Algebra worksheet — GCSE Foundation

1.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

2.Which of these is an equation, rather than an expression, a formula or an identity?

3.In which quadrant does the point (−3, 0.5) lie?

4.Which of these is a formula?

5.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

6.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

7.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

8.Work out the coordinates of the reflection of (6, −3) in the y-axis.

9.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.

10.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

11.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

12.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

13.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

14.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

15.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.