Algebra worksheet — GCSE Higher

1.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

2.Which expression means 'triple c, then add double d'?

3.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

4.Describe a sequence of two transformations that maps the graph of y = x² onto the graph of y = −(x − 5)².

5.A student attempts to prove that the sum of any three consecutive integers is a multiple of 3. Line 1: Let the three consecutive integers be n, n + 1 and n + 2. Line 2: Their sum is n + (n + 1) + (n + 2) = 3n + 2. Line 3: 3n + 2 leaves a remainder of 2 when divided by 3, so it is not a multiple of 3. Line 4: So the sum of three consecutive integers is not always a multiple of 3. Which line contains the FIRST error?

6.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.

7.Describe the single transformation that maps the graph of y = x² onto the graph of y = x² + 3.

8.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.

9.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

10.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

11.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.

12.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

13.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

14.Work out the value of a² − 2b when a = −3 and b = 4.

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