Algebra worksheet — GCSE Foundation

1.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

2.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

3.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

4.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

5.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

6.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

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

8.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

9.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

10.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

11.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.

12.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

13.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.

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

15.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.