Algebra worksheet — GCSE Foundation

1.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

2.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

3.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

4.n = 3. Work out the value of (2n)².

5.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

6.Solve 3x − 5 = 4.

7.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.

8.Work out the value of 2(x + 2) when x = −5

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

10.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

11.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

12.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

13.Write down the expression that means the same as m × m × m × n.

14.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

15.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.