NATIONAL CERTIFICATE (VOCATIONAL) MATHEMATICS (Second Paper) NQF LEVEL 3 NOVEMBER 2009

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1 NATIONAL CERTIFICATE (VOCATIONAL) MATHEMATICS (Secod Paper) NQF LEVEL 3 NOVEMBER 009 (050053) 5 November (Y-Paper) 3:00 6:00 Calculators may be used. This questio paper cosists of 6 pages ad a -page formula sheet.

2 (050053) -- NC60(E)(N5)V TIME: 3 HOURS MARKS: 00 INSTRUCTIONS AND INFORMATION Aswer ALL the questios. Read ALL the questios carefully. Number the aswers accordig to the umberig system used i this questio paper. Write eatly ad legibly.

(050053) -3- NC60(E)(N5)V QUESTION. The sketch below shows a traditioal South Africa hut. The roof is i the shape of a coe while the walls form the shape of a cylider.

3 (050053) -3- NC60(E)(N5)V QUESTION. The sketch below shows a traditioal South Africa hut. The roof is i the shape of a coe while the walls form the shape of a cylider. I the costructio of the hut, the cylidrical portio had o base ad o top. The builder added i oly oe door ad oe widow. The followig dimesios are applicable to this structure: Height of door = 0 cm Width of door = 88 cm Height of widow = 60 cm Width of widow = 30 cm 300 cm 350 cm 800 cm.. Determie the volume of the coical roof. (3).. The ower wats to pait the outside of the hut. Determie the total surface area of the outside wall. (5). The followig is give as poits: D(4 ; ), E( ; 3 ) ad F( ; 4). Fid the equatio of the straight lie parallel to DE passig through F. (3).3 Make use of a calculator ad determie the value of sec4 + cosec 49 correct to THREE decimal places. ().4 Evaluate ta (90 x). si (80 x). ta (360 + x) cos 40.ta 5 (ta y sec y) without the use of a calculator. (7).5 Determie the value of x for [ 0 ; 360 ] si x 0,4 = 0 x if: (3)

4 (050053) -4- NC60(E)(N5)V.6 Make use of trigoometric idetities to prove the followig: si A + cot A = cos ec A + cos A (5).7 From a poit o top of a buildig, the agle of elevatio of the top of a earby tower is 5 ad the agle of depressio of the bottom of the tower is 0. If the height of the tower is kow to be 30 m, how far from the tower is the observer? m (8) [35] QUESTION. The umber of days 4 NCV learers were abset for the year are give as follows: 6; 9; 34; 7; 5; 54; 59; 78; 00; 8; 85; 87; 93; 68.. Work out a FIVE umber summary for the iformatio give above. (5).. Draw a box ad whisker diagram of the data. (5)..3 Calculate the variace ad the stadard deviatio for the above data. (9). The table give below shows the frequecy at which stalls are hired at a local festival depedig o the retal beig charged. Complete the table below. Write oly the aswers ext to the questio umber (....8) RENTAL ( RANDS ) FREQUENCY < CUMULATIVE FREQUENCY (0 to < 50) 3.. (50 to < 00 ) 5..3 (00 to < 50 ) 9..4 (50 to < 00 ) 3..5 (00 to < 50 ) 0..6 (50 to < 300 ) 4..7 (300 to < 350 ) 6..8 TOTAL:.. (4)

5 (050053) -5- NC60(E)(N5)V.3.4 Costruct a less tha ogive curve by usig the iformatio obtaied i QUESTION Determie the media value by usig the iformatio obtaied i the graph. (9) () [34] QUESTION 3 3. Defie the followig terms: 3.. Expeses of a social club () 3.. Icome of a social club () 3. Thokozile, the treasurer at a local social club, had to preset a Icome ad Expediture Statemet to the chairperso. Some of the icome ad expediture of the club are as follows: Icome: Cotributios of 60 R300 per studet Doatios of R6 800 from local taxi associatio Ticket sales Expediture: Accommodatio R3 00 Trasport R3 000 Study the Icome ad Expediture Statemet show below ad aswer the questios that follow. All values are give i rads. INCOME EXPENDITURE Items Amout Items Amout Doatios Accommodatio 3 00 Cotributios (a) Trasport Tickets sales (b) Pritig 50 Sudry (Icidetal expeses) 400 TOTAL 9 00 TOTAL (c) SURPLUS/DEFICIT (d) Determie what amouts are represeted by (a) to (d). (8)

6 (050053) -6- NC60(E)(N5)V 3.3 If the doatio (refer to the taxi associatio doatio i Questio 3.) was kept i a savigs accout, calculate the fial amout that will be available after 3 years, if the iterest is calculated at: 3.3. Simple iterest at 5% per aum (4) 3.3. Compoud iterest at 4,5% per aum compouded quarterly (5) Idicate which form of savig is better ad give a reaso for the aswer () 3.4 Malcolm deposited R5 000 ito a savigs scheme at 7% compoud iterest for 5 years. Two years later he deposited a further R 000 ito the scheme ad the rate of iterest was icreased to 8% Represet the above iformatio o a time lie. (4) 3.4. Determie his accumulated amout at the ed of 5 years. (6) [3] TOTAL: 00

7 (050053) -7- NC60(E)(N5)V FORMULAE SHEET. Slat surface area of a pyramid = a l. Area of curved surface of a coe = π r l l = h + 3. Slat height of a coe = 4. Volume of a sphere = 4 V = π r 3 5. Area of a sphere = A= 4π r 6. Volume of a pyramid = ( area of base ) height 3 7. Volume of a coe = ( area of base ) height 3 3 r 8. y m = x y y = x x x + x y + y 9. ( xm ; ym ) = ; 0. Distace = siθ. = taθ cosθ cosθ. = cotθ siθ 3. si θ + cos θ = 4. + ta θ = sec θ 5. + cot θ = cosec θ 6. x = i= x 7. variace = i ( x y s = x) + ( y ) ( x i x) ( x i x) 8. stadard deviatio = s = 9. r P r t I = A0 t or I = or A = P ( + i) t m r At = A0 + or 00 m r i = 00 si A si B si C a = b = a = b + c bc cos A ^ A= ab si C c ^ r A ) 00 t = P ( + or A = P ( + i)

8 (050053) -8- NC60(E)(N5)V

GRADE 11 NOVEMBER 2012 MATHEMATICS P1

GRADE 11 NOVEMBER 2012 MATHEMATICS P1 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