MATHEMATICS P1 COMMON TEST JUNE 2014 NATIONAL SENIOR CERTIFICATE GRADE 12

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1 Mathematics/P1 1 Jue 014 Commo Test MATHEMATICS P1 COMMON TEST JUNE 014 NATIONAL SENIOR CERTIFICATE GRADE 1 Marks: 15 Time: ½ hours N.B: This questio paper cosists of 7 pages ad 1 iformatio sheet. Please Tur Over

2 Mathematics/P1 Jue 014 Commo Test INSTRUCTIONS AND INFORMATION Read the followig istructios carefully before aswerig the questios This questio paper cosists of 8 questios. Aswer ALL the questios. 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. A approved scietific calculator (o-programmable ad o-graphical) may be used, uless stated otherwise. If ecessary, aswers should be rouded off 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 this questio paper. Number the aswers correctly accordig to the umberig system used i this questio paper. Write eatly ad legibly. Please Tur Over

3 Mathematics/P1 3 Jue 014 Commo Test QUESTION Solve for : (3) (3) (3) (5) 1. Simplify, without the use of a calculator: (3) 1.3 Solve for ad y where: ad (6) [3] QUESTION.1 Give the sequece: ; 5 ; 8 ;.1.1 If the patter cotiues, the write dow the et two terms. (1).1. Prove that oe of the terms of this sequece are perfect squares. (5). 1; 3; 5 are the first three terms of the first differeces of a quadratic sequece. The 7 th term of the quadratic sequece is Determie the 6 th ad 5 th terms of the quadratic sequece. (4).. Determie the th term of the quadratic sequece. (5).3 Prove that the sum to terms of a geometric sequece is give by: a( r 1) S ; r 1 (4) r 1.4 Calculate the value of if: k 1 k (5) [4] Please Tur Over

4 Mathematics/P1 4 Jue 014 Commo Test QUESTION 3 Give ad. 3.1 Draw graphs of ad o the same set of aes. Clearly show the itercepts with both aes, as well as the asymptote(s) where applicable. (8) 3. Write dow the value(s) of t if f ( ) t has: 3..1 equal roots. () 3.. oe root equal to 0. () 3.3 Write dow the equatio of the asymptote of h if () [14] QUESTION 4 y A(4 ; 6) a The diagram above shows the graph of f ( ) q. A(4 ; 6) is a poit o the graph. p 4.1 Determie the value(s) of a, p, ad q. (4) 4. Write dow the rage of g if g() = f(). () 4.3 If the graph of f is symmetrical with respect to the lie y = + c, determie the value of c. (3) [9] Please Tur Over

5 Mathematics/P1 5 Jue 014 Commo Test QUESTION Give: Determie. () 5. Give 5..1 Determie the iverse of i the form.. () 5.. Give a reaso why the iverse of is ot a fuctio. () 5..3 Write dow TWO ways i which you ca restrict the domai of so that its iverse is a fuctio. () 5..4 Hece, sketch the graphs of the fuctio. (4) 5..5 Determie the value(s) of for which h 1 ( ). () [14] QUESTION Determie the derivative of 3 f ( ) from first priciples. (5) 6. Calculate the derivative of the followig: (4) h( ) (4) [13] Please Tur Over

6 Mathematics/P1 6 Jue 014 Commo Test QUESTION 7 3 The graph below represets the fuctios f ad g with f ( ) a c ad g( ). A ad D( 1; 0) are the -itercepts of f. The graphs of f ad g itersect at A ad C. D 7.1 Determie the coordiates of A. () 7. Show by calculatio that a = 1 ad c = 3. (5) 7.3 Determie the coordiates of B, a turig poit of f. (4) 7.4 Determie the -coordiate of the poit of iflectio of f. () 7.5 Write dow the values of k for which f ( ) k will have oly ONE root. (3) 7.6 Write dow the values of for which f '( ) < 0. () [18] Please Tur Over

7 Mathematics/P1 7 Jue 014 Commo Test QUESTION 8 h A crate used o vegetable farms i the Pooo Area is i the form of a rectagular prism which is ope o top. It has a volume of 1 cubic metre. The legth ad the breadth of its base is, ad metres respectively. The height is h metres. The material used to maufacture the base of this cotaier costs R00 per square metre ad for the sides, R10 per square metre. 8.1 Epress h i terms of. () 8. Show that the cost, C, of the material is give by: C() = (3) 8.3 Calculate the value of for which the cost of the material will be a miimum ad hece the miimum cost of the material. (5) [10] Please Tur Over

8 Mathematics/P1 8 Jue 014 Commo Test INFORMATION SHEET: MATHEMATICS b b 4 ac a A P( 1 i) A P( 1 i) A P( 1 i) T a ( 1) d S a ( 1) d 1 T ar ar 1 S Please Tur Over ; r 1 r 1 1 i 1 [1 (1 i) ] F P i i f ( h) f ( ) f '( ) lim h 0 h ( ) ( ) d 1 y y1 M y ; y m c y y m ) a y b r 1 ( y S A P( 1 i) a ; 1 r 1 1 r y y1 m m ta a b c IABC: a b c 1 bc. cos A area ABC ab. si C si A 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 1 si si si. cos cos 1 i f i1 ( A) P( A) P(A or B) = P(A) + P(B) P(A ad B) S yˆ a b b ( ) 1 ( y y)

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