GRADE 11 NOVEMBER 2012 MATHEMATICS P1

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1 Provice of the EASTERN CAPE EDUCATION NATIONAL SENIOR CERTIFICATE GRADE 11 NOVEMBER 01 MATHEMATICS P1 MARKS: 150 TIME: 3 hours This questio paper cosists of 14 pages, icludig a iformatio sheet ad a page diagram sheet.

2 MATHEMATICS P1 (NOVEMBER 01) INSTRUCTIONS AND INFORMATION Read the followig istructios carefully before aswerig the questios. 1. This questio paper cosists of 8 questios.. Aswer ALL the questios. 3. Clearly show ALL calculatios, diagrams, graphs, et cetera that you have used i determiig the aswers. 4. A approved scietific calculator (o-programmable ad o-graphical may be used), uless stated otherwise. 5. Aswer oly will ot ecessarily be awarded full marks. 6. If ecessary, aswers should be rouded off to TWO decimal places, uless stated otherwise. 7. Number the aswers correctly accordig to the umberig system used i this questio paper. 8. Diagrams are NOT draw to scale. 9. A iformatio sheet with formulae is attached. 10. A diagram sheet is supplied for QUESTIONS.4, 3..1, 5.3 ad 8.. Write your ame i the space provided ad the had the diagram sheet i with your ANSWER SHEET. 11. Write legibly ad preset your work eatly.

3 (NOVEMBER 01) MATHEMATICS P1 3 QUESTION Solve for x (correct to two decimal places where ecessary): ( )( ) (4) 1.1. (3) (5) 1. Solve for x ad y simultaeously i the followig set of equatios. (8) 1.3 ( ) Show that by completig the square that: ( ) ( ) (4) 1.4 Solve for x:. (3) [7]

4 4 MATHEMATICS P1 (NOVEMBER 01) QUESTION ( ) ( ) ( ) ( ).1 Write dow the co-ordiates of the y-itercept of the graph f. (1). Give the equatios of the asymptotes of f ad h. (3).3 Which of the fuctios are decreasig? ().4 Sketch the graphs of f, g ad h o the same system of axes. Show all asymptotes. (4).5 Write the equatio of the graph obtaied by reflectig f i the y-axis. (1).6 Give the equatio of the graph obtaied by shiftig g vertically up by five uits. (1) [1]

5 (NOVEMBER 01) MATHEMATICS P1 5 QUESTION The geeral term of: 5 ; 1 ; 9 ; 48 ; 77 ; is T = 3 + Is this statemet true? Show workig to motivate your aswer. (4) 3. The first four shapes of a sequece are show below. The table below shows the umber of white ad black triagles i the first three shapes. Shape umber, Number of white triagles Number of black triagles Total umber of triagles Copy the table ad complete it. (6) 3.. How may triagles will there be altogether i the 1 th shape? () 3..3 Determie the geeral term for the umber of black triagles i the th shape. (7) 3..4 The umber of black triagles i the th shape is 190. Determie the value of. (5) [4]

6 6 MATHEMATICS P1 (NOVEMBER 01) QUESTION A compay bought machiery valued at R The depreciatio is calculated at a rate of 1% p.a. o a straight-lie basis. Calculate the value of the machiery at the ed of six years. (3) 4. R 500,00 is deposited ito a savigs accout at 15% iterest per aum compouded mothly What is the mothly omial iterest rate? (1) 4.. Determie the effective yearly iterest rate, correct to two decimal places. (4) 4..3 Calculate the amout of moey i the savigs accout at the ed of seve years. (4) 4.3 A ew car depreciates i value by 18% i the first year Determie the origial cost if it is ow worth R after oe year. (4) 4.3. If the car depreciates o reducig balace by 15% i the secod year ad by 1% i the third ad fourth years, calculate the value of the car to the earest rad after four years. (4) 4.4 Deeo takes out a loa of R i order to fiace her ew busiess. After four years she expads her busiess ad borrows a further R Three years after this she pays off the total debt i oe paymet. The iterest rate of the loa was 18% p.a. compouded quarterly. Determie the value of her paymet. (5) [5]

7 (NOVEMBER 01) MATHEMATICS P1 7 QUESTION 5 Give: ( ) ( ) ad ( ) 5.1 Calculate the co-ordiates of the x-itercept ad the y-itercept of g. (3) 5. Calculate the co-ordiates of the x-itercepts of f. (3) 5.3 O the same set of axes, sketch the graphs of f ad g. Idicate all itercepts with the axes ad the co-ordiates of the turig poit of f. (7) 5.4 Write dow the rage of g. () 5.5 What is the miimum value of f(x)? (1) 5.6 For which values of x will both f (x) ad g (x) icrease as x icreases? () [18]

8 8 MATHEMATICS P1 (NOVEMBER 01) QUESTION 6 The graph of f(x) = 1 + a. f (a is a costat) passes through the origi as show below. y x 6.1 Show that a = -1 () 6. Determie the value of f(-15) correct to five decimal places. () 6.3 Determie the value of x if P(x ; 0,5) lies o the graph of f. (3) 6.4 If the graph of f is shifted two uits to the right to give the fuctio h, write dow the equatio of h. () [9]

9 (NOVEMBER 01) MATHEMATICS P1 9 QUESTION 7 The sketch shows the graphs of f(x) = -x x + 3 ad g(x) = mx + c. A ad B are the itercepts o the x-axis. C ad D are the itercepts o the y-axis. T is the turig poit o the graph of f. T y C g A S O B x D f 7.1 Determie the legths of OC ad AB. (5) 7. Determie the equatio of the axis of symmetry of the graph of f. () 7.3 Show that the legth of ST = 4 uits. (3) 7.4 The graph of g is parallel to AC. Determie: the gradiet of AC. (3) 7.4. the equatio of g. (4) [17]

10 10 MATHEMATICS P1 (NOVEMBER 01) QUESTION 8 A compay makes two types of clocks. The wall models sell for R40 each ad the table models for R50 each. The maximum umber of wall models that ca be made i a day is 35 ad the maximum umber of table models is 0. The dispatch departmet ca oly pack 50 clocks per day. The miimum icome eeded to cover costs is R 000 per day. Let the umber of wall models made per day be x ad the umber of table models be y. 8.1 Write dow all the costraits. (4) 8. Draw a graph to show the costraits ad clearly idicate the feasible regio. (5) 8.3 Calculate the critical poits (vertices) of the feasible regio. (4) 8.4 The profit o a wall model is R0 ad o a table model R10. Write dow the equatio of the objective fuctio (profit lie). (1) 8.5 Determie the maximum as well as the miimum profit. (4) [18] TOTAL: 150

11 (NOVEMBER 01) MATHEMATICS P1 11 INFORMATION SHEET: MATHEMATICS b b 4 ac x a A P( 1 i) A P( 1 i) A P( 1 i) A P( 1 i) i1 1 i1 i ( 1) si cos cos a ( i 1) d a ( 1) d i1 i1 ar F i1 a r 1 r 1 x 1 i 1 i ; r 1 i a i1 ar ; 1 r r x[1 (1 i) ] P i d ( x ) ( ) x1 y y1 M x1 x y1 y ; y mx c y y m x ) y y1 m ta x x I ABC: 1 si a A area ABC 1 ( x1 f ( x h) f ( x) f '( x) lim h 0 h m x a b c a b c bc. cos A si B si C 1 ab. si C y b si.cos cos. si si si.cos cos. si cos.cos si. si cos si 1 si cos 1 cos cos.cos si. si si si. cos r xi x i1 fx x ( A) P( A) (A or B) = P(A) + P(B) P(A ad B) S

12 1 MATHEMATICS P1 (NOVEMBER 01) DIAGRAM SHEET NAME: QUESTION.4 0 QUESTION 3..1 Shape umber, Number of white triagles Number of black triagles Total umber of triagles

13 (NOVEMBER 01) MATHEMATICS P1 13 DIAGRAM SHEET NAME: QUESTION 5.3 0

14 14 MATHEMATICS P1 (NOVEMBER 01) DIAGRAM SHEET NAME: QUESTION 8.

GRADE 12 JUNE 2016 MATHEMATICS P1

GRADE 12 JUNE 2016 MATHEMATICS P1 NATIONAL SENIOR CERTIFICATE GRADE 1 JUNE 016 MATHEMATICS P1 MARKS: 150 TIME: 3 hours *MATHE1* This questio paper cosists of 14 pages, icludig a iformatio sheet. MATHEMATICS P1 (EC/JUNE 016) INSTRUCTIONS