Mathematical Skills

Question 1

What are the basic rules of indices?

Answer 1

a^(n) = a * a * a *... (n times)
a^(-n) = 1/a^(n)
a^(1/n) = nth root of a
a^(x) * a^(y) = a^(x+y)
a^(x) / a^(y) = a^(x-y)
(a^(x))^(y) = a^(xy)

Question 2

How are indices presented in units?

Answer 2

e.g. velocity units = m/s -> ms^(-1), acceleration units = m/s^(2) -> ms^(-2)

Question 3

What is standard form?

Answer 3

Standard form is a way of presenting a number with many digits easily. It is usually written as a digit from 1-10 x10^(n). e.g. 300000000 ms^(-1) = 3.00 x10^(8) ms^(-1), 0.000015 A = 1.5 x10^(-5) A

Question 4

What is a fraction? What is a percentage?

Answer 4

a/b is a fraction, it means a divided by b.

Fractions can be written as percentages by multiplying them by 100. e.g. a/b * 100

Question 5

What are radians?

Answer 5

Radians are another way of measuring angles instead of degrees. Radians use the symbol c (suspended) instead of ° or can be written in terms of pi.

360° = 2π
180° = π
etc.

Question 6

What symbols represent less then and greater than; much less than and much more than; less than or equal to and more than or equal to?

Answer 6

x less than y. x y

x much less than y. x > y

x less than or equal to y. x ≤ y
x more than or equal to y. x ≥ y

Question 7

What is direct and inverse proportion?

Answer 7

Direct proportion -
y ∝ x -> y = kx
(As one increases, the other increases proportionally)

Inverse proportion -
y ∝ 1/x -> y = k/x
(As one increases, the other decreases proportionally)

k is a constant.

Question 8

Which symbol represents ‘change in’?

Answer 8

Delta Δ. e.g. Δv means a change in velocity.

Question 9

Which symbol is commonly used to represent an angle?

Answer 9

Theta θ.

Question 10

Which symbol means ‘approximately equal to’?

Answer 10

x is approximately equal to y. x ≈ y

Question 11

What is the quadratic formula?

Answer 11

For… ax^(2) + bx + c = 0 where a, b, and c are constants.

x = [-b ± (b^(2) -4ac)^(1/2)] / 2a

Question 12

How do you find the areas and volumes of different geometrical figures?

Answer 12

rectangle - A = bh
cuboid - V = bhl
parallelogram - A = b * (perpendicular h)
circle - A = πr^(2) or πD^(2) / 4
circle - V = πD or 2πr
triangle -  A = bh or 1/2ab * sinC
trapezium - A = 1/2(a+b)h
sphere - A = 4πr^(2)
sphere - V = 4/3πr^(3)

Question 13

What is SOHCAHTOA?

Answer 13

Sin x = Opposite/Hypotenuse
Cos x = Adjacent/Hypotenuse
Tan x = Opposite/Adjacent

Question 14

What is Pythagoras’ theorem?

Answer 14

a^(2) + b^(2) = c^(2)

As long a c is the hypotenuse of a right-angled triangle.

Question 15

What is the sum of angles in a triangle?

Answer 15

180° or π rad

Question 16

How can you convert from degrees to radians? and from radians to degrees?

Answer 16

θ°/180 * π = Radians

θc/π *180 = Degrees