Geometry and measures worksheet — GCSE Foundation

1.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.

2.A ramp's sloped surface crosses two horizontal parallel rails. At the top rail, the angle between the ramp and the rail on the right of the ramp is (3x + 10)°. At the bottom rail, the angle between the ramp and the rail on the left of the ramp is (5x − 30)°. Work out the value of x.

3.Triangle ABC has AB = (2x + 3) cm, BC = 11 cm and angle B = 90°. Triangle DEF has DE = 13 cm, EF = 11 cm and angle E = 90°. Given that the two triangles are congruent by SAS, work out the value of x.

4.In quadrilateral ABCD, side AB is parallel to side DC. Which statement correctly uses geometric notation to show this?

5.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.

6.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.

7.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

8.The bearing of a campsite B from a walker's position A is 070°. What is the bearing of A from B?

9.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?

10.To construct a perpendicular to a line at a given point P on the line, compasses are first opened to draw two arcs crossing the line, one on each side of P. What is the correct next step?

11.The diagram shows the plan of the base layer of a solid built from identical cubes. A second layer of cubes is added on top, filling the entire base layer to a height of 2 cubes everywhere. Work out how many squares are visible in the plan view of this solid.

12.A polygon has one more side than a heptagon. What is the polygon called?

13.Write down the column vector, from the options given, that would move a point to the right and downwards.

14.Write down the exact value of cos 30°.

15.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?