Geometry and measures worksheet — GCSE Foundation

1.Work out the exact value of (sin 30°)² + (cos 30°)².

2.Triangle ABC is translated by the column vector with top number 3 and bottom number −5 to form triangle A′B′C′. Triangle A′B′C′ is then translated by the column vector with top number −7 and bottom number 2 to form triangle A″B″C″. Work out the single column vector that translates triangle ABC directly to triangle A″B″C″.

3.A perpendicular bisector is drawn through the midpoint of a line segment AB. Which set of points does this construction show?

4.A locus consists of all the points that are the same perpendicular distance from two parallel lines 6 cm apart. Describe this locus.

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

6.a is the column vector with top number 3 and bottom number −2. Work out 4a, giving your answer as a column vector in the form (top, bottom).

7.A line segment joins two points on the circumference of a circle, without necessarily passing through the centre. Write down the general term for this line segment.

8.Work out the exact value of sin 45° × cos 45°.

9.Triangles ABE and CDE share the vertex E, where lines AC and BD cross at E. AE equals CE, and BE equals DE. Angle AEB and angle CED are formed as vertically opposite angles where the lines cross. Which condition proves that triangle ABE is congruent to triangle CDE?

10.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.

11.How many edges does a cube have?

12.A student draws a net using 5 identical squares arranged in a row of four with one extra square attached to the side of one of them. Can this net be folded to make a closed cube?

13.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

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