MATHS by Jessica Duddington

Method 1

jduddington20 — 2018-04-18 09:38:12 UTC

Fractions:
A = 2/9
J = 7/9

36 ÷ 9 x 2 = 8
36 ÷ 9 x 7 = 28 = 8:28

Method 2

jduddington20 — 2018-04-18 09:40:04 UTC

Addition:

+ 2+7=9
÷ 36÷9=4
x A = 2x4=8
J = 7x4=28

Method 3

jduddington20 — 2018-04-24 08:56:36 UTC

The block method...

A = ⬛️⬛️ - 8
J = ⬛️⬛️⬛️⬛️⬛️⬛️⬛️ -28

5 blocks = 20
Each block is 4

Now you can work out how many are in total or how many one person has by timesing 4 but the amount of blocks

Problem Solving

jduddington20 — 2018-04-24 08:57:26 UTC

Use the bar method to draw out the question in real life.
It then allows you to see the difference and amounts.

Roatation (1)

jduddington20 — 2018-04-24 09:22:49 UTC

Rotate this triangle by 90 degrees anti-clockwise around A:

Translation

jduddington20 — 2018-04-25 09:01:08 UTC

Either a vector is given or you have to find the vector:
Choose a vertice and move ...
(3) - across three
(2) - up two

Post 1

jduddington20 — 2018-05-01 09:03:19 UTC

y = mx + c
m= gradient
c= y intercept

Post 2

jduddington20 — 2018-05-01 09:07:27 UTC

3y = 6x + 3

3y ÷ 3 = y
6x ÷ 3 = 2x
3 ÷ 3 = 1

y = 2x + 1

Enlargement

jduddington20 — 2018-05-01 09:20:13 UTC

From the centre of enlargement it is (1,1).
When enlarged you double this so it’s (2,2).

jduddington20 — 2018-05-01 09:24:48 UTC

Centre of Enlargement

jduddington20 — 2018-05-02 09:05:01 UTC

Negative Enlargement

jduddington20 — 2018-05-02 09:12:07 UTC

Congruent Shapes

jduddington20 — 2018-05-04 10:07:04 UTC

Congruent: The sand shape and size which can only be rotated or flipped.
Exam Questions ask how to prove congruence:

1: SAS - Two sides and the included angle.
2: ASA - Two angles are the same and a side.
3: SSS - Three sides all the same.
4: RHS - Right-angle, hypotenuse and another side.

Similarities

jduddington20 — 2018-05-08 09:19:00 UTC

Shapes which are the same just different sizes.
Must be equiangular
Must be enlarged.
Use corresponding angles and sides.

An Example

jduddington20 — 2018-05-08 15:43:17 UTC

Use the graph to tell you details about the equation.

Similar Triangles

jduddington20 — 2018-05-09 09:06:09 UTC

Using algebra name the side and work out ‘x’.

REDUCTION - small ÷ big
ENLARGE - big ÷ small
You must always multiply later though!

AREA SCALE FACTOR = LSF²
New area is LSF²x the old area.

1 - Expand and Simplify

jduddington20 — 2018-05-10 10:16:43 UTC

Expand and Simplify (2x + 1)²
(2x+1)(2x+1) - 4x² + 2x + 2x + 1
= 4x² + 4x + 1

2 - Factorising

jduddington20 — 2018-05-10 10:18:51 UTC

Factorise fully 50xy² - 25xy
50xy² - 25xy ➡️ 25xy(26 - 1)

3 - Factorising

jduddington20 — 2018-05-10 10:20:49 UTC

Factorise 100x² - 64
(10x - 8)(10x - 8) ⬇️
You have to squareroot both 100x and 68.

4 - Algebra

jduddington20 — 2018-05-10 10:24:35 UTC

z = 9x² - y Find the value of z when x = - 1/3 and y = -1/4
z = 9x² - y
= 9x (-1/3)² - (-1/4)
=9 x 1/9 + 1/4
= 1+ 1/4
= 1and a quarter.

5 - Fractional Simplify

jduddington20 — 2018-05-10 10:29:59 UTC

Work out (1 3/5)²=
(1 3/5)²➡️ 64/25
Then turn into a mixed number: 2 14/25

Similar Volume

jduddington20 — 2018-05-10 10:38:03 UTC

Enlarge: LSF = 2
New Volume : 8 or 2³
NEW VOLUME: LSF³x Old Volume

3 FORMULAS

jduddington20 — 2018-05-10 10:42:49 UTC

New Length = LSF¹x Old Length
New Area = LSF²x Old Area
New Volume = LSF³x Old Volume

The First Step

jduddington20 — 2018-05-11 10:48:21 UTC

Roots that cannot be written as exact decimals are called SURDS. Leaving an answer in sure form means the answer is exact.

Formulas

jduddington20 — 2018-05-11 10:49:57 UTC

Here are the formulas of how to work out SURDS with an example.

Angles with a COMPASS

jduddington20 — 2018-05-16 09:02:06 UTC

jduddington20 — 2018-05-16 09:08:10 UTC

6 - Factorising

jduddington20 — 2018-05-17 10:16:26 UTC

Factorising is putting something into brackets.

Loci

jduddington20 — 2018-05-17 10:34:14 UTC

Constructing Shapes

jduddington20 — 2018-05-17 10:42:31 UTC

jduddington20 — 2018-05-17 10:43:00 UTC

RULER AND COMPASS

jduddington20 — 2018-05-17 10:43:33 UTC

jduddington20 — 2018-05-17 10:43:46 UTC

Circles

jduddington20 — 2018-05-17 10:45:36 UTC

Perpendicular

jduddington20 — 2018-05-17 10:46:38 UTC

jduddington20 — 2018-05-17 10:48:21 UTC

Basics

jduddington20 — 2018-05-19 09:15:55 UTC

-An angle measured from the north line
-Measured in a clockwise direction
-Must be written in three figures

Scale Factors

jduddington20 — 2018-05-19 09:20:18 UTC

To find a scale factor between two similar figures, find two corresponding sides and write the ratio of the sides.

Smaller number first = less than 1
Bigger number first = more than 1

Three Figure Bearings

jduddington20 — 2018-05-19 09:22:20 UTC

The answer must be written in three figures.
Also with the degrees sign.
Eg: = 058^o

Formulae Area

jduddington20 — 2018-05-21 11:41:14 UTC

Formula of different shapes ...

Composite Shapes

jduddington20 — 2018-05-21 15:48:02 UTC

These are when you divide a shape into sections to make it easier to work out the are/volume.
Often it will be an irregular shape split into triangles and squares.

Eg:

Circles

jduddington20 — 2018-05-21 15:55:29 UTC

Circumference: πd (perimeter)
Area: πr²
Sector: ¹/₂r²x (angle given)

Circles

jduddington20 — 2018-05-21 15:55:29 UTC

Circumference: πd (perimeter)
Area: πr²
Sector: ¹/₂r²x (angle given)

Circles

jduddington20 — 2018-05-21 15:55:29 UTC

Circumference: πd (perimeter)
Area: πr²
Sector: ¹/₂r²x (angle given)

Highest Common Factor

jduddington20 — 2018-05-25 16:40:43 UTC

The highest number that can be divided into two or more numbers exactly

Eg: WHATS THE HCF OF 24 and 40??
Factors of 24: 1,2,3,4,6,8,12,24
Factors of 40: 1,2,4,5,8,10,20,40

The highest number which is in both list is eight there fore it is the highest common factor.

=8

Lowest Common Multiple

jduddington20 — 2018-05-25 16:45:07 UTC

The lowest quantity that is a multiple of two or more given quantities.

Eg: WHAT IS THE LCM OF 6 & 10??
Multiples of 6 are: 6,12,18,24,30,36,42
Multiples of 10 are: 10,20,30,40,50

Therefore the lowest common multiple is 30 because it’s the smallest number in both lists.

=30

Solve

jduddington20 — 2018-05-31 14:42:56 UTC

Simplify

jduddington20 — 2018-05-31 14:43:22 UTC

Lesson 1

jduddington20 — 2018-06-26 09:05:47 UTC

Range: lowest - largest
Mean: average
Mode: difference between them
Median: middle number

Coefficient

jduddington20 — 2018-06-27 09:07:20 UTC

The number infront of the algebraic term.
-3y ➡️ -3 is the coefficient number

Frequency Polygons

jduddington20 — 2018-06-28 10:14:48 UTC

Putting data from a two collum table into a graph.
Plot according to the data.
Join up with straight lines.

Finding he Modal Class Interval

jduddington20 — 2018-06-28 10:32:00 UTC

Find the highest frequency (MODE)
Read off coresponding class interval.

Eg: 1040 or 3-7

Mean, Median, Mode & Range

jduddington20 — 2018-06-29 10:08:30 UTC

Inner Quartile & Outer Quartile

jduddington20 — 2018-07-04 09:04:52 UTC

Rule

jduddington20 — 2018-07-04 09:11:56 UTC

The rule for lower&upper quartile:
EVEN number of items = Find middle of bottom half
ODD number of items = Throw away middle item, find medium of remaining half.

For lots of items

jduddington20 — 2018-07-04 09:14:54 UTC

Stem and Leaf diagrams

jduddington20 — 2018-07-04 09:21:51 UTC

Put the numbers in order.
Draw a line of numbers 1-5 down.
Put the tens in the front collum and list them on the other side of the line. ( eg 1 | 4 = 14 )
Then you put it in order.
Write the key.

BOX PLOTS

jduddington20 — 2018-07-05 10:13:46 UTC

CUMLATIVE FREQUENCY GRAPHS

jduddington20 — 2018-07-05 10:43:13 UTC

Inter Quartile Range

jduddington20 — 2018-07-06 10:30:14 UTC

To work out the inter Quartile range is the lower Quartile minus the upper Quartile.

DIFFERENCES BETWEEN BAR&HISTOGRAM

jduddington20 — 2018-07-10 09:21:40 UTC

FREQUENCY DENSITY = FREQUENCY ÷ CLASS WIDTH

jduddington20 — 2018-07-11 09:03:56 UTC

Relative Frequency

jduddington20 — 2018-07-13 10:30:51 UTC

Relative frequency of an event = frequency if an event divided by the number of trials

jduddington20 — 2018-07-17 09:16:17 UTC

If the probability of an event occurring is p then the probability of it not happening is 1 - p.

jduddington20 — 2018-07-17 09:16:44 UTC

Outcomes are mutually exclusive if they cannot happen at the same time.

jduddington20 — 2018-07-17 09:17:43 UTC

In probability ‘or’ means +.
In probability ‘and’ means x.

EXAMPLE:

jduddington20 — 2018-07-17 09:21:33 UTC

jduddington20 — 2018-07-18 09:35:17 UTC

Independent events are the outcome if one doesn’t affect the other.

jduddington20 — 2018-07-18 09:35:56 UTC

5! = 5x4x3x2x1 ➡️ 5 factorical

jduddington20 — 2018-07-18 09:36:18 UTC

Factorising Quadratics

jduddington20 — 2018-09-11 11:38:54 UTC

jduddington20 — 2018-09-11 11:41:01 UTC

Rearranging Formula

jduddington20 — 2018-09-13 08:34:11 UTC

a(x-b)=j this would then become x=j+ab divided by a.
To make x the subject you have to do the reverse of each part.

Simple example:

jduddington20 — 2018-09-13 08:35:33 UTC

x+a= t ➡️ x =t-a

(Note: t must stay on that side because only a was carried over)

Example

jduddington20 — 2018-09-13 08:43:36 UTC

Forming Equations

jduddington20 — 2018-09-18 11:37:03 UTC

More on Factorising

jduddington20 — 2018-09-21 08:24:43 UTC

Completing the square

jduddington20 — 2018-09-27 08:40:55 UTC

Inverse functions

jduddington20 — 2018-10-09 11:20:49 UTC

Three steps of inverting a function.

jduddington20 — 2018-10-09 11:25:51 UTC

Simultaneous Equations

jduddington20 — 2018-10-17 11:02:05 UTC

You have to make sure that either the y or x’s are the same by multiplying the whole equation by something.

SohCahToa

jduddington20 — 2018-11-02 09:39:39 UTC

Finding missing sides and angles

jduddington20 — 2018-11-13 12:12:53 UTC