Algebra worksheet — GCSE Foundation

1.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

2.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.

3.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

4.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

5.Solve x² − 2x − 24 = 0.

6.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

7.Which of these is an identity?

8.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

9.Work out the value of 5y + 9 when y = 0

10.Which expression is equivalent to 6x − (2x − 5)?

11.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.

12.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

13.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

14.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

15.Write down the coefficient of p in the expression 7 − 4p + 9q.