NATIONAL SENIOR CERTIFICATE GRADE 12

Size: px

Start display at page:

Download "NATIONAL SENIOR CERTIFICATE GRADE 12"

Delphia Preston
6 years ago
Views:

1 NATIONAL SENIOR CERTIFICATE GRADE 1 MATHEMATICS P1 NOVEMBER 016 MARKS: 150 TIME: 3 hours This questio paper cosists of 9 pages ad 1 iformatio sheet. Please tur over

2 Mathematics/P1 DBE/November 016 INSTRUCTIONS AND INFORMATION Read the followig istructios carefully before aswerig the questios This questio paper cosists of 1 questios. Aswer ALL the questios. Number the aswers correctly accordig to the umberig system used i this questio paper. Clearly show ALL calculatios, diagrams, graphs, et cetera that you have used i determiig your aswers. Aswers oly will ot ecessarily be awarded full marks. You may use a approved scietific calculator (o-programmable ad o-graphical), uless stated otherwise. If ecessary, roud off aswers to TWO decimal places, uless stated otherwise. Diagrams are NOT ecessarily draw to scale. A iformatio sheet with formulae is icluded at the ed of the questio paper. Write eatly ad legibly. Please tur over

3 Mathematics/P1 3 DBE/November 016 QUESTION Solve for : () (correct to TWO decimal places) (3) (5) (4) 1. Give: f Solve for if 0 f () 1.. Solve for if f 0 () / 1..3 Determie the values of for which 0 f () 1.3 Solve for ad y: y ad 5y 4 (4) [4] QUESTION Give the fiite arithmetic sequece: 5 ; 1 ; 3 ;... ; 83 ; 87.1 Write dow the fourth term (T4) of the sequece. (1). Calculate the umber of terms i the sequece. (3).3 Calculate the sum of all the egative umbers i the sequece. (3).4 Cosider the sequece: 5 ; 1 ; 3 ;... ; 83 ; 87 ; ; Determie the umber of terms i this sequece that will be eactly divisible by 5. (4) [11] Please tur over

4 Mathematics/P1 4 DBE/November 016 QUESTION The first four terms of a quadratic umber patter are 1 ; ; 3 ; Calculate the value(s) of. (4) 3.1. If = 0, determie the positio of the first term i the quadratic umber patter for which the sum of the first first differeces will be greater tha 50. (4) 3. Rectagles of width 1 cm are draw from the edge of a sheet of paper that is 30 cm log such that there is a 1 cm gap betwee oe rectagle ad the et. The legth of the first rectagle is 1 cm ad the legth of each successive rectagle is 85% of the legth of the previous rectagle util there are rectagles draw alog the etire legth of AD. Each rectagle is coloured grey. A B 30 cm 1 cm 1 cm D 1 cm C 3..1 Calculate the legth of the 10 th rectagle. (3) 3.. Calculate the percetage of the paper that is coloured grey. (4) [15] Please tur over

5 Mathematics/P1 5 DBE/November 016 QUESTION 4 Sketched below is the graph of a, a 0. The poits P( ; 9) ad Qb ; h R is the y-itercept of h lie o h. y D P( ; 9) h Q b ; 81 1 R Write dow the equatio of the asymptote of h. (1) 4. Determie the coordiates of R. (1) 4.3 Calculate the value of a. () 4.4 D is a poit such that DQ y-ais ad DP -ais. Calculate the legth of DP. (4) 4.5 Determie the values of k for which the equatio h ( ) k 0 will have a root that is less tha 6. (3) [11] Please tur over

6 Mathematics/P1 6 DBE/November 016 QUESTION 5 Sketched below is the parabola f, with equatio 4 3 equatio p y t 3. f ad a hyperbola g, with B, the turig poit of f, lies at the poit of itersectio of the asymptotes of g. is the -itercept of g. A( 1; 0) y g B A(1 ; 0) 0 g f 5.1 Show that the coordiates of B are ( ; 1) () 5. Write dow the rage of f. (1) 5.3 For which value(s) of will 0? g () 5.4 Determie the equatio of the vertical asymptote of the graph of h if h ( ) g( 4) (1) 5.5 Determie the values of p ad t. (4) 5.6 / Write dow the values of for which ( ). g 0 f (4) [14] Please tur over

7 Mathematics/P1 7 DBE/November 016 QUESTION 6 Give: f ( ) 3 ad g( ) log 6.1 O the same set of aes, sketch the graphs of f ad g, clearly showig ALL itercepts with the aes. (4) 6. Write dow the equatio of, g 1 the iverse of g, i the form y = () 6.3 Eplai how you will use QUESTION 6.1 ad/or QUESTION 6. to solve the equatio log 3. (3) 6.4 Write dow the solutio to 3. log (1) [10] QUESTION 7 O 1 Jue 016 a bak grated Thabiso a loa of R at a iterest rate of 15% p.a. compouded mothly, to buy a car. Thabiso agreed to repay the loa i mothly istalmets commecig o 1 July 016 ad edig 4 years later o 1 Jue 00. However, Thabiso was uable to make the first two istalmets ad oly commeced with the mothly istalmets o 1 September Calculate the amout Thabiso owed the bak o 1 August 016, a moth before he paid his first mothly istalmet. () 7. Havig paid the first mothly istalmet o 1 September 016, Thabiso will still pay his last mothly istalmet o 1 Jue 00. Calculate his mothly istalmet. (4) 7.3 If Thabiso paid R9 000 as his mothly istalmet startig o 1 September 016, how may moths sooer will he repay the loa? (5) 7.4 If Thabiso paid R9 000 as a mothly istalmet startig o 1 September 016, calculate the fial istalmet to repay the loa. (4) [15] Please tur over

8 Mathematics/P1 8 DBE/November 016 QUESTION Determie f / ( ) from first priciples if f ( ) 3 (5) / 8. Joh determies g ( a), the derivative of a certai fuctio g at = a, ad arrives at 4 h the aswer: lim h0 h Write dow the equatio of g ad the value of a. () 8.3 Determie dy d if y (4) g 8 0 is a taget to a b 18 f at = 1. Calculate the values of a ad b. (5) [16] QUESTION 9 For a certai fuctio f, the first derivative is give as f / Calculate the -coordiates of the statioary poits of f. (3) 9. For which values of is f cocave dow? (3) 9.3 Determie the values of for which f is strictly icreasig. () If it is further give that f a b c d ad f 0 18, determie the equatio of f. (5) [13] QUESTION 10 The umber of molecules of a certai drug i the bloodstream t hours after it has bee take is 3 represeted by the equatio Mt t 3t 7t, 0 t Determie the umber of molecules of the drug i the bloodstream 3 hours after the drug was take. () 10. Determie the rate at which the umber of molecules of the drug i the bloodstream is chagig at eactly hours after the drug was take. (3) 10.3 How may hours after takig the drug will the rate at which the umber of molecules of the drug i the bloodstream is chagig, be a maimum? (3) [8] Please tur over

9 Mathematics/P1 9 DBE/November 016 QUESTION 11 A survey was coducted amog 100 boys ad 60 girls to determie how may of them watched TV i the period durig which eamiatios were writte. Their resposes are show i the partially completed table below. WATCHED TV DURING EXAMINATIONS DID NOT WATCH TV DURING EXAMINATIONS Male 80 a TOTALS Female 48 1 Totals b Calculate the values of a ad b. () 11. Are the evets 'beig a male' ad 'did ot watch TV durig eamiatios' mutually eclusive? Give a reaso for your aswer. () 11.3 If a learer who participated i this survey is chose at radom, what is the probability that the learer: Watched TV i the period durig which the eamiatios were writte? () Is ot a male ad did ot watch TV i the period durig which eamiatios were writte? () [8] QUESTION 1 The digits 1 to 7 are used to create a four-digit code to eter a locked room. How may differet codes are possible if the digits may ot be repeated ad the code must be a eve umber bigger tha 5 000? [5] TOTAL: 150

10 Mathematics/P1 DBE/November 016 INFORMATION SHEET b b 4 ac a A P( 1 i) A P( 1 i) A P( 1 i) A P( 1 i) S a ( 1 d T a ( 1) d T ar F 1 1 i 1 i S ) r 1 a r 1 P ; r i i S a 1 r ; 1 r 1 f '( ) lim h 0 f ( h) h f ( ) 1 y1 y d ( 1 ) ( y y1) M ; y m c y y m ) a y b r 1 ( 1 I ABC: y y1 m m ta a si A 1 b si B c si C si cos a b c area ABC bc. cos A 1 ab. si C si.cos cos. si si si.cos cos. si cos.cos si. si cos cos.cos si. si cos si cos 1 si si si. cos cos 1 ( i i 1 ( A) P( A) P(A or B) = P(A) + P(B) P(A ad B) S yˆ a b b ) ( y y) ( )

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