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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…

Page 2

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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




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Page 3

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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…

Page 4

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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.3



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Page 5

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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…

Page 6

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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…

Page 7

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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.1 x2 - kx + 2k = 0




Polynomials

A polynomial has terms which are powers of x…

Page 8

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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…

Page 9

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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 =…

Page 10

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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…

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