Algebra worksheet — GCSE Higher

1.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = f(x) − 6 crosses the y-axis.

2.Which line of algebra shows that the sum of two consecutive odd numbers is always a multiple of 4?

3.Work out the gradient of a line that is perpendicular to the line with equation 2x + 3y = 6.

4.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

5.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

6.Solve 5(x + 3) = 40

7.The graph of y = f(x) has x-intercepts at x = −1 and x = 4. Which statement correctly describes the x-intercepts of y = f(2 − x)?

8.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

9.Expand and simplify (x − 3)²

10.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

11.The point (3, 6) lies on the circle x² + y² = 45. The tangent to the circle at (3, 6) crosses the x-axis at the point P. Work out the coordinates of P.

12.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

13.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

14.The equation x² − 4x + k = 0 has two different real solutions. Work out the range of values of k.

15.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.