Lapping Racing Drivers

Good – or more dangerous – racing drivers are faster than other racing drivers. Towards the end of a race, the slower drivers may find themselves being lapped by other racing drivers who have completed one more circuit than they have. If the speeds of the racing drivers areandwithon a circuit ofmiles, how long will […]

Continue Reading

Rules of Inequalities

In order to solve inequalities, we have to simplify them. In simplifying inequalities, we have to observe four rules. 1. If we add or subtract the same number to both sides of an inequality, the inequality sign is maintained, i.e.and Example: Ifthen 2. If we multiply or divide both sides by a positive number the […]

Continue Reading

Proof of Pythagoras Theorem

The above diagrams represent rearrangements of sets of shapes. The blue triangles are all right angled, with the right angles at the corners of the yellow square, and congruent so all have the same area and the yellow squares are congruent so have the same area. We can find the area of the square on […]

Continue Reading

Speeds – There and Back

Travelling to some place and back again might involve travelling twice the distance of only travelling there, but might well not mean taking twice as long. Going in one direction might mean travelling uphill or going against the wind or travelling in rush hour, meaning that this part of the total journey takes longer. To […]

Continue Reading

Solving Equations Involving Algebraic Fractions

An algebraic fraction is any expression with fraction which include x terms in numerator and/or denominator. If this expression is equal to something then typically we can solve it by reararranging the fraction into a linear or quadratic equation and solving. For example, ifthen we can multiply both sides byto clear the fraction, obtaining Expanding […]

Continue Reading

Problem Solving II

More advanced problem solving questions involve simultaneous equations or quadratics. Example: The height of a rectangle is 2 cm longer than the base. If the area is 48 cm2 find the length of the base. If the base isthe height is The area isand equating this to 48 givesExpanding the brackets and subtracting 48 gives […]

Continue Reading