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Math(Every single chapter), l - Coggle Diagram
Math(Every single chapter)
Textbook 2A
Chapter 1:Linear Graphs and Simultaneous Linear equations
Chapter 1.1
Equation of a straight line is y=mx+c
m = gradient
c = y-intercept
Equation of a horizontal line is y=c
Chapter 1.2
Equation of a vertical line is x=a
Another way to represent the formula of a straight line is ax+by=k
Chapter 1.3(Practice is Key!)
Using graphical method to solve simultaneous equations
ie: 2x-5y=32 and 2x+3y=0
Chapter 1.4(Practice is key!)
Using elimination and substitution method to solve simultaneous linear equations
Reduces both simultaneous equations into two variables into one equation
Chapter 1.5(Practice is key!)
Using graphical, elimination and substitution method to solve scenarios that are applicable irl.
Chapter 2: Linear inequalities
Chapter 2.1
x>y symbolizes that the value of x is greater than y
x<y symbolizes that the value of x is smaller than y
x≥y symbolizes that the value of x is greater than or equal to y
x≤y symbolizes that the value of x is smaller than or equal to y
Chapter 2.2(Read Read abit can)
Representing inequalities on a number line
Hollow circles represents ">" or "<" and shaded circle represents "≥" or "≤"
Simplify an inequality so that one side only shows the algebraic value while the other shows the other value
x-3≤7 = x≤10
-2y+4<3 = Y>0.5
Chapter 2.3(Practice is key!)
Using linear inequalities to solve irl problems
Chapter 3: Expansion and factorisation of Algebraic Expressions(Practice is key!)
Chapter 3.1
Addition and subtraction of quadratic expressions
x²+(-6x²) = -5x²
Chapter 3.2(Read Read abit can)
Laws regarding the form (a+b)(c+d) expression
(a+b)(c+d) = ac+ad+bc+bd
Chapter 3.3(Practivce is key!)
Expansion and simplification of quadratic expressions
Question examples:7a(2a+1)-4(8a+3)
Chapter 3.4(Practise is key!)
Factorisation of quadratic expressions
Use of multiplication frame to factorise questions with the expression form x²+bx+c
x²+x-6
Question examples
Factorise -xy²z²-x²y^3
Factorise -a²+2a+35
Chapter 3.5(Practice is Key!)
Factorising quadratic alegabraic expressions into the form (a+b)(c+d)
Use the multiplication frame and work backwards with all 4 values that you are given
Question examples
Factorise ab+ad+2bc+2cd
Factorise x+xy+2y+2y²
Chapter 4: Expansion and Factorisation using special algebraic identities(Practice is key!)
Chapter 4.1(Practice is key!)
The three special identities of expansion
Second: (a-b)² = a²-2ab+b²
Third:(a+b)(a-b) = a²-b²
First:(a+b)² = a²+2ab+b²
Examples of questions
Evaluate 104²
Chapter 4.2(Practice is key!)
Factorisation using special algebraic identities
Chapter 5: Quadratic Equation and Graphs
Chapter 5.1
Solving quadratic equations by factorisation by isolating unknown values on the other side of the equation
x(x-3)=0
x = 0 x-3=0 x=3
Chapter 5.2(Practice is key!)
Graphs of quadratic expression y = ax²+bx+c
Key words: Upwards/Downwards, Minimum point/maximum point ,Line of symmetry ,turning point, smaller and wider
y=x² opens upwards while y= -x² opens downwards
Line of symmetry is x=0
Chapter 6: Algebraic fractions and Formulae(Practice is key!)
Chapter 6.1(Read read abit can)
Simplifying algebraic fractions
Question examples include h²+7hk/5hk
Chapter 6.2(Practice is key!)
Multiplication and division of algebraic fractions
h²-h-6/h²-9 x h²/h²+2h
Chapter 6.3(Practice is key!)
Addition and subtraction of algebraic fractions
3/x+5 + 1/x-3
Chapter 6.4(Practicee is key!)
Solving equations involving algebraic fractions
a-2/5 + a-1/3 = 1
Chapter 6.5(Practice is key!)
Manipulation of algebraic formulae
Making an algebraic value the subject of the formulae by moving it around an equation
Make x the subject of the formulae in y=2-x/3+2x
Chapter 7:Direct and inverse proportion(Practice is key!)
Chapter 7.1
Direct proportion mean that when one side of an equation increases by a certain amount, the other side also will.
Example: Amount of Biscuits is directly proportional to it's price.
when amounts of biscuits increase, Price MUST also increase
Chapter 7.2(Practice is key!)
If y is directly proportional to x, y/x = k or y=kx
The graph of y=kx(directly proportioned) is a straight line that passes through the origin.
Chapter 7.3(Read read abit can one)
y and x may not always be directly proportioned to each other but y² and x² is.
Chapter 7.4
Inverse proportion is the opposite of direct proportion in which if one side increases or decreases a certain amount, the other side will do the opposite and increase or decrease depending on the other value.
Amount of taps is inversely proportioned to the amount of time the tank will be filled.
When the amount of taps increase, the time WILL decrease
Chapter 7.5(Practice is key!)
If y is inversely proportioned to x, xy=k or y=k/x
The graph of y inversely proportioned to x is a hyperbola
Chapter 7.6(Practice is key!)
y could also be inversely proportioned to x²
Textbook 2B
Chapter 8: Congruence and Similarity
Chapter 8.1
Geometrical shapes are congruent when they have the exact same SHAPE and SIZE
They can be mapped onto each other under translation, rotation and reflection.
All of their corresponding sides and angles are also equal
Factors such as colors and patterns do not matter
Chapter 8.2
Geometrical shapes are similar when they have EXACTLY THE SAME SHAPE and not necessarily the same SIZE
Al of their corresponding angles are equal and the ratio of their corresponding lengths are equal
Chapter 8.3
Similarity and Enlargement
Maps, room sizes and size scales
Chapter 9:Pythagoras' Theorem(Practice is key!)
Chapter 9.1(Practice is Key!)
Pythagoras Theorem tells us that the the Hypoternuse is equivalent to the squares of both the other sides of a right angled triangle sum.
The formula is c²=a²+b²
Chapter 9.2(Practice is key!)
Use of Pythagoras Theorem in real-world applications
Chapter 9.3
Converse of Pythagoras Theorem.
Trying to prove if a triange is right-angled given it's lengths
Chapter 10: Trigonometric ratios(Practice is key!)
Chapter 10.1
sin A=opp/hyp(Sine)
cos A = adj/hyp(Cosine)
tan A = opp/adj(Tangent)
In a right-angled triangle, we can find the each sides using the acronyms, toa cah soh
Chapter 10.2(Practice is key!)
Using triganometric ratios to find unknown sides of a right-angled triangle
No examples available :)
Chapter 10.3(Practice is key!)
Using Trigonometric ratios to find unknown angles in a right-angled triangle
sin-1, cos-1,tan-1
sin-1(15/22)
Chapter 10.4(Practice is key!)
Use of trigonometric ratio in real-world context
Chapter 11: Volumes and surface area of Pyramids ,Cones and spheres(Practice is key!)
Chapter 11.1(Practice is key!)
A pyramid is a geometrical shape with slanted faces and a base. The apex of a pyramid is the pointy where all sides meet which makes all the sides triangular. The vertex is the edges of the base. The slant height is the height of the sides which are triangles in the pyramid
Volume of pyramid = 1/3 x base area x height
(not slant height)
Surface area of pyramid = surface area of the base x 4(surface area of the sides[Triangles])
Chapter 11.2(Practice is key!)
A cone is a geometrical shape with a circular base and a closed curve. It also has an apex where the edge of the closed curve is.
Volume of cone = 1/3πr²h
Surface are of a cone = πrl+πr²
Chapter 11.3(Practice is key!)
Sphere = 3d circle
d
a
b
s**
volume of sphere = 4/3πr^3
surface area of sphere = 4πr²
Chapter 11.4(Practice is key!)
Volume and surface area of composite solids Aka the ultimate geometrical test
Chapter 12:Probability of single events
Chapter 12.1
The sample space and the amount of probable outcomes in an event
sample space = listing the different outcomes in a pair of braces "{ }"
Chapter 12.2
The probability of an event is given by p(E) = number of favourable outcomes for event E/total number of possible oiutcomes
The probability that an event is not gonna happen is given by P(not E) = 1-P(E)
Chapter 12.3(Practice is key!)
Using probability to solve harder questions basically
Chapter 12.4(Practice is key!)
Relative frequency = number of occurence/total number of traits
Chapter 13:Statistical diagrams(Practice is key!)
Chapter 13.1
Dot diagrams displays numerical data and are suitable for displaying a small set of numerical data.
However, they are not suitable to display a data set with many different values or large range and a large set of numerical data
To describe the distribution of a diagram, you must follow these steps
Clusters. Areas where data of certain values are grouped together
Extreme data. Data which is found furthest from other data
Range of values from the lowest to the highest
Symmetry. Is there symmetry to the graph? Yee or nay?
Chapter 13.2
Histograms for ungrouped data are similar to bar graphs but instead it displays numerical data because the frequency is determined through the area of a column and not the actual height.
Histograms are suitable for displaying large groups of numerical data
However, they are more abstract and may be misinterpreted if the frequency axis doesn't start from 0
Chapter 13.3
Stem-and-leaf diagrams is used to display grouped numerical data and are very flexible. They can have split-stems and also back-to-back which make them good at comparing different diagrams side-by-side
Stem-and-leaf diagrams are can display a data set with many different values into equal class intervals. It also retains individual values and can be displayed using back-to-back stem-and-leaf diagram for easy comparison.
Tedious to construct if there are too many data values and cannot be grouped into certain class intervals.
Chapter 13.4
Basically chapter 13.2 but the histogram displays grouped data.
It can display data sets with many different values and is easier to construct than a stem-and-leaf
It's more abstract and individual data values are lost as it displays an entire data set.
Chapter 14: Averages of statistical diagrams(Coming soon)
Disclaimer: This is to consolidate your understanding and make Math EOY study easier. Practice is still key!!! THE TEXTBOOK IS STILL THE MASTER OF METH(amphetamine)
Legend
"(Practice is key!)" used to symbolise that a chapter or it's sub-section is important
"Read read abit then can" used to symbolize that a chapter or it's sub section is less important
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