Algebra worksheet — GCSE Foundation

1.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

2.Expand 2(x − 13)

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.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

5.Factorise fully 5x + 5y − 5

6.Solve x² − 6x = 0.

7.x = 5. Work out the value of 3x² − 4.

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.Which expression is equivalent to 4(x − 2) + 10?

10.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

11.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.

12.Write down the expression that means the same as p + p + p + q.

13.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

14.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

15.Solve x² + 7x = 0.