Geometry and measures worksheet — GCSE Foundation

1.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.

2.a is the column vector with top number 3 and bottom number −2. b is the column vector with top number −1 and bottom number 5. Work out 2a + b, giving your answer as a column vector in the form (top, bottom).

3.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.

4.Triangle ABC has AB = 5 cm and BC = 7 cm. Triangle DEF has DE = 5 cm and EF = 7 cm. Which extra fact would prove the triangles are congruent by SAS?

5.Vertex X of a triangle is at (−3, 5). After a translation, the image of X is at (2, −1). Write down the column vector of this translation.

6.The column vector r has top number 2 and bottom number 6. Which of these column vectors is parallel to r?

7.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

8.A builder props a straight plank against a vertical wall to reach a window ledge. The foot of the plank is 2.1 m from the base of the wall, and the plank is 3.5 m long. Work out how high up the wall the plank reaches.

9.Write down the exact value of cos 45°.

10.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.

11.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.

12.Write down the exact value of cos 60°.

13.A solid has one curved surface and two flat circular faces of equal size, one at each end. What is the name of this solid?

14.A warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?

15.The point A(2, 5) is translated to the point B(7, 3). Write down the column vector that describes this translation.