MATHEMATICS: PAPER III (LO 3 AND LO 4) PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY

Size: px

Start display at page:

Download "MATHEMATICS: PAPER III (LO 3 AND LO 4) PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY"

Hilary Atkins
6 years ago
Views:

NATIONAL SENIOR CERTIFICATE EXAMINATION EXEMPLAR 008 MATHEMATICS: PAPER III (LO 3 AND LO 4) Time: 3 hours 100 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1.

1 NATIONAL SENIOR CERTIFICATE EXAMINATION EXEMPLAR 008 MATHEMATICS: PAPER III (LO 3 AND LO 4) Time: 3 hours 100 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This questio paper cosists of 16 pages icludig a page iformatio sheet. Please check that your paper is complete.. Read the questios carefully. 3. Aswer all the questios o the questio paper. There is extra space o the last page for additioal workig. Do ot had i ay other piece of paper. 4. You may use a approved o-programmable ad o-graphical calculator, uless otherwise stated. 5. Roud off your aswers to two decimal digits where ecessary. 6. All the ecessary workig details must be clearly show. 7. It is i your ow iterest to write legibly ad to preset your work eatly. IEB Copyright 008 PLEASE TURN OVER

2 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page of 16 SECTION A QUESTION 1 th 1.1 The geeral explicit form of the k term of a particular sequece is give by: Tk 5 4k. Determie the recursive formula for this sequece. (4) 1. The recursive formula for Tk + 1 of a sequece is give by: T where k Tk k T 1 5 Fid the explicit form of the sequece i the form: T ak + bk+ c k (5) [9] IEB Copyright 008

3 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 3 of 16 QUESTION All aswers usig factorials (!) must be evaluated, e.g. 4! 4.1 You have to choose a password for your ew 'Facebook' profile. The password must be of the format: ###@@ where # is ay digit (0's are NOT allowed) is ay of the vowels (a, e, i, o or u). You may repeat ay digit but you may ot repeat a vowel. How may differet passwords ca be formed? (4). The probability that a certai rugby team has all its players fit to play is 70%. The probability that they will wi a game if all their players are fit is 90%. Whe they are ot fit the probability of them wiig becomes 45%. Calculate the probability of them wiig their ext game. (6).3 How may arragemets of all the letters i the word 'EXEMPLAR' start with 'X' ad ed i 'P'? (4) [14] IEB Copyright 008 PLEASE TURN OVER

4 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 4 of 16 QUESTION 3 A compay has 13 employees workig i their Gauteg brach. The distace (x), i kilometres, they travel to work each day is summarised i the followig group frequecy table: Iterval Frequecy 0< x 5 1 5< x < x < x < x < x Determie the media iterval for this data. (1) 3. Determie the estimated mea distace covered. 3.3 Determie the stadard deviatio for the data. IEB Copyright 008

5 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 5 of Draw a ogive (cumulative frequecy curve) for this data o the axes give below. 140 y x Estimate the media distace usig your graph. (1) 3.6 By referrig to the relatioship betwee the mea ad the media, state whether the distributio of the data is ormal, positively skewed or egatively skewed. [14] IEB Copyright 008 PLEASE TURN OVER

6 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 6 of 16 QUESTION A ewspaper makes the followig statemet: 'Over 65% of the houses were sold this moth for more tha the average sellig price.' Commet o whether the word 'average' i this statemet could refer to: (a) (b) (c) the mea; the mode; or the media. Motivate your aswer. 4. A school aouces i its media release: 'The Grade 1 pass rate has improved by a 100% from last year.' Why is this statemet misleadig? () 4.3 Data was collected to compare the legth of time (x), i moths couples have bee datig to the amout of moey (y), i rads, spet whe goig out o a date. The equatio of regressio was determied to be: y 165 6,3x What does the slope of the lie tell us about the cost of a average date as the duratio of the relatioship icreases? () 4.3. Ca we use this lie to predict the cost of a date i a 3 year log relatioship? Motivate your aswer. () [9] IEB Copyright 008

7 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 7 of 16 QUESTION 5 The percetages achieved by 10 learers studyig Mathematics Core i Grade 11 were recorded. They the chaged to Mathematical Literacy i Grade 1 ad their results were recorded i the table below. Cadidate umber Mathematics Core Mathematical Literacy Draw a scatter plot of the data o the axes give. 100 y Mathematical Literacy Mathematics Core 5. Calculate the equatio of the regressio lie of best fit. (4) 5.3 Calculate the correlatio coefficiet for the data. () IEB Copyright 008 PLEASE TURN OVER

8 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 8 of Describe the stregth of the correlatio. () 5.5 Which cadidate appears to be a outlier? (1) 5.6 David wats to study a course at Uiversity that requires a Level 3 (40% - 50%) for Mathematics Core or a Level 7 (80% 100%) for Mathematical Literacy. He is curretly i Grade 11 ad achieved a Level (38%) o his latest report. Would you advise him to cotiue with Mathematics Core? Motivate your aswer. () [14] 60 marks IEB Copyright 008

PQR is a taget to the circle STVWQ. Give: S ˆ ˆ 30 ad W1 70. ST QW ad VT VW.

9 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 9 of 16 SECTION B REASONS TO BE GIVEN UNLESS OTHERWISE STATED QUESTION Refer to the give diagram. PQR is a taget to the circle STVWQ. Give: S ˆ ˆ 30 ad W1 70. ST QW ad VT VW. Determie the size of the followig: ˆ V 6.1. ˆQ 1 (1) ˆ T IEB Copyright 008 PLEASE TURN OVER

10 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 10 of Refer to the give diagram. I Δ AEG BD FE ad CD AE F C 4 B 3 G a D 8 b E A 6..1 Determie the value of a. () 6.. Determie the value of b. IEB Copyright 008

NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 11 of 16 6.

C, the cetre of the smaller circle, lies o the circumferece of the larger circle.

11 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 11 of Refer to the give diagram. Two circles cut each other i B ad D. C, the cetre of the smaller circle, lies o the circumferece of the larger circle. AC produced cuts the smaller circle i E. Prove: ˆB ˆ A (4) 6.3. Bˆ ˆ 1 D (6) IEB Copyright 008 PLEASE TURN OVER

KLMN is a trapezium with KL MN. NL is a diagoal of KLMN.

12 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 1 of C ˆ ˆ ˆ 4 A+ B1 6.4 Refer to the diagram. KLMN is a trapezium with KL MN. NL is a diagoal of KLMN. OM is draw such that MO ML. Oˆ K ad MN ML. Prove: ΔKLN Δ ONM (4) 6.4. NL NK (5) IEB Copyright 008

13 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 13 of Two cocetric circles cetred at O have radii of 5cm ad 8,5cm respectively. QR 6 cm ad OT PS. Determie the legth of PS. (6) 40 marks TOTAL FOR THIS PAPER 100 MARKS IEB Copyright 008 PLEASE TURN OVER

14 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 14 of 16 SPACE FOR ADDITIONAL WORKING OR DIAGRAMS IEB Copyright 008

15 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 15 of 16 MATHEMATICS INFORMATION SHEET x b ± b a 4ac i 1 1 i ( + 1) i 1 i 1 [ a + ( i 1 ) d ] [ a + ( 1) d ] i 1 a r i 1 ( r ) a 1 ; r 1 i 1 a a r ; 1 < r < 1, r 0 r 1 1 r i 1 T a + b + c ( 1) ( 1)( ) s T T1 + f + where f is the first term of the first differece ad s is the secod differece f ( x) lim h 0 f ( x + h) f ( x) h P ( 1 i) A P ( 1 i) A + P ( 1 i) A P ( 1 i) A + F x ( 1 + i) 1 1 ( 1 + i) i P x i x1 + x y1 + y d ( x x1 ) + ( y y1) M ; y m x + c y y m ( x ) y y 1 m m ta θ x x1 1 x1 ( x a) + ( y b) r IEB Copyright 008 PLEASE TURN OVER

16 NATIONAL SENIOR CERTIFICATE EXEMPLAR: MATHEMATICS: PAPER III Page 16 of 16 I Δ ABC : a si A b si B c si C a b + c b c. cos A area Δ ABC 1 a b. si C si ( α + β) si α.cosβ + cos α. si β si ( α β) si α.cosβ cos α. si β cos ( α + β) cos α.cosβ si α. si β cos ( α β) cos α.cosβ + si α. si β cos α cos α si 1 si α cos α 1 α si α si α. cos α ( x y) (( x cos α y si α) ; ( y cos α + x si α) ) ; A A A A x x x f x var i 1 ( xi x) ( xi x) var 1 i 1 s. d i 1 ( x x) i P ( A) ( A) ( S) P ( A or B) P ( A) + P ( B) P ( A ad B) IEB Copyright 008

NAME OF SCHOOL NATIONAL SENIOR CERTIFICATE GRADE 12 MATHEMATICS ALTERNATE PAPER PAPER 2 SEPTEMBER 2016

NAME OF SCHOOL NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS ALTERNATE PAPER PAPER SEPTEMBER 06 MARKS: 50 TIME: 3 hours This paper cosists of 3 pages ad a formula sheet INSTRUCTIONS Read the followig istructios