Algebra worksheet — GCSE Foundation

1.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

2.Which of these equations gives a straight-line graph when plotted?

3.Write down the gradient of the line with equation y = 6 + 4x.

4.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

5.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

6.Solve x² − 2x − 24 = 0.

7.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

8.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.

9.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.

10.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

11.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.

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

13.The point B has coordinates (−2, −2). In which quadrant is B?

14.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

15.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.