Definitions
What is a coefficient?
It is the number placed directly in front of (and multiplied by) a letter or symbol.
Simplify: 3x + 5x
8x
Expand 3(x + 2)
3x+6
Solve x + 6 = 13
x=7
Write an expression for: 5 more than x
x+5 OR 5+x
The difference between and expression and equation?
An equation states that two mathematical expressions are equal (indicated by an equal sign), whereas an expression is simply a mathematical phrase representing a value.
Simplify: 4y + 6 + 3y
7y + 6
Expand 5(a - 1)
5a - 5
Solve 2x = 18
x=9
Double n take away 15
2n - 15
What is the mathematical operation represented when a number is directly next to a letter?
For example: 6x
Multiplication
Simplify: 8m - 5 + 2m + 9
10m + 4
Expand 2(3x + 4)
6x + 8
Solve x - 8 = 11
Twice a number, then add 7, square the result
(2x +7)2
What is the first index law? For example, x2 multiplied by x4
The first index law (or index law for multiplication) states that when you multiply two or more terms with the same base, you keep the base the same and add their exponents (indices) together.
12x2 + 4 - 7x2 - 9 - x0
5x2 -5 - 1 =5x2 -6
Expand and simplify: 4y(2y - 3) + 7y
8y2- 12y+7y = 8y2- 5y
Solve 3x + 4 = 19
x = 5
A gym charges a $20 joining fee and $15 per week. Write an expression for the total cost after w weeks.
15w+20
What is Algebra?
A branch of maths that uses symbols and letters (like x, y, or z), to represent unknown numbers and quantities.
A way of representing relationships and rules.
6x2 + 8xy -7x2- 2x(x +2y)
-3x2 +6xy
Expand 3(2m + 5) + 4(3x +2)
6m+15 + 12x+8
= 6m +12x + 23
5(x - 2) = 30
x = 8
A batsman scores 4 runs every time they hit a boundary. If they hit b boundaries and also score 15 runs by running between the wickets, write an expression for their total runs.
4b+15