Related Angles Lines AB and CD are parallel to one another (hence the » on the lines). a and d are vertically opposite angles. Vertically opposite angles are equal. (b and c, e and h, f and g are also vertically opposite). g and c are corresponding angles. Corresponding angles are equal. (h and d,
Proportion If a is proportional to b, a µ b and a = kb, where k is a constant The value of k will be the same for all values of a and b. Example: If a µ b, and b = 10 when a = 5, find an equation connecting a and b. a
Standard form is a way of writing down very large or very small numbers easily. 10³ = 1000, so 4 × 10³ = 4000 . So 4000 can be written as 4 × 10³ . This idea can be used to write even larger numbers down easily in standard form. Small numbers can also be
If the ratio of one length to another is 1 : 2, this means that the second length is twice as large as the first. If a boy has 5 sweets and a girl has 3, the ratio of the boy’s sweets to the girl’s sweets is 5 : 3 . The boy has 5/3
A percentage is a fraction whose denominator is 100 (the numerator of a fraction is the top term, the denominator is the bottom term). So 30% = 30/100 = 3/10 = 0.3 To change a decimal into a percentage, multiply by 100. So 0.3 = 0.3 × 100 = 30% . Example: Find 25% of
Numbers can either be positive or negative. Often brackets are put around negative numbers to make them easier to read, e.g. (-2). If a number is positive, the + is usually missed out before the number. So 3 is really (+3). Adding and multiplying combinations of positive and negative numbers can cause confusion and so
Speed, Distance and Time The following is a basic but important formula which applies when speed is constant (in other words the speed doesn’t change): Speed = distance time Remember, when using any formula, the units must all be consistent. For example speed could be measured in m/s, distance in metres and time in seconds.
Equations of straight lines are in the form y = mx + c (m and c are numbers). m is the gradient of the line and c is the y-intercept (where the graph crosses the y-axis).
Finding the gradient of a straight-line graph It is often useful or necessary to find out what the gradient of a graph is. For a straight-line graph, pick two points on the graph. The gradient of the line = (change in y-coordinate)/(change in x-coordinate) . In this graph, the gradient = (change in y-coordinate)/(change in
a < b means a is less than b (so b is greater than a) a £ b means a is less than or equal to b (so b is greater than or equal to a) a ³ b means a is greater than or equal to b etc. a > b