Algebra worksheet — GCSE Foundation

1.Which expression means 'add 3 to n, then multiply the result by 4'?

2.Solve the inequality 4x + 1 > 2x + 9.

3.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

4.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

5.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

6.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

7.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

8.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.

9.Which expression is equivalent to 4(x − 2) + 10?

10.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

11.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

12.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

13.a = 2 and b = 5. Work out the value of ab².

14.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

15.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.