Higher Maths

• • The set N contains...
  • Natural numbers; numbers you can count with (1,2,3...)
• • The set N is a subset of W, which is a subset of Z, which is a subset of Q,...
  • True
• • The set R contains...
  • Real numbers; all points on the number line (rational numbers and irrational numbers, such as p...
• • The set Q contains...
  • Rational numbers; numbers which can be written as fractions of integers (-3, 1/3, 0.25, -1/2)
• • The set Z contains...
  • Integers; positive and negative whole numbers (...-2,-1,0,1,2...)
• • The set W contains...
  • Whole numbers; natural numbers and zero (0,1,2,3...)
• • The empty set has...
  • no elements
• • A is a subset of B if...
  • all of the objects in A are also in B
• • A set is...
  • a collection of objects (usually numbers)
• • The three angle bisectors of a triangle are concurrent
  • True
• • The three perpendicular bisectors in a triangle are concurrent
  • True
• • The three altitudes of a triangle are concurrent
  • True
• • The three medians of a triangle are concurrent
  • True
• • Lines are concurrent when...
  • there is a point which they all pass through
• • A perpendicular bisector is a line...
  • which cuts through the midpoint of a line at right-angles
• • An altitude of a triangle is a line...
  • through a vertex and perpendicular to the opposite side
• • A median of a triangle is a line...
  • through a vertex and the midpoint of the opposite side
• • The gradient of the line with equation y = mx + c is...
  • m
• • A line parallel to the x-axis and crossing the y-axis at point c has the eq...
  • y = c
• • A line parallel to the y-axis and crossing the x-axis at point k has the eq...
  • x = k
• • A straight line through the point (a,b) with gradient m has the equation...
  • y − b = m(x − a)
• • The general form of the 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 a...
• • 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 (un...
• • Lines are perpindicular when...
  • they are at right-angles to each other
• • Points are proven to be collinear when...
  • the gradient between the first and second points is the same as the gradient between the second...
• • Points which are collinear are..
  • on the same straight line
• • Lines are parallel when they have...
  • the same gradient
• • The gradient of a line parallel to the y-axis is...
  • undefined
• • Lines with a gradient of zero are...
  • parallel to the x-axis (flat)
• • Lines with negative gradients slope...
  • down; from left to right
• • Lines with postive gradients slope...
  • up; from left to right
• • 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...