Key Words in Maths Algebra Exams
Some questions in algebra exams use key words which tell students what is required.
simplify | expand | factorise | evaluate | solve | rearrange | sketch | label
Simplify
- Combine like terms (terms which have the same variables).
- Cancel common factors in fractions. This is easier to do when writing fractions with horizontal lines. (Remember that dividing by a number is the same as multiplying by its reciprocal.)
2xy - 3x + 2xy = 4xy -3x
4ab/2d ÷ 2a/d
= 4ab/2d × d/2a
= 4abd/4ad
= b
See simplifying for more information.
Expand
- Remove brackets.
- You should then simplify if required.
(2x + 3y)(5x - 4y)
= 10x2 - 8xy + 15xy - 12y2
= 10 x2 + 7xy - 12y2
See expanding for more information.
Factorise
- Convert to a product of factors (write it using brackets).
2x2 - 6x
= 2x(x - 3) |
4x2 - 16
4(x2 - 4)
4(x + 2)(x - 2) |
See Factorisation Algebra and Factorising Quadratic Equations for more information.
Evaluate
- Find the value of an expression (sometimes by substituting values in for variables in the expression).
- Not the same as solve.
Evaluate |z - x| where x = 6, z = -2
|-2 - 6| = |-8| = 8
√(26) = √(23 x 23) = 23 = 8
Solve
- Find possible values for the variable(s).
- Simultaneous equations will have two or more variables to be solved.
- May involve expanding (and simplifying) or factorising.
- Not the same as evaluate.
x2 + 12 = 7x
⇒ x2 - 7x + 12 = 0
(x - 3)(x - 4) = 0
⇒ x - 3 = 0 or x - 4 = 0
⇒ x = 3 or x = 4 |
(x - 4)/2 + (2x - 5)/3 = 1
⇒ 3(x - 4) + 2(2x - 5) = 6
⇒ 3x - 12 + 4x - 10 = 6
⇒ 7x - 22 = 6
⇒ 7x = 28
⇒ x = 4 |
See factorising quadratic equations for more information.
Rearrange
- Make a particular variable the subject of an equation.
- The variable ends up on one side of the equation and everything else is on the other side of the equation.
- The variable is said to be expressed in terms of everything else.
Rearrange to make t the subject in s = ½at2
t2 = 2s/a
t = √(2s/a)
Being good at rearranging equations is very useful in physics.
Sketch
- Draw a graph as neatly as possible.
- Perfect accuracy is not expected but key points should be accurate.
- There will likely be some known points or key points, such as where the graph intercepts the x and y axes, or the minimum/maximum point of a parabola.
- Often used with label.
Label
- Write the equation of a graphed line in a convenient location next to the line.
- Often used with sketch.
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