Higher Maths
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
