Flashcards in Mathematical Skills Deck (16)

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1

## What are the basic rules of indices?

###
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)

2

## How are indices presented in units?

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

3

## What is standard form?

### 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

4

## What is a fraction? What is a percentage?

###
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

5

## What are radians?

###
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.

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?

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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

7

## What is direct and inverse proportion?

###
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.

8

## Which symbol represents 'change in'?

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

9

## Which symbol is commonly used to represent an angle?

### Theta θ.

10

## Which symbol means 'approximately equal to'?

### x is approximately equal to y. x ≈ y

11

## What is the quadratic formula?

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

x = [-b ± (b^(2) -4ac)^(1/2)] / 2a

12

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

###
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)

13

## What is SOHCAHTOA?

###
Sin x = Opposite/Hypotenuse

Cos x = Adjacent/Hypotenuse

Tan x = Opposite/Adjacent

14

## What is Pythagoras' theorem?

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

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

15

## What is the sum of angles in a triangle?

### 180° or π rad

16