Algebra problems
From words to an equation
- say what x is: "let Ben be x years old"
- write every quantity with x: Amira is x + 5, Chloe is 2x
- use the fact you are given: x + 5 + x + 2x = 41
- solve: 4x + 5 = 41, so 4x = 36 and x = 9
- 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.
When the algebra gives two answers
An area often gives a quadratic.
A rectangle (x + 2) by (x − 5) with area 18:
- (x + 2)(x − 5) = 18
- x² − 3x − 10 = 18, so x² − 3x − 28 = 0
- (x − 7)(x + 4) = 0, so x = 7 or x = −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.
Inequalities and sequences
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.
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