Algebra worksheet — GCSE Foundation

1.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

2.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

3.y = x + 10. Work out the value of y when x = 0.

4.Make a the subject of the formula b = 20 − a.

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

6.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

7.Which of these quadratic graphs does NOT cross the x-axis at all?

8.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

9.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

10.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

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

12.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.

13.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

14.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

15.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?