Algebra worksheet — GCSE Foundation

1.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

2.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.

3.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?

4.Which of these equations is equivalent to 5x − 2 = 3x + 8?

5.Which expression means 'triple c, then add double d'?

6.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

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

8.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

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

10.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

11.A photo printing service has two adverts for its price. Advert A: cost in pounds = 3(2n + 4) for n photos. Advert B: cost in pounds = 6n + 12. A customer says the two adverts always charge the same amount. Is the customer correct?

12.Solve the inequality x + 5 < 12.

13.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

14.Solve the inequality 3x − 1 ≤ 11.

15.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.