Formula

Question 1

Perfect square formula

Answer 1

 (a+b)^2≡a^2+2ab+b^2

 (a−b)^2≡a^2−2ab+b^2

Question 2

Perfect cube formula

Answer 2

 (a+b)^3≡a^3+3a^2b+3ab^2+b^3

 (a−b)^3=a^3−3a^2b+3ab^2−b^3

Question 3

Diference of two squares formula

Answer 3

 a^2−b^2≡(a−b) × (a+b)

Question 4

Difference of two cubes

Answer 4

 a^3−b^3≡(a−b) × (a^2+ab+b^2)

Question 5

Sum of two cubes

Answer 5

 a^3+b^3≡(a+b) × (a^2−ab+b^2)

Question 6

How to complete the square

Answer 6

Half the coefficient of x, square it and add and minus it from the original equation.

Question 7

Quadratic equation

Answer 7

x=(-b±√(b^2-4ac))/2a

Question 8

U symbol and upside down U symbol

Answer 8

U symbol represents union and contains all elements from both sets. Upside down U represents the intersection between two sets.

Question 9

What do the symbols N, Z, Z+, Q and R represent.

Answer 9

• N represents natural numbers
• Z represents integers
• Z+ represents positive integers
• Q represents rational numbers
• R represents real numbers (both rational and irrational numbers)

(Z+ and N are the same)

Question 10

How to describe the inputs and outputs of a function.

Answer 10

f: Z→Z

Question 11

What is a polynomial

Answer 11

nvolves non negative integer exponents of a variable.

Question 12

Limit as x approaches inifinity

Answer 12

Same degrees: ratio of coefficients

Bottom heavy: 0

Top heavy: infinity

Question 13

Continuity

Answer 13

A function is continuous only if the limit as x a pproaches a value from both the positive and negative side is equal to the f(said point).

Question 14

List the trigonometric functions

Answer 14

• Sec(θ) = 1/cos(θ) = hyp/adj
• Csc(θ) = 1/sin(θ) = hyp/opp
• Cot(θ) = 1/tan(θ) = adj/opp
• cos^2(θ) + sin^2(θ)=1
• tan(θ) = sin(θ)/cos(θ)
• cot(θ) = cos(θ)/sin(θ)
• sec^2(θ) = tan^2(θ) + 1
• csc^2(θ) = cot^2(θ) + 1

Question 15

State the sine rule

Answer 15

a/sin(A) = b/sin(B) = c/sin(C)

Question 16

State the cosine rule

Answer 16

• cosine rule: c^2 = a^2+b^2-2abcos(C)

Question 17

State the triangle area formula

Answer 17

• Triangle area formula: Area = 1/2absin(C)

Question 18

State the compound angle formula

Answer 18

 sin(A(+/-)B) = sin(A)cos(B)(+/-)cos(A)sin(B)

 cos(A(+/-)B) = cos(A)cos(B)-(+/-)sin(A)sin(B)

tan(A(+/-)B) = (tan⁡(A)(+/-)tan⁡(B))/(1-tan⁡(A)tan⁡(B))

Question 19

State the double angle formula

Answer 19

Derived by taking the positive variants of the compund angle forulas and subbing in A=B=theta

 Sin(2θ) = 2sin(θ)cos(θ)

Tan(2θ) = (2 tan⁡(θ))/(1-〖tan〗^2 (θ))

 The cos variant can be simplified into two forms:
o cos(2θ) = 2cos^2(θ)-1
o cos(2θ) = 1-2sin^2(θ)

Question 20

State the auxillary angle formula

Answer 20

asin(x) + bcos(x) can be rewritten as Rsin(x+alpha)

R= √(a^2+b^2 )

tan(α) = b/a

 The expression can also be rewritten with cos by instead subtracting alpha from x and finding alpha as tan(a/b)

Question 21

Half angle formula

Answer 21

sine and cos are derived from double angle formula by replacing theta with theta over 2. Tan is found by taking the half angle formula of sine over that of cos.

sin(x/2) = ±√((1-cos⁡(x))/2)

cos(x/2) = ±√((1+cos⁡(x))/2)

tan(x/2) = (1-cos⁡(x))/(sin⁡(x))