Algebra worksheet — GCSE Foundation

1.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

2.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.

3.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

4.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

5.Work out the value of 5y + 9 when y = 0

6.Simplify 2b − 1 + 2b − 4 + 2b

7.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

8.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

9.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

10.Make x the subject of the formula y = 5x + 3.

11.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

12.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

13.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

14.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

15.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.