Not all graphs are straight lines or quadratic (such as) graphs. Other common graphs are shown below. Graph Equation Positive gradient of 2 and a– intercept of 1. Negative gradient of -2 and a– intercept of 1. ‘Happy’ quadratic with equation ‘Sad’ Quadratic curve with equation Reciprocal curve with equation Reciprocal Curve with equation Cubic […]

# Archive | Notes

## Angles of Elevation and Depression

The angle of elevation of an object is the angle a line of sight to the object makes above the horizontal, and the angle of depression is the angle of a line of sight to the object below the horizontal. We can find angles of elevation or depression using simple trigonometry. Consider the diagram below. […]

## Finding the Locus of Points Equidistant From Two Given Points

Intuitively the set of points equidistant from two given points is the set of points halfway between them. The locus will be a straight line halfway between the two points. We can construct this line by drawing circles of equal radius centred at A and B. The radius should be over half the distance AB. […]

## The Hours, Minutes and Seconds Calculator Button

Many modern calculators have a special button for converting hours, minutes and seconds into hours written as a decimal, and vice versa. The button is useful for calculating speeds in miles per hour when the time is given in terms of hours, minutes and seconds. Suppose a car travels 100 miles in 2 hours 15 […]

## Bisecting an Angle

We can bisect an angle using only compasses. Put the point of the compass at O and draw arcs that crosses both lines that constitute the angle. From each point where an arcs just drawn cross a line construct other arcs to cross as shown. Now draw a line from O to where the two […]

## Angles and Straight Lines

Opposite angles are equal Alternate angles when a line is drawn to intersect parallel lines are equal. To recognise when this rule can be used look for ‘Z’ shapes. Supplementary or complementary angles when a line is drawn to intersect parallel lines add to 180 Degrees, soAgain look for ‘Z’ shapes. The supplementary angles are […]

## Prime Numbers

A number is a prime number if the only numbers which divide it are 1 AND the number itself. This means that every prime number has two numbers that divide it. 1 is not a prime number cos the only number that divides 1 is 1. The prime numbers less than 100 are 2, 3, […]

## Bisecting a Line

To bisect a line AB, or cut it in half, we need to draw a line through the middle of the line AB, perpendicular to AB. We use a compass. Put the needle at A, open the compass to more that half the distance of the line AB and draw an arc through the line. […]

## Graphical Inequalities

Often we have to solve simultaneously equations of the form We start be sketching the linesThe result is shown below. We want the region whereThis is above the line WhereThis is below the line WhereThis is below the line The result is the two regions labelledin the diagram below, which satisfies all three inequalities.

## Gradients and Equations of Lines

The general equation of a line may be wriiten as (1) where m is the gradient andis the– intercept, or whereis again the gradient. We may be asked: Find the equation of the line which passes through the two pointsand we have to find the gradient We can then use either equation (1) in which […]