Algebra worksheet — GCSE Foundation

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

2.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

3.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

4.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

5.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

6.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

7.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

8.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.

9.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

10.Which expression is equivalent to 6x − (2x − 5)?

11.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

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

13.Solve x² + 7x = 0.

14.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

15.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.