Algebra worksheet — GCSE Higher

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

2.Expand and simplify (2x − 1)(x + 5)(x − 2). Write down the coefficient of x in your answer.

3.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

4.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

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

6.Simplify 2/(x + 1) + 3/(x − 2), giving your answer as a single fraction.

7.Which of these values of x is a solution of x² + 2x − 15 = 0?

8.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

9.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

10.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

11.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

12.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

13.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.

14.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

15.f(x) = x³ − 3x − 5. Given that f(2.2) = −0.952 and f(2.3) = 0.267, work out what this shows about the equation x³ − 3x − 5 = 0.