Algebra III
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33 Terms
What are natural numbers?
Positive whole numbers
Symbol for natural numbers
N
How are natural numbers represented on a number line?
Dots on a number line
What are integers?
Positive and negative whole numbers
Symbol for integers
Z
How are integers represented on a number line?
Dots on a number line
What are rational numbers?
Fractions
Symbol of Rational numbers
Q
What are irrational numbers?
Numbers that cannot be written as a fraction e.g. surds. π
Symbol for irrational numbers
R/Q
What are real numbers?
All rational and irrational numbers
Symbol for real number
R
What does a full dot on a numberline mean?
Includes the whole number on the dot
What does a hollow dot on a numberline mean?
Does not include the whole number on the dot
When solving an equation with surds, what should you do?
Check the answer
How to solve inequalities
Treat inequality sign as an equal sign and solve for x
What happens when you divide an inequality by a negative number
Sign should point to other side
How to solve double inequalities e.g. 3 > x-2 >-5
Split them into two separate equations with the middle in both e.g. 3> x-2. x-2>-5
> means …
Above the x-axis
≥ means …
On or above the x-axis
< means ..
Below the x-axis
≤ means …
On or below the x-axis
How to cancel algebraic fractions in an inequality?
Multiply both sides by the denominator squared
What is the absolute value/modulus?
The distance of a real number away from zero on the number line
Modulus/absolute value is …
Always positive
How to cancel out modulus?
Square it and square it out
How to cancel a square root?
Square other terms, but terms in the square root don’t change
When a number is outside of a modulus bracket, what happens when you try solve it?
It also gets squared
What proof is used for inequalities? e.g. p2 +1 ≥ 2p
(real)2 ≥ 0
what is the discriminant? What does it do?
b2-4ac. Determines whether the graph cuts, touches, or doesn’t cut the x-axis
What does it mean when the discriminant is greater than zero? (2)
Cuts the x-axis. 2 real different roots
What does it mean when the discriminant is equal to zero? (2)
Touches the x-axis. 2 real equal roots
What does it mean when the discriminant is less than zero? (2)
Doesn’t cut the x-axis. 2 non-real (imaginary) roots