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)
= 10x^{2}  8xy + 15xy  12y^{2}
= 10 x^{2} + 7xy  12y^{2}
See expanding for more information.
Factorise
 Convert to a product of factors (write it using brackets).
2x^{2}  6x
= 2x(x  3) 
4x^{2}  16
4(x^{2}  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
√(2^{6}) = √(2^{3} x 2^{3}) = 2^{3} = 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.
x^{2} + 12 = 7x
⇒ x^{2}  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 = ½at^{2}
t^{}^{2} = 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.
