.A construction for the perpendicular bisector of AB begins by opening a pair of compasses to more than half the length of AB, then drawing an arc centred at A. What is the next step?

12.Write down the name given to a triangle whose three sides are all the same length.

13.A zip-wire is fixed at an angle of 60° to the horizontal ground. The zip-wire is 12 m long. Using the exact value of cos 60°, work out the exact horizontal distance it covers.

14.A designer creates a repeating tile pattern. Each tile is translated from the one before it by the column vector with top number 4.5 and bottom number −2.5 (in centimetres). The first tile has its bottom-left corner at (1.5, 3). Work out the coordinates of the bottom-left corner of the third tile.

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?