Algebra worksheet — GCSE Foundation

1.The point B has coordinates (−2, −2). In which quadrant is B?

2.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

3.Make b the subject of the formula a = 5b.

4.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

5.The diagram shows the graph of a quadratic function. Which equation could it represent?

6.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

7.Which expression means 'add 3 to n, then multiply the result by 4'?

8.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

9.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

10.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

11.Which of these is a term, rather than a whole expression, an equation, or a formula?

12.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

13.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

14.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

15.Factorise x² − 3x − 10.