Section 3 - Math

Question 1

What are real numbers?

Answer 1

They are numbers that can be represented on a number line.

Question 2

What is an Absolute value?

Answer 2

It refers to how far a real number is from 0 and can be represented by a ‘|’ placed on either side of the number. It removes any negative sign so it can only be 0 or positive. E.g. |-3| = 3.

Question 3

Name the order of operations.

Answer 3

B - brackets, O - operations, D - division, M - multiplication, A - addition, S - subtraction

Question 4

What are the rules on zero?

Answer 4

• the result of multiplying or dividing by 0 is 0.

Question 5

What are these fractions as decimals? 1/2 1/3 1/4 1/5 1/6 1/8 1/10

Answer 5

1/2 = 0.5 1/3 = 0.33 1/4 = 0.25 1/5 = 0.5 1/6 = 0.167 1/8 = 0.125 1/10 = 1

Question 6

Rules for exponents:

1. a⁰ = ?
2. aⁿ a^m = ?
3. (aⁿ)^m = ?
4. a¹ = ?
5. aⁿ / a^m = ?
6. a^1/n = ?

Answer 6

1. a⁰ = 1
2. aⁿ a^m = a^n+m
3. (aⁿ)^m = a^nm
4. a¹ = a
5. aⁿ/a^m = a^n-m
6. a^1/n = n square root a

Question 7

Square and cube these numbers

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

20

Answer 7

1² = 1 1³ = 1

2² = 4 2³ = 8

3² = 9 3³ = 27

4² = 16 4³ = 64

5² = 25 5³ = 125

6² = 26

7² = 49

8² = 64²

9² = 91

10² = 100

11² = 121

12² = 144

13² = 169

14² = 196

15² = 225

20² = 400

Question 8

Root 2?

Root 3?

Answer 8

Root 2 = 1.4

Root 3 = 1.7

Question 9

1. How many inches are there in a foot?
2. How many feet are there in a yard?
3. How many yards are there in a mile?
4. How many ounces in a pound?

Answer 9

1. 1 foot = 12 inches
2. 1 yard = 3 feet
3. 1 mile = 5280 feet
4. 1 pound = 16 ounces

Question 10

What does this stand for?

King

Henry

Died

Unexpectedly

Drinking

Chocolate

Milk

Answer 10

T - tera,T, 10¹²

G - Gig, G, 109

M - Mega, M, 10⁶

K - Kilo, k, 10³

H - Hecto, h, 10²

D - Deca, da, 10¹

U - BASE UNIT 10⁰

D - Deci, d, 10^-1

C - Centi, c, 10^-2

M - Mili, m, 10^-3

M - Micro, µ, 10^-6

N - Nano, n, 10^-9

P - pico, p, 10^-12

Question 11

What is the #1 Rule of Algebra?

Question 12

What is the equation of a line?

Answer 12

y = mx + b

m = slope (y²-y¹ / x² - x¹) (area under curve)

b = y intercept

Question 13

What are the rules of Logarithms?

• log_aa =
• log_aM^k =
• log_a(MN) =
• log_a(M/N) =
• 10^log10M =
• log_a(1) =

Question 14

What is Pythagorean Theorem?

Answer 14

a² + b² = c²

• c = long side

Question 15

What is the area of a triangle?

Answer 15

1/2 base x height

Question 16

How do you work out the area of a Right Triangle?

Answer 16

1/2(a x b)

Question 17

Circles:

Diameter?

Radius?

Circumference?

Area?

Answer 17

• Diameter = 2 x r
• Radius = 1/2d
• Circumference = 2πr
• Area = πr²

Question 18

Spheres:

• Surface area?
• Volume?

Answer 18

• Surface area = 4π x r²
• Volume = (4/3)π x r³

Question 19

Cylinders:

• Surface area?
• Volume?

Answer 19

• Surface area = 2(π x r²) + (2π x r) x h
• Volume = (π x r²) x h

Question 20

Triangles:

1. What is the sum of the internal angles?
2. What is the sum of the external angles?
3. The value of an exterior angle is equal to the sum on what?

Answer 20

1. 180º
2. 360º
3. the value of an exterior angle is equal to the sum of the opposite two interior angles.

Question 21

SOH CAH TOA

Answer 21

• Sine = Opposite / Hypotenuse
• Cosine = Adjacent / Hypotenuse
• Tangent = Opposite / Adjacent

Question 22

2π radians = ?

Question 23

Important angles and their sine and cosine values

• 0º
• 30º
• 45º
• 60º
• 90º

Answer 23

• 0º, radians = 0, sine = 0, cosine = 1
• 30º, radians = π/6, sine = 1/2, cosine =(root 3/2)
• 45º, radians π/4, sine = 1/root2, cosine 1/root2
• 60º, radians = π/3, Sine = root3/2, cosine 1/2
• 90º, radians = π/2, Sine = 1, Cosine = 0

Question 24

Average?

Answer 24

Sum of numbers / number of numbers

Question 25

Probability?

Answer 25

number of ways the outcome can occur / number of possible outcomes