MATHEMATICS P1 JUNE 2014 GRADE 12 - HUDSON PARK

1 MATHEMATICS /P1 1 june 2014 Common Test NSC Please Turn Over Copyright Reserved Marks: 125 Time: 2 hours : This question paper consists of 7 pages and 1 information sheet. NATIONAL SENIOR CERTIFICATE GRADE 12 MATHEMATICS P1 COMMON TEST june 2014 MATHEMATICS /P1 2 june 2014 Common Test NSC Please Turn Over Copyright Reserved INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions.

2 Question paper consists of 8 ALL the questions. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers. Answers only will not necessarily be awarded full marks. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise. If necessary, answers should be rounded off to TWO decimal places, unless stated are NOT necessarily drawn to scale. An information sheet with formulae is included at the end of this question the answers correctly according to the numbering system used in this question neatly and legibly. MATHEMATICS /P1 3 june 2014 Common Test NSC Please Turn Over Copyright Reserved QUESTION 1 Solve for x: 0652 xx (3) 02432 xx (3) 022d xx (3) xx (5) Simplify, without the use of a calculator: 22228829872xxx (3) Solve for x and y where: and (6) [23]QUESTION 2 Given the sequence: 2 ; 5 ; 8.

3 If the pattern continues, then write down the next two terms. (1) Prove that none of the terms of this sequence are perfect squares. (5) 1; 3; 5 are the first three terms of the first differences of a quadratic sequence. The 7th term of the quadratic sequence is 35. Determine the 6th and 5th terms of the quadratic sequence. (4) Determine the nth term of the quadratic sequence. (5) Prove that the sum to n terms of a geometric sequence is given by: 1;1)1(z rrraSnn (4) Calculate the value of n if: 5314403211 nkk (5) [24] MATHEMATICS /P1 4 june 2014 Common Test NSC Please Turn Over Copyright Reserved QUESTION 3 Given and.

4 Draw graphs of and on the same set of axes. Clearly show the intercepts with both axes, as well as the asymptote(s) where applicable. (8) Write down the value(s) of t iftxf )( has: equal roots. (2) one root equal to 0. (2) Write down the equation of the asymptote of h if (2) [14] QUESTION 4 The diagram above shows the graph of qpxaxf )(. A(4 ; 6) is a point on the graph. Determine the value(s) of a,p, and q.

5 (4) Write down the range of g ifg(x) = f(x) 2 . (2) If the graph of fis symmetrical with respect to the line y = x + c, determine the value of c. (3) [9] xyA(4 ; 6) MATHEMATICS /P1 5 june 2014 Common Test NSC Please Turn Over Copyright Reserved QUESTION 5 Given: Determine . (2) Given Determine the inverse of in the form .. (2) Give a reason why the inverse of is not a function.

6 (2) Write down TWO ways in which you can restrict the domain of so that its inverse is a function. (2) Hence, sketch the graphs of the function . (4) Determine the value(s) of x for which 2)(1d xh. (2) [14] QUESTION 6 Determine the derivative of 3)(xxf from first principles. (5) Calculate the derivative of the following: xx112 (4) xxxxh3)(32 (4) [13] MATHEMATICS /P1 6 june 2014 Common Test NSC Please Turn Over Copyright Reserved QUESTION 7 The graph below represents the functions f and g with 2)( and 2)(3xxgcxaxxf.

7 A and D( 1; 0) are the x-intercepts of f . The graphs of f and g intersect at A and C. Determine the coordinates of A. (2) Show by calculation that a = 1 and c = 3. (5) Determine the coordinates of B, a turning point of f. (4) Determine the x-coordinate of the point of inflection of f. (2) Write down the values of k for which kxf)( will have only ONE root. (3) Write down the values of x for which (2) [18] D . 0'<fx)( MATHEMATICS /P1 7 june 2014 Common Test NSC Please Turn Over Copyright Reserved QUESTION 8 A crate used on vegetable farms in the Ponono Area is in the form of a rectangular prism which is open on top.

8 It has a volume of 1 cubic metre. The length and the breadth of itsbase is 2x, andx metres respectively. The height is h metres. The material used to manufacture the base of this container costs R200 per square metre and for the sides,R120 per square metre. Express h in terms of x. (2) Show that the cost , C, of the material is given by: C(x) = 400x2 + 360x 1 (3) Calculate the value of x for which the cost of the material will be a minimum and hence the minimum cost of the material. (5) [10] 2xxhMathematics/P1 8 june 2014 Common Test NSC Please Turn Over Copyright Reserved INFORMATION SHEET: MATHEMATICS aacbbx242 r )1(niPA )1(niPA niPA)1( niPA)1( dnaTn)1( dnann)1(22S 1 nnarT 11 rraSnn ; 1zr raS f1; 11 r >@iixFn11 [1 (1)]nxiPi hxfhxfxfh)()(lim)('0 o 22)()(1212yyxxd M 2.

9 22121yyxx cmxy )(11xxmyy 1212xxyym Ttan m 222rbyax In 'ABC: CcBbAasinsinsin ' 1cos2sin21sincos2cos2222 DDDDD nfxx nxxnii221 V SnAnAP)()( P(A or B) = P(A) + P(B) P(A and B)bxay 2)()(xxyyxxb