Geometry and measures worksheet — GCSE Foundation

1.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

2.A solid has 5 faces, 9 edges and 6 vertices. Two of its faces are triangles and the other three are rectangles. Which solid is it?

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

4.Shape S has an area of 48 cm². It is enlarged by a scale factor of 1/4 to give shape T. Work out the area of shape T.

5.In an isosceles triangle each of the two base angles is 46°. Work out the size of the angle at the apex.

6.A jug holds 750 ml of water. Work out what fraction of a litre this is.

7.A garden shed is shaped like a triangular prism: two identical vertical triangular end walls (the gable ends), joined by a sloping rectangular roof and a vertical rectangular back wall. Looking at the shed from directly above (the plan view), what shape is seen?

8.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

9.Two similar flags have widths in the ratio 2 : 5. The width of the smaller flag is 8 cm. Work out the width of the larger flag.

10.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 4. Work out a + b, giving your answer as a column vector in the form (top, bottom).

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

12.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?

13.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.

14.A radar station is at the origin of a grid, where each unit represents 1 km. A boat is detected at the point (7, 24). Work out the boat's distance from the station, then work out how many hours it will take the boat to reach the station travelling directly towards it at 5 km per hour.

15.Triangle ABC and triangle DEF both contain a right angle, at B and E respectively, and the hypotenuses AC and DF are equal in length. Which extra fact would prove the triangles are congruent by RHS?