Algebra worksheet — GCSE Higher

1.A distance-time graph is a straight line from (0, 0) to (4, 100), where time is in hours and distance is in kilometres. Work out the gradient of the line.

2.Work out the gradient of the straight line with equation y = (2x/5) − 3.

3.Describe the single transformation that maps the graph of y = x² onto the graph of y = x² + 3.

4.Work out the value of 2(x + 2) when x = −5

5.Work out the integer values of x that satisfy x² − 2x − 8 ≤ 0.

6.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

7.A rectangular lawn is 4 m longer than it is wide. Its area is 96 m². Work out the length of the lawn.

8.The point (−4, 3) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the equation of the tangent to the circle at (−4, 3), giving your answer in the form y = mx + c.

9.The point (9, 12) lies on the circle x² + y² = 225, which has centre (0, 0). The tangent to the circle at (9, 12) crosses the x-axis at the point P. Work out the x-coordinate of P.

10.Simplify (5x² + 3x − 2) − (2x² − x + 5)

11.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

12.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.

13.A student attempts to prove that the product of two consecutive integers is always even: (i) Let the two consecutive integers be n and n + 1. (ii) Since n(n + 1) is even, one of n and n + 1 must be an even number. (iii) Therefore, n(n + 1) is even. At which statement does the proof first assume the very fact it is trying to prove?

14.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

15.Solve the simultaneous equations y = 3 − x and x² + y² = 9, giving both pairs of solutions.