Cambridge International Mathematics

Example 4 Self Tutor Consider y= x^4 5 . State which two variables are directly proportional and determine the proportionality c ...

IfTis the period andlis the length, then T/ p l. a l 25 70 T 1 : 00 lis multiplied by^7025 ) p l is multiplied by q 70 25 ) T is ...

3 State which two variables are directly proportional and determine the proportionality constantk: a A=4: 9 t^2 b K=2x^3 c T= p ...

If two painters can paint a house in 3 days, how long would it take four painters working at the same rate to paint the house? T ...

Example 8 Self Tutor Consider the table: x^12345 y 24 12 8 6 4 : 8 Explain why the variablesxandyare inversely proportional. xan ...

Method 2: V/ 1 t t 280 V 40 50 V is multiplied by^5040 =^54 ) 1 t is multiplied by^54 fas V/ 1 t g ) tis multiplied by^45 ) t= 2 ...

8 Consider gas trapped inside an airtight cylinder. For a given mass of gas kept at a constant temperature, the volume is invers ...

Discussion Possible models #endboxedheading abc In some cases, we know what type of variation exists. We use the data values giv ...

Example 12 Self Tutor A small glass ball is rolled down a sloping sheet of hard board. At timetseconds it has rolled a distanced ...

EXERCISE 30C 1 Find the variation model for these data sets: a x^12345 y 4 32 108 256 500 b x 1 214 4 9 y 3 412 6 9 c x 1 2 3 4 ...

v 10 20 30 40 R 0 : 5 4 13 : 5 32 7 The designer of a car windscreen needs to find the relationship between the air resistanceRa ...

Example 14 Self Tutor Gravity is the force of attraction which exists between any two objects in the universe. The force of attr ...

Mass (mkg) 0 : 02 0 : 5 4 20 50 100 500 Heat required (hJoules) 25 170 630 1670 2500 4200 16 750 a Obtain a power model for this ...

What to do: 1 Which of the following ideas have merit when finding the period of the pendulum for a particular length? ² Several ...

b What features of the graph suggest that D= k p p is an appropriate model for the data? c Determinek. d FindD, correct to 1 dec ...

Challenge #endboxedheading 9 The diameter of a scallop is measured at regular intervals of 3 months. The results were: Age(nquar ...

Logarithms 31 Contents: A Logarithms in basea [3.10] B The logarithmic function [3.10] C Rules for logarithms [3.10] D Logarithm ...

For example, since 8=2^3 we can write 3 = log 28. The two statements ‘ 2 to the power 3 equals 8 ’ and ‘the logarithm of 8 in ba ...

Thelogarithmic functionis f(x) = logaxwhere a> 0 , a 6 =1. Consider f(x) = log 2 x which has graph y= log 2 x. Since y= log 2 ...

Example 3 Self Tutor Find the inverse function f¡^1 (x) for: a f(x)=5x b f(x) = 2 log 3 x a y=5x has inverse function x=5y ) y= ...