MATH
 Round off at the end
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SCIENTIFIC NOTATION
 First number must be between 1-10 not including 10
 Multiply by a power of 10
 Smaller to larger number is a negative index(to the right)
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is not approximation
REFLECTIONS FUNCTIONS AND GRAPHS
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Relation/Mapping maps one object onto another must have input(domain/x) and
output(range/y), rule and a direction
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Rules are for eg 2x= y
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Order pair is {2, 5} {domain, range}
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Codomain is everything that is accepted by the function and the range is what is accepted
by the function mapped onto
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Types of relations are one to one, one to many, many to one, many to many and they show
how the elements are paired
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A function is when one input is paired to one output. One to one and many to one are
functions
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Inverse is the opposite of f. For eg 2x-1, the inverse is (x-1)/2
1. Make f(x) into y
2. Interchange y and x
3. Solve for y
 Composite functions, you put the second one into the first one
Coordinate Geometry
 X coordinates come first then y
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Y intercept is c
 At the x intercept the value of y is 0
 Gradient is m
 The find y(x intercept) equate the thing to 0 and solve
 On the y axis y intercept is (0,7) and on the x axis the x intercept is (7,0)
 Gradient formula is y2-y1÷ x2 – x1
 Horizontal line gradient is 0
 Upwards is positive
 Downwards is negative
 Vertical is undefined/infinitive
 When asked for y intercept put (0, number)
 To find the equation, calculate the gradient then substitute into the equationnto find c
 Midpoint of a line segment is
𝑥1+𝑥2 ,𝑦1+𝑦2
2
2
 Length of the line segment √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2
 Parallel lines have the same gradient
 For perpendicular lines the gradient of one line, multiplied by the other line, must be equal
to -1
 To solve write it in the form y=mx + c and then solve
Linear Programming
 Calculate the inequality to find the two nb points for eg when y >= 1/2x solve for y and
solve for x using two points
when x is = 0 y=1/2(0) and when x =6
y=1/2(6)
and plot those points
 To identify where to shade, choose a test point for eg (4,1) substitute into the equation and
see if the inequality is true. IF it is shade that side
 Y = 2x -1 substitute
 When you have an inequality x = to a constant it is a line parallel to the y axis, y= constant
is parallel to the x axis
 Y=x is a straight line diagonal
 X + y <= 12 for g both x and y should connect to 12
 Always label you r lines
 Use the vertices to work out profit
 Don’t shade with color, shade with lines
Solving for linear inequalities
 Less than or equal to you must shade the circle on top of the number on the number line
 Treat the >/< as an equal sign
 If they ask what numbers it night be you must include the base number when it says equal
to but not if it doesn’t, for eg less than or equal to 8 must include 8
 When the coefficient that has x is negative, you can switch both values right to left and left
to right and switch the sign to get x on one side OR divide by the negative and switch the
sign.
Quadratic Functions
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f(x) is y
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roots a x intercepts are the same
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axis of symmetry is the x value. So x = ……
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h is the x value, k is the y value
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y intercept is where the line cuts th y value
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rots can be found by perfect square equation = 0
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coordinates of the minimum point is completing the square or drawing the axis of
symmetry and adding the roots and dividing then substituting into the equation
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x intercept is the c from the equation
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if they ask to sketch the coordinates of the minimum point the x is positive n the y
negative
Trigonometry 1
 Length of the hypotenuse is equal to the length of adjacent + the opposite.
 Angles are opposite to the sides
 The side opposite the right angle is the hypotenuse, the sign opposite the angle is the
opposite, adjacent is the other one
 Sine rule is used with a complete pair of opposite sides and angle and a half pair.
 Cosine is three sides and needs an angle or side angle side when the angle is in between
the two sides.