METRO EAST EDUCATION DISTRICT NATIONAL SENIOR CERTIFICATE GRADE 12 MATHEMATICS PAPER 1 SEPTEMBER 2014

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1 METRO EAST EDUCATION DISTRICT NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS PAPER SEPTEMBER 04 MARKS: 50 TIME: 3 hours This paper cosists of 7 pages ad a iformatio sheet.

2 GR Mathematics- P MEED September 04 INSTRUCTIONS AND INFORMATION Read the followig istructios carefully before aswerig the questios.. This questio paper cosists of questios.. Aswer ALL the questios. 3. Number the aswers correctly accordig to the umberig system used i this questio paper. 4. Clearly show ALL calculatios, diagrams, graphs, et cetera that you have used i determiig your aswers. 5. Aswers oly will ot ecessarily be awarded full marks. 6. You may use a approved scietific calculator (o-programmable ad o-graphical), uless stated otherwise. 7. If ecessary, roud off aswers to TWO decimal places, uless stated otherwise. 8. Diagrams are NOT ecessarily draw to scale. 9. A iformatio sheet with formulae is icluded at the ed of the questio paper. 0. Write eatly ad legibly.

3 GR Mathematics- P MEED September 04 QUESTION. Solve for x (to decimals if ecessary).. ( )( ) ().. (4)..3 (4)..4 (3). Solve for x ad y simultaeously:.3 Calculate, without usig a calculator, the value of a ad b if a ad b are itegers ad: (7) (4) QUESTION [4]. The followig arithmetic sequece is give: 0 ; 3 ; 6 ; 9; ; 0.. How may terms are there i this sequece? ().. The eve umbers are removed from the sequece. Calculate the sum of the terms of the remaiig sequece. (6). Study the geometric series:.. Determie the -th term i terms of x. ().. Determie the value(s) of x for which the series will coverge. (3).3 The sum of terms i a sequece is give by S = ² +5. Determie the 3rd term. (3) QUESTION 3 [6] The sequece 3 ; 9 ; 7 ; 7 ; is quadratic. 3. Determie a expressio for the -th term of the sequece. (4) 3. What is the value of the first term of the sequece that is greater tha 69? (4) [8] 3

4 GR Mathematics- P MEED September 04 QUESTION 4 The graphs of ( ) ad ( ) are give. The graphs itersect at A ad Q. A ad B are the -itercepts of. 4. Determie the legth of AB. (4) 4. Determie the coordiates of Q. (4) 4.3 Show that the coordiates of the turig poit are ( ) () 4.4 For which values of is ( ) ( ) () 4.5 Determie for which value of, will have two equal roots? () QUESTION 5 5. Sketch the graph of showig the asymptotes ad the itersectios with the axes. (3) 5. Give the equatio of the: 5.. vertical asymptote () 5.. axis of symmetry with a egative gradiet. () 5..3 graph that would result if you shift this graph 4 uits upwards ad 4 uits to the left. () [4] QUESTION 6 6. Determie the equatio of ( ) i the form if A( ) ad the equatio of the horizotal lie is. Y [8] X (4) 6. Determie the equatio of the reflectio of i the -axis i the form. () 6.3 Give the rage of ( ). () [6] 4

5 GR Mathematics- P MEED September 04 QUESTION 7 The graphs of ( ) ; ad ( ) for are give. 7. Determie the coordiates of A, the poit of itersectio betwee ad. (4) 7. Determie the equatio of. (3) 7.3 Give the equatio of the graph which is obtaied whe ( ) is reflected i the lie. () [9] QUESTION 8 8. Dr Kwakere deposits R ito his bak accout. It takes this ivestmet year to grow to R The iterest rate is,5% p.a, compouded yearly. Calculate. (4) 8. I 006 you bought a machie for R The value of the machie depreciated at a rate of 6% p.a o the reducig balace for 3 years. Thereafter the depreciatio rate chaged to 8,% p.a. 8.. What was the book value of the machie after 7 years? (3) 8.. Calculate the average depreciatio rate per aum over the 7 years. (3) 8.3 A school will eed to replace some of its equipmet i 6 years time. The pricipal calculated that the ew equipmet will cost R The school establishes a sikig fud to pay for the ew equipmet ad makes a immediate deposit of R6 300 ito the fud, which geerates iterest at 6,85% p.a. compouded mothly Show that the value of the sikig fud that the school must deposit moey ito will be R35 008,65 after depositig the R (Cosider the fact that R6300 has eared iterest for the 6 years.) (3) 8.3. How much moey should the school deposit each moth so that the fud will have eough moey to cover the cost of the ew equipmet? (3) 5 [6]

6 x GR Mathematics- P MEED September 04 QUESTION 9 9. Determie the derivative of f(x) = by usig first priciples. (4) 9. Determie the followig derivatives: 9.. if () 9.. [ ] (4) 9.3 Give ( ) A taget to the graph of f has a gradiet of ad x itercept (a ; 0). Determie the value of a. (5) [5] QUESTION 0 Give: ( ) 0. Determie the itercepts of f with the axes. (4) 0. Determie the coordiates of the turig poits of f. (4) 0.3 Draw a eat sketch graph of f. Clearly show all the turig poits ad itercepts. (3) [] QUESTION r A cylider fits perfectly ito a sphere with radius of 4 3 cm ( ). If the height of the cylider is x, show that the radius of the cylider is give by cm (). Hece, show that the volume of the cylider i terms of x is give 3 by V 96x x (3).3 Calculate the height of the cylider so that the volume is a maximum. (4) [9] 6

7 GR Mathematics- P MEED September 04 QUESTION. P(A) = ad P(A or B) =. Determie P(B), as a simplified fractio, if: 3.. A ad B are mutually exclusive evets. (3).. A ad B are idepedet evets. (5). Cosider the word: EINSTEIN... How may differet letter arragemets are possible if all the letters are used? ().. What is the probability that idetical letters will be grouped together? (4) [4] TOTAL: 50 7

8 INFORMATION SHEET b b 4 ac x a A P( i ) A P( i) A P( i) A P( i) T a ( )d S [a ( ) ] d a T ar S x i F i f f ( x h) f ( x) '( x) lim h 0 h r ; r r P x i i S a r ; r d ( x ) ( ) x y y M x x y y ; y mx c y y m x ) x a y b r I ABC: a si A ( x y y m m ta x x b c a b c bc.cos A area ABC ab.sic si B sic si si.cos cos. si si si.cos cos. si cos cos.cos si. si cos cos.cos si. si cos si cos si si si. cos cos fx x i x x ( A ) P( A ) S P(A or B) = P(A) + P(B) P(A ad B) ŷ a bx ( x x )( y y ) b ( x x ) i

GRADE 12 SEPTEMBER 2015 MATHEMATICS P1

GRADE 12 SEPTEMBER 2015 MATHEMATICS P1 NATIONAL SENIOR CERTIFICATE GRADE 1 SEPTEMBER 015 MATHEMATICS P1 MARKS: 150 TIME: 3 hours *MATHE1* This questio paper cosists of 10 pages, icludig a iformatio sheet. MATHEMATICS P1 (EC/SEPTEMBER 015) INSTRUCTIONS