Algebra worksheet — GCSE Foundation

1.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

2.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

3.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

4.Mia buys 3 identical notebooks and a pen costing £1.50. She pays a total of £9.90. Form an equation using n for the cost of one notebook, and solve it to find n.

5.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

6.Write down the expression that means the same as m × m × m × n.

7.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?

8.Solve 5(x + 3) = 40

9.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.

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

11.Solve x² = 49.

12.Solve 2(x + 3) = 10

13.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.

14.a = 3 and b = 5. Work out the value of a²b.

15.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?