Algebra worksheet — GCSE Foundation

1.Solve 3(2x − 1) = 27

2.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

3.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

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

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

6.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

7.Work out the value of 2x² when x = −3

8.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

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

10.Make c the subject of the formula k = 6c.

11.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

12.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

13.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

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

15.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?