Algebra worksheet — GCSE Foundation

1.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

2.Solve 2x − 2 = 2

3.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

4.Work out the gradient of the straight line with equation 3y = 12 − 6x.

5.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

6.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

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

8.Which of these equations describes a vertical line?

9.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

10.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

11.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.

12.Simplify k + k + k + k + k.

13.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

14.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

15.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.