Algebra worksheet — GCSE Higher

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

2.Which of these rules generates the sequence 6, 11, 16, 21, …?

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

4.A car's speed, in m/s, during a journey is: 0 at t = 0 s, 8 at t = 4 s, and 8 (constant) from t = 4 s to t = 10 s, increasing at a constant rate between t = 0 and t = 4. Estimate the total distance the car travels, using the areas of a triangle and a rectangle.

5.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.

6.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

7.Which expression is equivalent to 3(2x − 5) + 4x?

8.p = 4. Work out the value of 2p³.

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

10.Work out the value of 3x² − 4x when x = −2.

11.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

12.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

13.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

14.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

15.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.