Algebra worksheet — GCSE Foundation

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

2.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

3.Expand and simplify 2(a + 6) − 2(a − 7)

4.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?

5.Solve 4x − (2x − 6) = 18

6.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

7.Work out the value of 2(x + 2) when x = −5

8.Make x the subject of the formula y = 4x − 3.

9.Which expression is equivalent to 3(2x − 5) + 4x?

10.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.

11.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

12.Write down the expression that means 5 more than half of n.

13.The formula for the energy stored in a stretched spring is E = (1/2)kx², where E is in joules, k is the spring constant in N/m and x is the extension in m. A spring with a spring constant of 40 N/m is stretched so that its extension is 0.3 m. Work out the energy stored in the spring.

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

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