Expression: any arrangement of: letter symbols; numbers; +, -, x and ÷ signs; powers; and brackets. eg 2a(8b2-4cq)
Equation: A statement asserting the equality of two expressions, containing symbols that are separated into left and right sides and joined by an equal sign. eg 2p + 3q = 49
Formula: An equation that desribes a rule concerning the real-life behaviour of something. eg Boyles Law in Physics PV = k
Identity: A connection between expressions that remains true whatever the values of the letter symbols.
Function: a relationship between two sets of values such that a value from the first set maps on to a unique value in the second set.
Shorthand way of writing down a multiplication in algebraic expressions: eg m x n can be written as mn and ap x aq can be written as apaq. ie. the times sign (x) can be left out.
| Multiplication and division | ap x aq = ap+q |
| ap ÷ aq = ap-q | |
| Brackets | (ap)q = apxq |
| Zero index | a0 = 1 (and remember a1 = a) |
| Reciprocal index | 1/ap = a-p |
Note: ap + aq does NOT equal ap+q. It can’t be simplified any more.
Problems to solve:
Simplify:
Square root of a8
Square root of a2b4
80
(85)0
(x5)0
(x3y7)0
41
(x5)1
(55)1
(x3y7)
(6-4) ÷ (6-2)
(x-4) ÷ (x-2)
(9-374) ÷ (9-272)
(x-3y4) ÷ (x-2y2)