Core One Notes

Sorry the examples are missing because I've written in my own. This is a really dumbed down copy of notes but hopefully it'll be useful

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Maths Notes- Core 1
Basics of Straight Lines
Equation of a straight line
y = mx + c
ax + by + c = 0
C is the y-intercept
M is the gradient
Gradient of a line
change in y
gradient = change in x
Distance between two points
Use Pythagoras
distance = (change in x) + (change in y)
2 2
Midpoint of a line
x1+x2 , y1+y2
2 2
Parallel and Perpendicular Lines
Parallel lines have the same gradient
Perpendicular gradients: gradient 1 ×gradient 2 =- 1
-1
gradient 1 = gradient 2
1

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Maths Notes- Core 1
Intersection of Straight Lines
Eg Where does y = 3x - 1 meet y = 1
2x = 5 ?
Intersection of curves and straight lines
Where does y = x2 - 7x + 6 meet y = 3
2x + 2
2…read more

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Maths Notes- Core 1
Surds
Rational numbers can be expressed as a with aand bas integers
b
Irrational numbers cannot
The square root of a non-square number
Rules for surds
ab = ab
o E.g. 98 = 49×2 = 72
a a
b = b
o E.g. 13 13
4 = 2
a + b and a - b are called conjugates. Used to rationalise fractions involving surds
o E.g.…read more

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Maths Notes- Core 1
Quadratics
Parabolas
Equations of the form y = ax2 + bx + c are parabolas
E.g. 1
E.g.2
E.g.…read more

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Maths Notes- Core 1
Completing the square
A quadratic form (x + p)2 + q is in completed square form
(x + a)2 = x2 + ax + ax + a2
E.g.1 Factorise x2 - 8x + 3
(x - 4)2 + 3 - 16
(x - 4)2 - 13
E.g.…read more

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Maths Notes- Core 1
If b2 - 4ac > 0 there are two real roots and two points of intersection
If b2 - 4ac = 0 there is one root and one point of intersection
If b2 - 4ac < 0 there are no real roots and no points of intersection
Inequalities
Linear Inequalities
Solve just the equation except if an inequality is multiplied by a negative number
E.g.…read more

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Maths Notes- Core 1
x=4 x =- 3
Inequality x <- 3 x > 4
Inequalities and the discriminant
b2 - 4ac < 0 No real roots
b2 - 4ac0 Real Roots
E.g.…read more

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Maths Notes- Core 1
x3 - 4x2 - 11x + 30
Sketching cubic graphs
Sketch y = (x - 2)(x + 3)(x - 5)
Cross the x axis at x = 2 x =- 3 x = 5
Solving Cubic Equations of the type ax3 + bx2 + cx
2x3 - 10x2 + 12x
2x(x2 - 5x + 6)
2x(x - 3)(x - 2)
x = 0, 2, 3
Multiplying polynomials
f (x) = x2 + 3x - 2 and g(x) = 2x2 - 7x…read more

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Maths Notes- Core 1
b
(xa) = xab
x0 = 1
x-a = x1a
m n
x n = xm
Transformation of Graphs
Translations
Horizontal Left y = f (x + a)
Right y = f (x - a)
Vertical Up y = f (x) + a
Down y = f (x) - a
9…read more

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Maths Notes- Core 1
Stretches
Horizontal y = f (ax)
a>1 compress
a<1 stretch
Vertical y = af (x)
a>1 stretch
a<1 compress
Reflection
In x-axis y =- f (x)
In y-axis y = f (- x)
Sequences
Sequences can have a pattern or be random. Sequences are a set of numbers in an order.…read more

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