Geometry and measures worksheet — GCSE Higher

1.A solid is built from centimetre cubes standing on a table. Seen from the front, the left-hand column is 2 cubes high, the middle column is 2 cubes high and the right-hand column is 1 cube high. Work out how many squares make up the front elevation.

2.m is the column vector with top number 4 and bottom number 6. n is the column vector with top number −6 and bottom number −9. Given that n = k × m for some number k, work out the value of k.

3.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).

4.A shape is reflected in the x-axis and the image is then reflected in the y-axis. Which single transformation is equivalent to this combination for every point?

5.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.

6.Two traffic cones are geometrically similar. The smaller cone has height 6 m and the larger cone has height 9 m. Work out the ratio of the volume of the smaller cone to the volume of the larger cone, giving your answer in the form a : b in its simplest form.

7.An enlargement has a scale factor of −2. Priti says the image must be a mirror image of the original shape. Is Priti correct?

8.From an external point P, two tangents PA and PB touch a circle with centre O at the points A and B. Angle APB = 46°. C is a point on the major arc AB, the arc on the opposite side of AB from P. Work out the size of angle ACB.

9.Shape S has a vertex at (9, 6). It is enlarged by a scale factor of 1/3, centre the origin. Work out the coordinates of the image of this vertex.

10.A, B and C are points on a circle with centre O. B is on the minor arc AC. Angle ABC = 100°. Work out the size of the non-reflex angle AOC.

11.A wooden cube has edges of length 4 cm. Work out the total surface area of the cube.

12.A quadrilateral has all four sides equal in length and all four interior angles equal to 90°. Its diagonals are equal in length and bisect each other at right angles. Which quadrilateral matches this description exactly?

13.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?

14.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

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