Algebra problems

1. say what x is: "let Ben be x years old"
2. write every quantity with x: Amira is x + 5, Chloe is 2x
3. use the fact you are given: x + 5 + x + 2x = 41
4. solve: 4x + 5 = 41, so 4x = 36 and x = 9
5. answer the question asked: Amira is 9 + 5 = 14

The usual slip: stopping at x. The question asked for Amira's age, or the area, or the largest angle, so finish the job.

An area often gives a quadratic. A rectangle (x + 2) by (x − 5) with area 18:

1. (x + 2)(x − 5) = 18
2. x² − 3x − 10 = 18, so x² − 3x − 28 = 0
3. (x − 7)(x + 4) = 0, so x = 7 or x = −4
4. x = −4 gives a width of −9 cm, which is impossible, so x = 7

Say why you reject a value: it earns the mark.

With an inequality, the answer is often the largest or smallest whole number that fits: x < 13.5 gives 13. For a sequence, find the nth term first, then set it greater than the target and solve for n; n must be a whole number, so round up.