Algebra worksheet — GCSE Foundation

1.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?

2.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

3.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

4.The point A is at (5, −3). In which quadrant does A lie?

5.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

6.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

7.Write down the expression that means the same as w ÷ 6.

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

9.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

10.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

11.Which of these points lies in the first quadrant?

12.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

13.Which expression means 'y squared, multiplied by 3'?

14.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

15.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.