Cambridge International Mathematics

Discovery 2 Graphs of simple exponential functions #endboxedheading This discovery is best done using a graphing package or grap ...

x ¡ 3 ¡ 2 ¡ 1 0 1 2 3 y 4aComplete the table of values shown for the function f(x)=3x. b Use the table of values inato graph y=f ...

Since f(x)=ax is a one-one function, if ax=ak then x=k. If the base numbers are the same, we canequate indices. Example 4 Self T ...

SOLVING EXPONENTIAL EQUATIONS GRAPHICALLY In many exponential equations we cannot easily make the base numbers on both sides the ...

EXERCISE 28C.2 1 Solve forx, giving answers correct to 3 decimal places: a 2 x= 100 b 2 x=0: 271 c 2 x=¡ 3 d 5 x=8 e 7 ¡x=23 f 9 ...

Example 8 Self Tutor The currentIflowing through the electric circuit in a fan,tmilliseconds after it is switched off, is given ...

3 In Uganda, the number of breeding females of an endangered population of gorillas isG 0. Biologists predict that the number of ...

InChapter 22we were given data for two related variablesxandy, and we used technology to find aline of best fit y=ax+b to connec ...

EXERCISE 28E 1 Show that an exponential model is appropriate for the following data, and state the equation of the exponential m ...

7 Findkandngiven that k£ 2 n= 144 and k£ 8 n=9: 8 Solve forx, correct to 2 decimal places: a 5 x=90 b 3 ¡^2 x=0: 05 c 20 £ 20 :^ ...

Further trigonometry 29 Opening problem A triangular property is bounded by two roads and a long, straight drain. Can you find: ...

Example 1 Self Tutor a State the exact coordinates of: i A ii B b Find the coordinates of: i A ii B correct to 3 decimal places. ...

a angle AOP= (180o¡μ) biPis(cos(180o¡μ),sin(180o¡μ)) ii Pis(¡cosμ,sinμ) c cos(180o¡μ)=¡cosμ and sin(180o¡μ) = sinμ d tan(180o¡μ) ...

IMPORTANT TRIGONOMETRIC RATIOS IN THE UNIT CIRCLE InChapter 15we found the trigonometric ratios for the angles 0 o, 30 o, 45 o, ...

a sin 60o= p 3 2 cos 60o=^12 tan 60o= p 3 2 1 2 = p 3 b sin 150o=^12 cos 150o=¡ p 3 2 tan 150o= 1 2 ¡ p 3 2 =¡p^13 c sin 225o=¡p ...

For the obtuse angled triangle ABC alongside: Area of triangle ABC=^12 £AB£CN=^12 ch But sin(180o¡A)= h b ) h=bsin(180o¡A)=bsinA ...

2 Find the area of a parallelogram with sides 6 : 4 cm and 8 : 7 cm and one interior angle 64 o. 3 If triangle ABC has area 150 ...

FINDING SIDES Example 5 Self Tutor Find the length of side BC correct to 2 decimal places: Using the sine rule: BC sin 113o = 18 ...

Example 6 Self Tutor Find, correct to 1 decimal place, the measure of angleCin triangle ABC if AC=8cm, AB=12cm, and angleBmeasur ...

EXERCISE 29C.2 1 Find the value ofμ: abc 2 Solve forx: abc de f 3 In triangle ABC, find the measure of: a angleAif a=12: 6 cm, b ...