Algebra 3

Question 1

Surd equations

Answer 1

Get the √ on its own on 1 side of the equation.
Square both sides => removing the √
Solve the resulting equation.

Question 2

Why do you check both solutions of the original surd equation

Answer 2

When squaring both sides an EXTRA root can be generated which does not satisfy the original equation.

Question 3

√9 =

Answer 3

3 not +/-3

Question 4

Natural Numbers

Answer 4

POSITIVE WHOLE numbers →N = {𝟏,𝟐,𝟑,𝟒…} DOTS.

Question 5

Integers

Answer 5

ANY WHOLE number, POSITIVE, NEGATIVE or ZERO →Z = {…−𝟑,−𝟐,−𝟏,𝟎,𝟏,𝟐…} DOTS.

Question 6

Real numbers

Answer 6

ANY number that can be PLOTTED on a Number line. THICK LINE.

Question 7

When does the inequality flip

Answer 7

when you multiply or divide by a negative number

Question 8

The lengths of any two sides in a triangle added together are always…

Answer 8

greater than the length of the third side.

Question 9

Quadratic inequalities

Answer 9

Temporarily rewrite the inequality as an equation.
Solve this quadratic equation.
Use a rough sketch to determine the range of values of 𝒙.

Question 10

> means ___ the X axis + the solution set will be __ inequalities ___ your values

Answer 10

> means ABOVE the x-axis and the solution set will be TWO inequalities EITHER SIDE of your values.

Question 11

< means ___ the X axis + the solution set will be __ inequalities ___ you values

Answer 11

<means BELOW the x-axis and the solution set will be ONE inequality BETWEEN your values.  

Question 12

Rational inequalities

Answer 12

Multiply both sides by the (𝑫𝑬𝑵𝑶𝑴𝑰𝑵𝑨𝑻𝑶𝑹)² to ensure we’re multiply by something positive => don’t have to flip inequality

Question 13

|x| is

Answer 13

the ABSOLUTE VALUE or MODULUS of x

Question 14

The modulus is…

Answer 14

Geometrically it is how far a number is from zero on a number line.
ALWAYS a POSITIVE value

Question 15

|x| = 3

Answer 15

x = 3 OR x=-3

Question 16

To solve a modulus equation

Answer 16

Get the modulus on its own on one side of the equation.
SQUARE BOTH SIDES => removing the modulus.
Solve the resulting equation.

Question 17

g(x) = 4
The line

Answer 17

Is parralel to X axis
Goes through 4 on the Y axis

Question 18

If there are 2 modulus

Answer 18

get ONE ON EACH SIDE before squaring

Question 19

Does squaring both sides work on modulus inequalities

Answer 19

Yes

Question 20

Inequalities: Proofs

Answer 20

Get each term to 1 side and 0 on the other

Question 21

(any real no.)²

Answer 21

≥ 0

Question 22

-(any real no.)²

Answer 22

≤0

Question 23

Discriminants

Answer 23

𝒂𝒙²+𝒃𝒙+𝒄=𝟎 is a quadratic equation whose roots are given by 𝒙=(−𝒃±√𝒃² −𝟒𝒂𝒄)-2a
The value of 𝒃² −𝟒𝒂𝒄 =DISCRIMINANT

It tells us if the ROOTS are EQUAL, REAL or NON REAL.

Question 24

Real roots

Answer 24

𝒃² −𝟒𝒂𝒄 ≥ 0
Cuts x axis at 2 points

Question 25

Equal roots

Answer 25

𝒃² −𝟒𝒂𝒄 = 0
cuts x axis at 1 point

Question 26

Non real roots

Answer 26

𝒃² −𝟒𝒂𝒄 < 0
doesnt cut the x axis

Question 27

a > 0 graph shape

Answer 27

U shape

Question 28

a < 0 graph shape

Answer 28

n shape

Question 29

Do you have to state the discriminant formula every time

Answer 29

YES