# Archive | Algebra

## How Many Times Does a Wheel Turn When Travelling One Kilometre

If you take a cotton reel and hold the end of the cotton, then you roll the reel across the ground, the cotton will unwind from the reel. Each time the reel turns once, the length of cotton unrolled is equal to the circumference of the reel. The same holds for a bicycle or car […]

## Simultaneous Equations With One a Quadratic

When solving ordinary – linear – simultaneous equations we multiply the equations by constant factors to make the coefficient of some variable the same in magnitude, then add or subtract the equations to eliminate that variable. For example, solve  (1)  (2) (1)*2-(2)*3 eliminatesto give Substitution of this value ofinto (1) to find a gives If […]

## When Hour and Minute Clock Hands Coincide

The hour and minute hands of a clock coincide at midday and midnight. At one am and one pm, they do not coincide because the minute hand has made one complete turn but has to make just over one complete turn to coincide with the hour hand again. One compete turn is 360 degrees, so […]

## Solving Sine Equations for More Than One Solution

To solve the equationinvert both sides, obtaining This is not the only the solution. There are an infinite number of solutions. Typically though, we want solutions in the range 0° – 360°. We can use the sine curve below to find the solutions. Draw the horizontal line y=0.2 (because the equation to solve is sin x […]

## Proof of Formula for the Area of a Triangle

A triangle doesn’t need to be right – angled for the area to be easily found. For the triangle – not rightangled, equliateral or isosceles – labelled as below, The area is calculated from To prove this formula, draw a line from B to meet the line AC (the side labelled b) at right angles. […]

## The Ambiguous Case

The ambiguous case arises when using the Sine Rule to find an angle in a triangle. It occurs because the Sin function is symmetric about 90°, so that When we solve forthere is an acute solution,and an obtuse solution, Example: Find the angle A in the triangle below. The Sine Rule states Then This is […]

## The Difference Between an Expression, an Equation and a Formula

Many students get confused between anything in algebra involving‘s. Anything without an equals sign is an expression. are all expressions. The aim is always to simplify expressions. Anything with an equals sign containing x’s and no other letters, or containing more than two letters with no letter being the subject is an equation. are all […]

## Simple Interest

If you put money into a bank account, the bank will normally pay interest on the money in your account. If the interest is simple interest, then the yearly amount of interest will be calculated on the original deposit. This is unlike compound interest, for which the amount of interest is calculated on the balance […]

## Directed Numbers

Directed numbers are inequalities that describe a set of numbers. The inequalities may be represented on a number line. The diagram below represents the inequalityThe filled in black circle atindicates that 2 satisfies the inequality. The diagram below represents the inequalityThe white filled in circle atindicates thatdoes not satisfy the inequality. The above examples illustrate […]