Algebra worksheet — GCSE Higher

1.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

2.The 2nd term of a geometric sequence is 6 and the 4th term is 24. Given that all the terms of the sequence are positive, work out the common ratio.

3.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

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.Solve 7x − 5 = 3x + 11

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

7.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

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

9.Simplify 5a/6 − a/3

10.Simplify fully: (x + 2)/(3x) × 6x²/(x² − 4)

11.A circle has centre (0, 0) and passes through the point (7, 24). Work out the equation of the circle.

12.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

13.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

14.Write down the gradient of the line with equation y = −x + 3.

15.The curve y = −x² + 6x − 5 has a maximum point. Use completing the square to find its coordinates.