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By Allan Bonnick; NetLibrary, Inc

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10 Factorise nx + mx − yn − ym Rewrite the expression as nx + mx − yn + ym – the minus outside the bracket changes the sign of everything inside the bracket. This can now be reduced to x n + m − y n + m = n+m x−y . 6 Factorising Solving equations An expression such as 5x − 5y has two terms and 5 is common to both of them. 5 is therefore a common factor. A factor is defined as a common part of two or more terms that make up an algebraic expression. The expression 5x − 5y can be written as 5 x − y , and the factors of the expression are 5 and x − y .

Smoothed cumulative frequency graphs are known as ogives because of their shape. 100 90 Cumulative Frequency Relative frequency is the frequency of a class divided by the total frequency of all classes, and it is normally expressed as a percentage. For example, the table of heights of applicants for automotive training can be adapted to show relative frequencies. The percentage (relative) frequency is obtained by dividing each separate class frequency by the total number all frequencies. In this case the total number of frequencies of all classes is 100; the relative frequency of the class 66–68 is 42 so the relative frequency is 42 × 100/100 = 42%.

The friend earns £20 per week more. This may be expressed as a percentage as follows. 31 An engine that develops 120 kW is tuned to raise the power output to 145 kW. Calculate the percentage increase in power. 10 The binary system Arithmetic operations in systems that use computer logic are normally performed in binary numbers because the logic circuits for binary numbers are simpler than for other number systems. In binary numbers, each digit is multiplied by the appropriate power of 2. For example, binary 101 = 1 × 22 + 0 × 21 + 1 × 0 2 = 510 Hexadecimal numbers have a base of 16.

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