Algebra worksheet — GCSE Foundation

1.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

2.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

3.Work out the value of (x − 4)/2 + 3 when x = 10

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

5.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

6.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

7.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

8.Expand 4(2x − 3).

9.Which of these is a factor of 15x + 20?

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

11.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

12.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

13.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

14.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

15.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.