Higher Maths

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The gradient of a horizontal line is...

0

What are the objects in a set referred to as?

Elements. Eg. 7 is an element of S. We can write this using a symbol that looks like £

What techniques can be used when finding x and y where two lines intersect?

Elimination, equating or substitution

What is a subset?

Given two sets, A and B, we say A is a subset of B if all elements of A are also elements of B

A line is a tangent in a circle if....

It intersects the circle at only one point

f(x+a)

Moves graph left or right. Left if positive, right if negative.

f(x)+a

Moves graph up or down. Up if a is positive, down if a is negative.

To convert from radians to degrees

Multiply by 180 and divide by pi

To convert from degrees to radians

Multiply by pi and divide by 180

The gradient of a line sloping downwards will be...

Negative

b^2-4ac<0

No real roots.

Two lines at right angles to each other are...

Perpendicular

The gradient of a line sloping upwards will be...

Positive

-f(x)

Reflects graph in x axis.

f(-x)

Reflects graph in y axis.

b^2-4ac>0

Roots are real and distinct.

b^2-4ac=0

Roots are real and equal.

f(kx)

Scales the graph horizontally.

kf(x)

Scales the graph vertically.

(p-a)^2 + (q-b)^2 = r^2

The point lies on the circumference of the circle

If perpendicular lines have gradients m1 and m2 then...

m1 x m2 = -1

What relationship to degrees and radians have?

pi radians = 180 degrees

To find roots of a quadratic equation we can:

1. Factorise. 2. Complete the square. 3. Use the quadratic formula.

What is a set?

A collection of objects, usually numbers

What is a function?

A function relates a set of inputs to a set of outputs. The set of inputs is called the domain and the resulting set of outputs is called the range

A median of a triangle is...

A line through a vertex and the midpoint of the opposite side

An altitude of a triangle is...

A line through a vertex, perpendicular to the opposite side

A perpendicular bisector is...

A line which cuts through the midpoint of a line segment at right angles

What is a radian?

A unit used to measure angles

Points which lie on the same straight line are...

Collinear

A straight line and a circle can have.....points of intersection

Two, one or no points of intersection

The gradient of a vertical line is...

Undefined

What are restrictions on the domain?

You cannot divide by 0 so in functions involving fractions the domain must exclude numbers which would give a denominator 0

The discriminant

b^2-4ac

(p-a)^2 + (q-b)^2 > r^2

The point lies outwith the circle

(p-a)^2 + (q-b)^2 < r^2

The point lies within the circle


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