Algebra worksheet — GCSE Higher

1.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.

2.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

3.Solve 5x² − 15x = 0.

4.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

5.Which of these equations is equivalent to 5x − 2 = 3x + 8?

6.Solve 3(2x − 1) = 27

7.Work out the gradient of the straight line with equation 3y = 12 − 6x.

8.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

9.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

10.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

11.Work out the coordinates of the reflection of (6, −3) in the y-axis.

12.The graph of y = f(x) crosses the x-axis at x = −3 and x = 7, and crosses the y-axis at (0, 21). A second graph crosses the x-axis at x = −7 and x = 3, and crosses the y-axis at the same point, (0, 21). The second graph is y = g(x). Which of these could be the equation of g(x)?

13.The area under a speed-time graph between t = 0 and t = 6 seconds is estimated using three strips of equal width, using the speeds, in m/s, at t = 0, 2, 4 and 6: 0, 5, 9 and 12. Using the trapezium rule with these three trapezia, estimate the distance travelled.

14.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.

15.The point A(−6, 8) lies on the circle x² + y² = 100, whose centre is the origin O. The tangent to the circle at A crosses the y-axis at the point B. Work out the length of OB.