NATIONAL SENIOR CERTIFICATE GRADE 12
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1 NATIONAL SNIOR CRTIFICAT GRA MATHMATICS P3 XMPLAR 008 MARKS: 00 TIM: hours This questio paper cosists of 9 pages, diagram sheets ad a formula sheet. Please tur over
2 Mathematics/P3 o/xemplar 008 INSTRUCTIONS AN INFORMATION Read the followig istructios carefully before aswerig the questios This questio paper cosists of 9 questios. Aswer ALL the questios. Clearly show ALL calculatios, diagrams, graphs, et cetera, which you have used i determiig the aswers. A approved scietific calculator (o-programmable ad o-graphical) may be used, uless stated otherwise. If ecessary, aswers should be rouded off to TWO decimal places, uless stated otherwise. Number the aswers correctly accordig to the umberig system used i this questio paper. iagrams are NOT ecessarily draw to scale. TWO diagram sheets for aswerig QUSTION 3.4, QUSTION 5. ad QUSTIONS 6 9 are attached at the ed of this questio paper. Write your ame/examiatio umber i the spaces provided ad had them i together with your ANSWR BOOK. It is i your ow iterest to write legibly ad to preset the work eatly. Please tur over
3 Mathematics/P3 3 o/xemplar 008 QUSTION A sequece is defied as follows: T = 5 ad T k+ = T k + 3 for k.. Write dow the first FIV terms of the sequece. (3). Write dow the formula for T i its simplest form. () [5] QUSTION The followig extract was take from a televisio ews report durig May 007. 'Traset bosses claim that a chage i drivig attitudes is ecessary to combat accidets at railway crossigs. Sixtyoe people were killed over the last three years i collisios ivolvig trais ad motor vehicles. 0 farm workers lost their lives i oe such accidet last year. A trai travellig at reasoable speed requires kilometres to come to a stop. I a survey carried out at the same site where the farm workers were killed, the reporter oted that i a two-hour period oly out of 0 vehicles stopped before crossig the railway lie, therefore cofirmig the claim made by the Traset bosses.'. Calculate the average umber of people killed aually i collisios ivolvig trais ad motor vehicles over the last three years. (). How does the accidet ivolvig the farm workers ifluece the average? ().3 Is the ews reporter's observatio valid? xplai. () [5] Please tur over
4 Mathematics/P3 4 o/xemplar 008 QUSTION 3 Mary is employed as a huma resources officer at a compay. She collected data o the hourly earigs of all o-salaried employees at her compay ad orgaised the data ito the followig table. Hourly earigs (rad) Number of wome Number of me 9,70 < 9, ,90 <0, ,0 <0, ,30 <0, ,50 <0, Calculate the mea for the hourly earigs for the me. (4) 3. Calculate the stadard deviatio for the hourly earigs for the me. (5) 3.3 As part of her aalysis, Mary also calculated the statistics for wome. They are: Mea: R0,5 Stadard deviatio: R0,5 Mary reached the coclusio that there was little differece i the hourly earigs betwee me ad wome. o you agree with Mary? xplai. () 3.4 raw a ogive (cumulative frequecy curve) for the hourly earigs for the me. (4) [5] Please tur over
5 Mathematics/P3 5 o/xemplar 008 QUSTION 4 4. A cadidate writes a accoutig examiatio ad a mathematics examiatio. The cadidate believes that he has a 40% chace of passig the mathematics examiatio, a 60% chace of passig the accoutig examiatio ad a 30% chace of passig both of them. What is the probability that the cadidate passes mathematics or accoutig or both? (3) 4. A box of 40 pocket calculators is set to a store. The ower of the store is ot aware that 5 of the pocket calculators are defective. Two pocket calculators are selected at radom from the box, the first oe ot beig replaced before the secod oe is selected. 4.. What is the probability that the first oe chose is NOT defective? () 4.. What is the probability that of the two pocket calculators selected, oe calculator is defective ad the other is ot? (4) 4..3 What is the probability that both the pocket calculators selected were defective? (3) 4.3 Four differet mathematics books ad three differet sciece books were left o the table. You eed to place these books o a shelf If you decide to place ay book i ay positio, i how may differet ways ca you arrage the books o the shelf? (3) 4.3. If two particular books must be placed ext to each other, i how may differet ways ca you arrage the books o the shelf? () If all the mathematics books must be placed ext to each other ad all the sciece books must be placed ext to each other, i how may differet ways ca you arrage the books o the shelf? (3) [0] Please tur over
6 Mathematics/P3 6 o/xemplar 008 QUSTION 5 The ower of Star Travel ad Tours compiled the followig data which illustrate the relatioship betwee the aual profit of the busiess ad its aual advertisig expediture (both i thousads of rad). Aual advertisig expediture (x) Aual profit (y) Plot a scatter diagram for the data. (3) 5. Calculate the equatio of the least squares lie for the data. (4) 5.3 raw the least squares lie for the data. () 5.4 Predict the aual profit if the aual advertisig expediture is R () 5.5 Calculate the correlatio coefficiet. (3) 5.6 What coclusio ca you reach about the stregth of the relatioship betwee the aual profit ad the aual advertisig expediture? () [5] QUSTION 6 6. I the figure below, Ê = 60. ABC is a straight lie. 6.. Calculate, with reaso, the value of x. (3) 6.. Prove that AC is a taget to the circle. () 60º A 3x x B x C Please tur over
7 Mathematics/P3 7 o/xemplar The diagram below shows a clockface. is joied to the 4 ad to the 7 with straight lies AB ad C respectively. O is the cetre of the clockface. A 0 9 O 3 8 C B 6.. If AO ad O are joied, show that A O ˆ = 60. () 6.. If CO ad BO are joied calculate C O ˆB. () 6..3 Hece, calculate Ê. (3) [] QUSTION 7 I the figure below F is draw with = 3t uits; F = (4t + ) uits ad F = (3t ) uits with t > 0. 3t 3t 4t + F 7. Which side of F is the logest side? Motivate your aswer. () 7. Now calculate the values of t for which F will be right-agled. (4) [6] Please tur over
8 Mathematics/P3 8 o/xemplar 008 QUSTION 8 I the sketch below, A ad B are tagets to the circle at A ad B. AF = FB. AB produced cuts the lie through, which is parallel to FB, at C. AF produced meets C at ad  = x. 3 C F 3 B A x 8. Fid, with reasos, 5 agles each equal to x. (5) 8. Prove that AB is a cyclic quadrilateral. () 8.3 Prove that A Bˆ = 3 Â. (3) 8.4 Prove that A = BC. (3) [3] Please tur over
9 Mathematics/P3 9 o/xemplar 007 QUSTION 9 I the figure below, MR bisects LK // MR // NP. L Rˆ N with M o LN. LRP ad NRK are straight lies ad K P R 4 3 L M N Prove that: 9. LR LM = (4) RN MN 9. KLNP is cyclic () 9.3 KLP MRN (3) [9] TOTAL: 00
10 Mathematics/P3 o/xemplar 008 NAM/XAMINATION NUMBR: IAGRAM SHT QUSTION QUSTION
11 Mathematics/P3 o/xemplar 008 NAM/XAMINATION NUMBR: IAGRAM SHT QUSTION 6 QUSTION 7 9 A 0 O 3t 3 3t 8 C B 4t + F QUSTION 8 3 C F 3 B A QUSTION 9 K P R 4 3 L M N
12 Mathematics/P3 o/xemplar 008 b ± x = b 4 ac a FORMULA SHT: MATHMATICS FORMULBLA: WISKUN A = P( + i) A = P( i) A = P( i) i= = A = P( + i) i= ( + ) i = ( a + ( i ) d ) = ( a + ( ) d ) i= i= ar x F = f i ( r ) a = r [( + i) ] i f ( x + h) f ( x) '( x) = lim h 0 h ; r i= a r i ar = ; < r < x[ ( + i) ] P = i d = ( x ) ( ) x + y y M x + x y + y ; ( x y = mx + c y y = m x ) y y m = m = taθ x x ( x a) + ( y b) = r I ABC: si a A b c = = a b c = + bc. cos A area ABC = ab. si C si B si C ( α + β ) = α β + α β ( ) si si.cos cos.si cos si α β = si α.cos β cos α.si β ( α + β ) = cosα.cos β siα. si β cos ( α β ) = cosα.cos β + siα. si β cos α si α cos α = si α si α = siα. cosα cos α ( ) = xi x fx i= x = ( A) P( A) = P(A or B) = P(A) + P(B) P(A ad B) S ( )
NATIONAL SENIOR CERTIFICATE GRADE 12
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