Algebra worksheet — GCSE Foundation

1.Solve 5x − 9 = 16

2.y = 5 − 2x. Work out the value of x when y = 11.

3.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.

4.A number machine multiplies its input by 3. The output is 15. Work out the input.

5.Write down the number of terms in the expression 4x² − 7x + 3.

6.Expand 4(2x − 3).

7.Work out the distance of the point (−6, 4) from the x-axis.

8.Which expression is equivalent to 0.5(4x + 6) − x?

9.Which expression is equivalent to 7x − 3(2x − 6)?

10.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.

11.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

12.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.

13.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

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.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.