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4 x+3 = 4×x+4×3 Examples where V = final velocity, a = acceleration, u = initial velocity, and t = time taken; u = 30 m/s, a = 2 m/s2 , and t = 8 seconds. v can be calculated as follows: = 4x + 12 −3 4x − 2 = −12 x + 6 v = 30 + 2 × 6 Multiplying two binomial expressions in brackets v = 30 + 12 because multiplying is done before adding An expression such as a +b a +2 means a +b multiplied by a + 2 . 3 The diagram example shows how this type of situation is dealt with. 2 s= u+v t 2 In this case, s = distance covered, u = initial velocity, v = final velocity, t = time taken; u = 10 m/s, v = 60 m/s, and t = 20 seconds.

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.

14 The mean (average) test score for 20 vehicle technicians who had just completed a 5 day course on automatic transmission systems was 72. The test scores were found to be normally distributed and the standard deviation worked out at 5 marks. Between what number of marks might one expect to find 68% of the scores? Solution The upper mark is 72 + 5 = 77. The lower mark is 72−5 = 67. Frequency Mean 68% of cases – 1 STD + 1 STD Fig. 9 The normal curve and two standard deviations – (b) Fig. 10 (a) and (b) Skewness Measures of skewness and the effect on samples When the frequency distribution is perfectly symmetrical, the mean, median and mode coincide.