Algebra worksheet — GCSE Foundation

1.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.

2.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

3.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

4.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?

5.y = 3x − 2. Work out the value of y when x = 4.

6.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

7.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

8.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

9.Which expression means the same as a × a × a?

10.Write down the expression that means 5 more than half of n.

11.A vertical line passes through the point (4, 7). Write down the equation of this line.

12.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

13.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

14.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

15.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.