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Key Words in Maths Algebra Exams

Some questions in algebra exams use key words which tell students what is required.

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.

2xy - 3x + 2xy = 4xy -3x

4ab/2d ÷ 2a/d
= 4ab/2d x 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.