GRADE 12 LEARNER SUPPORT PROGRAMME

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1 Provice of the EASTERN CAPE EDUCATION Steve Vukile Tshwete Educatio Comple Zoe 6 Zwelitsha 5608 Private Bag X003 Bhisho 5605 REPUBLIC OF SOUTH AFRICA CHIEF DIRECTORATE CURRICULUM MANAGEMENT GRADE LEARNER SUPPORT PROGRAMME REVISION AND REMEDIAL TEACHING INSTRUMENT: QUESTIONS AND ANSWERS SUBJECT: MATHEMATICS FIRST PAPER Jue 009 This documet cosists of pages. Strictly ot for test/eamiatio purposes

2 MATHEMATICS FIRST PAPER (MATH) (COPYRIGHT 06/09) INSTRUCTIONS AND INFORMATION Read the followig istructios carefully before aswerig the questios:. This questio paper cosists of TWELVE questios. Aswer ALL the questios.. Show clearly ALL calculatios, diagrams, graphs, etcetera, which you have used i determiig the aswers. 3. A 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 your work eatly. 8. A iformatio sheet with formulae is attached. 9. A diagram sheet is supplied for QUESTION 7.4 ad QUESTION.. Write your ame i the space provided ad the had the diagram sheet i with your aswer book.

3 (COPYRIGHT 06/09) MATHEMATICS FIRST PAPER (MATH) 3 QUESTION. Solve for :.. (3 - )( + 3) = 4 (5) = 5 (4) ; >0 (5). Solve for ad y simultaeously: + y = 3 ad + y + = y. (7) [] QUESTION. How log will it take a sum of moey to be three times as big if the iterest rate is % p.a. compouded quarterly. (4). A carava costs R Sarah wats to pay R5 000 per moth for five years. The iterest rate o a dealer fiaced loa, compouded mothly, is 4,% p.a... How much will she have to give the dealer as a deposit? (5).. Calculate the effective iterest rate that she will pay the dealer per aum. (3).3 Sarah s brother, Mark, decides to buy a carava i 4 years time. He sets up a sikig fud to make provisio for the purchase price of R The accout used offers 8,5% iterest p.a. compouded mothly. Calculate his mothly paymets ito the sikig fud. (4) [6]

4 4 MATHEMATICS FIRST PAPER (MATH) (COPYRIGHT 06/09) QUESTION 3 3. Cosider the followig sequece: 3 ; -6 ; 8 If this patter cotiues cosistetly, determie: 3.. The 0 th term of the sequece. (3) 3.. The sum of the first 0 terms. (3) 3. Fid the value of if (9 - k) = 0 k = (5) [] QUESTION 4 Durig my summer vacatio, Uathi ejoyed buildig towers out of matchsticks. The picture below shows, ad 3 storey towers respectively. storey tower storey tower 3 storey tower 3 matchsticks 9 matchsticks 8 matchsticks 4. How may matchsticks are eeded to build a 4 storey tower? () 4. Give that a match is 4 cm log ad that we ca cosider each triagle to be equilateral, determie the approimate height of the 4 storey tower. (3) 4.3 Determie the formula for the umber of matchsticks i the th storey tower. (7) []

5 (COPYRIGHT 06/09) MATHEMATICS FIRST PAPER (MATH) 5 QUESTION 5 Give the series: ( + ) + ( + ) + ( + ) For which values of will the series coverge? (3) 5. If ( + ) + ( + ) + ( + ) =, determie the value of. (4) [7] QUESTION 6 The diagram below shows the graph of f() = a ad The poit Q (-;-) is the poit of itersectio of f ad g. y k g() =. g Q(-;-) f 6. Determie the value(s) of a ad k. (4) 4 6. If g() is trasformed to give h() = +, describe the trasformatio that occurred to get h. () 6.3 Determie the equatio of the iverse of f() i the form y = () 6.4 How must the domai of f() be restricted so that f - () will be a fuctio? () [0]

6 6 MATHEMATICS FIRST PAPER (MATH) (COPYRIGHT 06/09) QUESTION 7 Give: f() = 3 ad g() = Write the equatio of g() i the form y = a( p) + q (4) 7. Write dow the coordiates of the turig poit of g. () 7.3 Determie the ad y itercepts of g(). (4) 7.4 O the system of aes provided o the diagram sheet, draw eat sketch graphs of f ad g idicatig all the itercepts, asymptotes ad turig poits. (6) 7.5 Determie f - () i the form y = () 7.6 f() is reflected about the y-ais. Determie the equatio of the resultat fuctio h(). () [9] QUESTION 8 The graphs represet the followig fuctios: f() = si + a ad g() = b cos c for [-80 ; 80 ] 3 y Write dow the values of a, b ad c. (3) 8. What is the period of g? () 8.3 For which value(s) of is f() = 0? () [5]

7 (COPYRIGHT 06/09) MATHEMATICS FIRST PAPER (MATH) 7 QUESTION 9 9. Give: f() = 9.. Differetiate f() = from first priciples. (5) 9.. Hece, determie the gradiet of f at the poit with = -. () 9..3 Determie the equatio of the taget to the curve of f at (- ; - ). (3) dy 9. Determie : d y = 3 + (3) 9.. y = + (3) [6]

8 8 MATHEMATICS FIRST PAPER (MATH) (COPYRIGHT 06/09) QUESTION 0 3 The sketch represets the fuctio f() = a + b + c + d, which touches the -ais at = ad has aother of its turig poits at (p ; q). 3 y f What is the value of d? () 0. Usig the sketch above, write dow the roots of the equatio 3 f() = a + b + c + d = 0. () 0.3 If, for this graph, f () = , use this iformatio to calculate the value of p, the -coordiate of the turig poit. (3) 0.4 If f() = , determie the value of q, the y-coordiate of the turig poit. () 0.5 Determie the values of k for which the equatio f() = k will have three real roots. () [0]

9 (COPYRIGHT 06/09) MATHEMATICS FIRST PAPER (MATH) 9 QUESTION The figure below cosists of a rectagle with legth d ad width r joied to a semi-circle with radius r. The area of the figure give below is 0 m. d r r r r r Area of circle = πr Circumferece of circle πr. Prove that the distace d = 40 πr 4r (4). Show that the perimeter P of the figure is give by: 0 π.r P = + r + r ().3 Calculate the value of r whe P is a miimum. Roud your aswer off to oe decimal place. (4) [0] QUESTION A factory produces two types of motorbikes, amely Buzzbikes ad Speedbikes. A maimum of 8 Buzzbikes ad 6 Speedbikes ca be produced per day, but maagemet demads that i total at least 0 bikes must be maufactured daily. There are 3 labourers available per day. It requires labourers to produce oe Buzzbike ad 4 labourers to produce oe Speedbike, per day. The profit per Buzzbike is R900 ad R 00 per Speedbike. Let the umber of Buzzbikes be ad the umber of Speedbikes be y.. Write dow the costraits that satisfy the above iformatio. (4). Represet the costraits graphically o the graph paper provided, clearly idicatig the feasible regio. (5).3 Write dow a equatio to determie the profit, P. ().4 Determie the maimum daily profit. (4) [4] TOTAL: 50

11 (FORMULA SHEET 06/09) MATHEMATICS FIRST PAPER (MATH) FORMULA SHEET: MATHEMATICS FORMULEBLAD: WISKUNDE b ± b 4ac = a A = P( + i ) A = P( i ) A = P( i) A = P( + i) [( + i) ] [ (+ i) F = P = i i ( + ) = i = i = i = ( a + ( i ) d) = (a + ( ) d) i = i a( r ) i a ar = ; r ar = i = r i = r ; - < r < f ( + h) f ( ) f '( ) = lim h 0 h + y + y d = ( ) + ( y y ) M ; y = m + c y y = m( ) y y m = A = P( + i) ( a) + ( y b) = r I ABC: a A si b c = = a = b + c bc. cos A area Δ ABC = ab. sic sib sic 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 si α cos α = si α si α = si α. cos α cos α _ f = σ = i = ( i ) ( A) P ( A) = ( S) P( A or B) = P( A) + P( B) P( A ad B)

13 (DIAGRAM SHEET 06/09) MATHEMATICS FIRST PAPER (MATH) NAME/EXAMINATION NUMBER: DIAGRAM SHEET QUESTION y

15 MATHEMATICS FIRST PAPER (MATH) (DIAGRAM SHEET 06/09) NAME/EXAMINATION NUMBER: DIAGRAM SHEET QUESTION.

GRADE 12 NATIONAL SENIOR CERTIFICATE MATHEMATICS P1 PREPARATORY EXAMINATION 2008

GRADE 12 NATIONAL SENIOR CERTIFICATE MATHEMATICS P1 PREPARATORY EXAMINATION 2008 GRADE NATIONAL SENIOR CERTIFICATE MATHEMATICS P PREPARATORY EXAMINATION 008 MARKS: 50 TIME: 3 hours This questio paper cosists of 9 pages, a formula sheet ad diagram sheet. Mathematics/P DoE/Preparatory