Geometry and measures worksheet — GCSE Higher

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

2.Shape S is enlarged by scale factor −1, centre (0, 0). Which single transformation has the same overall effect as this enlargement, for every point?

3.AT is a diameter of a circle with centre O. PT is a tangent to the circle at the point T, and P is a point on this tangent such that A, T and P form a triangle. Angle PAT = 28°. Work out the size of angle APT.

4.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.

5.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

6.A solid has 6 faces: one pentagon and five triangles that all meet at a single point above the pentagon. What is the name of this solid?

7.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

8.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″.

9.A cuboid has length 3 cm, width 4 cm and height 12 cm. Work out the length of the diagonal that runs from one corner of the cuboid to the opposite corner.

10.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.

11.A rotation of 200° clockwise about the origin is applied, and the image is then rotated 250° anticlockwise about the origin. Work out the single angle of rotation, measured clockwise and between 0° and 360°, that has the same overall effect as the two rotations combined.

12.A textbook contains the instruction 'Draw AB' and, on the next line, the statement 'AB = 5 cm'. Which statement about the notation AB is correct?

13.A drinks company sells a novelty giant bottle that is geometrically similar to its standard 500 ml bottle, scaled up by a length factor of 1.5. Work out the capacity of the giant bottle, in ml.

14.Work out the exact value of sin 30° + cos 60°.

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