A
Example: y = x2
• x is an Independent Variable
• y is the Dependent Variable
y is 4 if we put in x=2
y is 9 if we put in x=3
dependent variable
The "Multiplicative Identity" is 1, because multiplying a number by 1 leaves it unchanged:
a × 1 = 1 × a = a
multiplicative identity
The result of multiplying an integer (not a fraction) by itself.
Example: 4 × 4 = 16, so 16 is a square number.
Here are the first few square numbers:
0 (=0×0)
1 (=1×1)
4 (=2×2)
9 (=3×3)
16 (=4×4)
25 (=5×5)
Square number
Finding what to multiply to get an expression. (Called Factorizing in British English.)
Example: 2y+6 = 2(y+3),
so the factors of 2y+6 are: 2 and (y+3)
factoring
In Algebra a term is either a single number or variable, or numbers and variables multiplied together.
Terms are separated by + or − signs, or sometimes by divide.
term
The result of multiplying a whole number by itself twice.
Example: 3 × 3 × 3 = 27, so 27 is a cube number.
The whole number is used three times, just like the sides of a cube.
Here are the first few cube numbers:
1 (=1×1×1)
8 (=2×2×2)
27 (=3×3×3)
64 (=4×4×4)
125 (=5×5×5)
cube number
Example: 3 × (2 + 4) = 3×2 + 3×4
So the "3" can be "distributed" across the "2+4" into 3 times 2 and 3 times 4.
distributive law
The "Additive Identity" is 0, because adding 0 to a number does not change it:
a + 0 = 0 + a = a
additive identity
A symbol for a value we don't know yet. It is usually a letter like x or y.
Example: in x + 2 = 6, x is the variable.
Why "variable" when it may have just one value? In the case of x + 2 = 6 we can solve it to find that x = 4. But in something like y = x + 2 (a linear equation) x can have many values. In general it is much easier to always call it a variable even though in some cases it is a single value.
variable
How much there is of something.
Example: What is the quantity of rice?
• We can say "a handful"
• Or use a measuring cup and say "40 milliliters"
• Or we can count them and say "1562"
quantity
A number used to multiply a variable.
Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient.
Variables with no number have a coefficient of 1.
Example: x is really 1x.
Sometimes a letter stands in for the number.
Example: In ax2 + bx + c, "x" is a variable, and "a" and "b" are coefficients.
coefficient
An "input" value of a function.
Example: y = x2
• x is an Independent Variable
• y is the Dependent Variable
Example: h = 2w + d
• w is an Independent Variable
• d is an Independent Variable
• h is the Dependent Variable
independent variable
A value, or values, we can put in place of a variable (such as x) that makes the equation true.
Example: x + 2 = 7
When we put 5 in place of x we get: 5 + 2 = 7
5 + 2 = 7 is true, so x = 5 is a solution
solution
The exponent of a number says how many times to use that number in a multiplication.
It is written as a small number to the right and above the base number.
In this example: 82 = 8 × 8 = 64
(The exponent "2" says to use the 8 two times in a multiplication.)
Another example: 53 = 5 × 5 × 5 = 125
(The exponent "3" says to use the 5 three times in a multiplication.
exponent
The power (or exponent) of a number says how many times to use the number in a multiplication.
It is written as a small number to the right and above the base number.
In this example the little "2" says to use 8 two times in a multiplication:
82 = 8 × 8 = 64
But power can also mean the result of using an exponent, so in the previous example "64" is also called the power.
Another example: 24 = 2 × 2 × 2 × 2 = 16
• the power is 4: "2 to the power 4 is 16"
• or we can say the power is the result of 16: "the 4th power of 2 is 16"
power