Algebra worksheet — GCSE Foundation

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

2.Which expression means the same as 3 × a × b?

3.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

4.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

5.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

6.Solve x² = 49.

7.Make m the subject of the formula w = m − 8.

8.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?

9.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

10.Which of these values of x is a solution of x² + 2x − 15 = 0?

11.Write down the gradient of the line with equation y = −x + 3.

12.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

13.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

14.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.

15.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.