Algebra worksheet — GCSE Foundation

1.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

2.Solve 4x + 3 = 19

3.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.

4.Which expression is equivalent to 2(x + 6)?

5.How many turning points does the graph of y = x² − 7x + 10 have?

6.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.

7.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

8.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

9.Work out the value of 3b − 4 when b = 6

10.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

11.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

12.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

13.Factorise fully 12x² + 18x.

14.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

15.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.