Higher maths

40 cards·by braineos

highersmaths

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natural numbers are

numbers you can count with (1

lines with postive gradients slope

up from left to right

lines with negative gradients slope

down from left to right

lines are parallel when they have

the same gradient

lines with a gradient of zero are

parallel to the x-axis (flat)

the gradient of a line parallel to the y-axis is

undefined

the gradient of a line is equal to

the change in height divided by the change in horizontal distance (y2-y1 / x2-x1) or the tan of the angle between the gradiated line and the

lines are proven to be perpindicular when

the gradient of the first line multiplied by the gradient of the second line is equal to -1 (unless the lines are parallel to the axes)

general form of equation of a straight line is

ax + by + c = 0; where (a,b) is a point on the line and c is the height it crosses the y-axis at)

natural numbers are

numbers you can count with (1

lines with positive gradients slope

up from left to right

lines with negative gradients slope

down from left to right

lines are parallel when they have

the same gradient

lines with a gradient of zero are

parallel to the x-axis (flat)

the gradient of a line parallel to the y-axis is

undefined

the gradient of a line is equal to

the change in height divided by the change in horizontal distance (y2-y1 / x2-x1) or the tan of the angle between the gradiated line and the

lines are proven to be perpindicular when

the gradient of the first line multiplied by the gradient of the second line is equal to -1 (unless the lines are parallel to the axes)

general form of equation of a straight line is

ax + by + c = 0; where (a,b) is a point on the line and c is the height it crosses the y-axis at)

A line parallel to the y-axis and crossing the x-axis at point k has the equation

x = k

the gradient of the line with equation y = mx + c is

lines are concurrent when

there is a point which they all pass through

points which are collinear are

on the same straight line

points are proven to be collinear when

the gradient between the first and second points is the same as the gradient between the second and third points

lines are perpendicular when

they are at right-angles to each other

a line parallel to the x-axis and crossing the y-axis at point c has the equation

y = c

the three altitudes of a triangle are concurrent

true

the three angle bisectors of a triangle are concurrent

true

median of a triangle is a line

through a vertex and the midpoint of the opposite side

altitude of a triangle is a line

through a vertex and perpendicular to the opposite side

three medians of a triangle are concurrent

true

the three perpendicular bisectors in a triangle are concurrent

true

a set is

a collection of objects (usually numbers)

A is a subset of B if

all of the objects in A are also in B

an empty set has

no elements

set R contains

real numbers; all points on the number line (rational numbers and irrational numbers, such as pi and the square root of 2)

set W contains

whole numbers; natural numbers and zero (0

set Z contains

integers; positive and negative whole numbers (...-2

set Q contains

rational numbers; numbers which can be written as fractions of integers (-3, 1/3, 0.25, -1/2)

the set N is a subset of W, which is a subset of Z, which is a subset of Q, which is a subset of R

true

a perpendicular bisector is a line

which cuts through the midpoint of a line at right-angles