Provice of the ESTERN CPE EDUCTION NTIONL SENIOR CERTIFICTE GRDE SEPTEMBER 0 MTHEMTICS P3 MRKS: 00 TIME: hours This questio paper cosists of 0 pages, formula sheet ad 5 diagram sheets.
MTHEMTICS P3 (SEPTEMBER 0) INSTRUCTIONS ND INFORMTION Read the followig istructios carefully before aswerig the questios.. This questio paper cosists of 0 questios. swer LL the questios.. Clearly show LL calculatios, diagrams, graphs, et cetera, which you have used i determiig your aswers.. 3 approved scietific calculator (o-programmable ad o-graphical) may be used, uless stated otherwise. 4. If ecessary, aswers should be rouded off to TWO decimal places, uless stated otherwise. 5. Number the aswers correctly accordig to the umberig system used i this questio paper. 6. Diagrams are NOT ecessarily draw to scale. 7. It is i your ow iterest to write legibly ad to preset work eatly. 8. FIVE diagram sheets for aswerig QUESTION 4.., QUESTION 6. ad Questios 7 to 0 are attached at the ed of this questio paper. Write your NME/EXMINTION NUMBER i the spaces provided ad had them i together with your NSWER BOOK.
(SEPTEMBER 0) MTHEMTICS P3 3 QUESTION The recursive formula for T k+ of a particular sequece is T k+ = T k + 4k where T = ad k.. Determie the first FOUR terms of the sequece. (3). Hece determie the explicit formula for the th term of the sequece i the form T =... (4) [7] QUESTION The circulatio of a popular ewspaper s mothly sales i the Easter Cape rose by,5% to 36 600 sales for the moth of May, partly because of good report writig ad profitable advertisig.. If the sales rose to 36 600 i May 0, how may ewspapers were sold the previous moth of pril 0? (). If the sales of the ewspaper rose to 4 000 i Jue 0, what was the percetage icrease for the moth of Jue 0? ().3 If the shareholders of the ewspaper demad 37 000 sales o average per moth, would you say that the ewspaper sales for the term pril to Jue 0 meet the demads set by the shareholders? Support your aswer with appropriate calculatios. () [6] QUESTION 3 The IQ scores for a geeral populatio are ormally distributed with a mea of 00 ad a stadard deviatio of 5. If this model is applicable to a populatio of 48 000 000 people... 3. How may people will have a IQ score above 5? () 3. How may people will have a IQ score below 30? () 3.3 What percetage of the populatio ca be regarded as highly itelliget? () 3.4 If a sample of 4,8 millio people were tested for IQ scores, are the above results valid ad reliable? Support your aswer with appropriate calculatios. () [8]
4 MTHEMTICS P3 (SEPTEMBER 0) QUESTION 4 4. Give: P() = 0,4 P(B) = 0,5 P(B) = 0,7 4.. Represet the data by usig a Ve diagram. (3) 4.. re evets ad B mutually exclusive? Support your aswer with appropriate calculatios. (3) 4..3 re evets ad B idepedet? Support your aswer with appropriate calculatios. (4) 4. survey is coducted amogst 300 schools i Regio X i the Easter Cape. The ages ad qualificatios of 3004 teachers are surveyed. The table below shows the results of the survey. ges 30 30 39 40 49 50 TOTLS Qualificatios 3 year, professioal 4 year, professioal Degree, professioal Higher degree, professioal Degree, o professioal TOTLS 5 5 0 43 337 3 66 578 98 45 7 37 3 55 45 5 4.. Complete the above table o DIGRMSHEET. () 4.. What is the probability that a teacher is uder the age of 40? () 4..3 What is the probability that a teacher is uder the age of 40 ad at least has a degree with a professioal qualificatio? () 4..4 What is the probability that a teacher has o degree? () 4..5 What is the probability that a teacher is over the age of 40 ad has o degree? () 4..6 re the ages ad the qualificatios of the teachers youger tha 30 years ad havig a 4 year professioal qualificatio mutually exclusive? Motivate your aswer with appropriate calculatios. (3) [3]
(SEPTEMBER 0) MTHEMTICS P3 5 QUESTION 5 5. libraria wats to classify 75 000 books i her library. systems desiger is asked to desig a ivetory system to idetify each book. Each umber uses oe capital letter followed by a series of digits (digits may repeat ad the digits from to 9 are allowed). example of such a book is X 3... How may digits must be used to esure that each book has a uique umber? (4) 5. court eeds both a frikaas ad isixhosa iterpreter for each court case. 5.. pair of iterpreters is to be selected from a group of eight people cosistig of FIVE frikaas speakers ad THREE isixhosa speakers. How may differet pairs of iterpreters ca be selected? () 5.. If all EIGHT people ca both speak frikaas ad isixhosa, how may pairs of iterpreters ca be selected? () [7]
6 MTHEMTICS P3 (SEPTEMBER 0) QUESTION 6 fter watchig a TV commercial o healthy livig, TEN teachers of a rural school decided to put themselves uder a strict diet ad rigorous exercises. The table below show the relatioship betwee their body mass (i kg) ad their waist lie (i cm) after six weeks. Body mass i kg 3 50 7 35 84 87 54 38 35 Waistlie i cm 3 06 99 04 98 05 96 89 4 04 6. Use DIGRM SHEET ad draw a scatter plot of the data. () 6. State the relatioship that you observe from your scatter plot betwee the body mass ad the waistlie. () 6.3 Determie the correlatio coefficiet correct to THREE decimal places. () 6.4 Use your calculator to calculate the least squares regressio lie, y = a + bx correct to ONE decimal place. (3) 6.5 Use the lie of best fit to predict the waist lie of a teacher who weighs 60 kg after six weeks. () 6.6 Use the equatio of the least squares regressio lie to predict the waistlie of a teacher whose body mass is 00 kg after six weeks. () []
(SEPTEMBER 0) MTHEMTICS P3 7 QUESTION 7 7. I the figure below BCD is a cyclic quadrilateral. Prove the THEOREM that states that the opposite agles of a cyclic quadrilateral are supplemetary ( + = 80 ). C B D [5]
8 MTHEMTICS P3 (SEPTEMBER 0) QUESTION 8 8. I the figure below O is the cetre of the circle, = 0 ad B = 55. B 3 0 0 C O 55 0 D Determie with reasos: 8.. () 8.. O D (4) 8. The figure below shows that TP ad TQ are tagets to the circle PQR, T Q = x ad RQ ST. P x S 3 T R Q 3
(SEPTEMBER 0) MTHEMTICS P3 9 8.. Name with reasos, THREE other agles i the give figure each equal x. (3) 8.. Prove that TPSQ is a cyclic quadrilateral. (3) 8..3 Hece or otherwise prove, that is bisected by TS. () 8..4 Hece or otherwise prove, that RQS is a isosceles triagle. () [6] QUESTION 9 I the figure DCFG is a cyclic quadrilateral; B is a taget ad FG E. E G F D C B Prove, statig reasos, that: 9. B = D.C (3) 9. CE /// ED (3) 9.3 B = E (3) [9]
0 MTHEMTICS P3 (SEPTEMBER 0) QUESTION 0 I the figure below E = EC, B = 3D, DE FC. D F E C B Determie with reasos: 0. () 0. () 0.3 if D = x (3) 0.4 (3) [8] TOTL: 00
(SEPTEMBER 0) MTHEMTICS P3 INFORMTION SHEET: MTHEMTICS b b 4 ac x a P( i) P( i) P( i) P( i) i F f x i i i f ( x h) f ( x) '( x) lim h 0 h ( ) i S a r r ( ) ( ( ) ) ; r ; r x[ ( i) ] P i d ( x ) ( ) x y y M x x y y ; y mx c y y m x ) x a y b r I BC: si a ( x y y m m ta x x b c a b c bc. cos area BC ab. si C si B si C si si.cos cos.si cos si si.cos cos.si cos.cos si. si cos cos.cos si. si cos si cos si si si. cos cos ( ) ( ) ( ) ( ) xi x i fx x ( ) P( ) P ( of B) = P () + P (B) P ( e B) y a bx S b x x y y x x
MTHEMTICS P3 (SEPTEMBER 0) NME/EXMINTION NUMBER: DIGRM SHEET QUESTION 4.. ges Qualificatios 3 year, professioal 4 year, professioal Degree, professioal Higher degree professioal Degree, o professioal 30 30 39 40 49 5 5 0 43 337 3 66 578 98 45 7 37 3 55 45 5 50 TOTLS TOTLS QUESTION 6. 60 Waistlie after 6 weeks 40 0 00 80 60 40 0 0 0 0 40 60 80 00 Weight after 6 weeks 0 40 60
(SEPTEMBER 0) MTHEMTICS P3 3 NME/EXMINTION NUMBER: DIGRM SHEET QUESTION 7 C B D
4 MTHEMTICS P3 (SEPTEMBER 0) NME/EXMINTION NUMBER: DIGRM SHEET 3 QUESTION 8. B 3 0 0 C O 55 0 D QUESTION 8. P x S 3 T R Q 3
(SEPTEMBER 0) MTHEMTICS P3 5 NME/EXMINTION NUMBER: DIGRM SHEET 4 QUESTION 9 E G F D C B
6 MTHEMTICS P3 (SEPTEMBER 0) NME/EXMINTION NUMBER: DIGRM SHEET 5 QUESTION 0 D F E C B