Algebra worksheet — GCSE Foundation

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

2.A square has sides of length y cm. Write down an expression for the perimeter of the square.

3.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

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

5.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

6.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.

7.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

8.Write down the gradient of the line with equation y = 7x − 2.

9.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

10.Solve the inequality 2(3x − 1) ≥ 4x + 8.

11.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.

12.Solve 4x − (2x − 6) = 18

13.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

14.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

15.y = 5 − 2x. Work out the value of x when y = 11.