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 […]

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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 […]

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Compounded Fractions and Percentages

Some fractions and percentage questions need to be read and well understood. Typical of these are questions that require you to find fractions or percentages of things and then fractions or percentages of the remainder. Example: If I start with £50, spend 20% of this on sweets and 30% of the remainder on a train […]

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Problem Solving I

Problem solving may involve interpreting a real situation, representing it mathematically and finding an equation to solve. Other problems may involve fractions, percentages, ratios and probabilities all mixed up in so many different ways. Whatever the problem, you have to start by understanding it. Because of the variety of questions that can be asked, the […]

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Number Sequences and Shapes

Number sequences and certain shapes are closely intertwined. Consider the number sequence 1, 3, 6, 10… The nth term of this number sequence isWe can picture the number sequences as triangles made up of dots. The nth triangle number is the number of dots in the nth triangle. Similarly, consider the number sequence 1, 4, […]

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Rational and Irrational Numbers

A rational number is any number that can be written as a fraction, one whole number divided by another. are all rational. Many decimals are rational too. If they only have so many decimal places then they are rational because they be written as something over 1 followed by some zeroes. For example 0.9786 is […]

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Advanced Indices

Advanced indices questions may take several forms. One of these may require you to compare the magnitude of different expressions. For example: Ifarrange in order of magnitude Ifthenincreases with increasingso a bigger value ofmeans a bigger value of Note thatand(1) Since we have Ifarrange in order of magnitude Ifthendecreases with increasingso a bigger value ofmeans a […]

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Simple Proofs

Simple proofs often involve simple manipulation of formulae or expressions. Proving an identity is often quite simple, and often shows several examples as an aid. For example The sum of any four consecutive numbers is equal to the product of the largest two minus the product of the smallest two. and and and A general […]

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Percentages, Decimals and Fractions

Percentages, fractions and decimals are essentially the same idea in different forms. A fraction is one whole number divided by another whole number eg.2 over 5, and so is a percentage, except that the denominator is always 100 eg. 40%=40 over 100. To change any fraction or percentage into a decimal we actually carry out […]

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Lowest Common Multiple (LCM) of Two Numbers

The lowest common multiple of two numbers is the smallest number that both numbers divide, as opposed to the highest common factor, which is the smallest number that both numbers divide. DON’T GET CONFUSED! Highest Common Factor (HCF) – Largest number that divides two numbers. Lowest Common Multiple (LCM) – Smallest number that two numbers […]

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