Mathematics Grade 12 KZN March 2017 Memo

Downloaded from hlayiso.com education y Department: Education PROVINCE OF KWAZULU-NATAL ENQUIRIES: MR B.A. SEWLALL CONTACT NO: 031 » 327 0462 DATE: 13 MARCH 2017 NATIONAL SENIOR CERTIFICATE: COMMON TEST MARCH 2017 GRADE 12 TO: THE CHIEF INVIGILATOR OF ALL SCHOOLS OFFERING MATHEMATICS ERRATA Please take note of the following change: PAGE NUMBER ERROR CORRECTION 5 QUESTION 4 we © (=p; a) C (p; q) (Statement) Kindly ensure that candidates are informed of the Errata. Zest tals] 2014 MS N.V. MCAMBI DATE DEPUTY MANAGER PROVINCIAL EXAMINATIONS SERVICES KWAZULU-NATAL DEPARTMENT OF ROUGATION «.Champloning Quality ducation-Creating and Securing a Brighter Future Postal Addiess: Private Bag X01 « Bast End » 4018 » Republic of South Africa j 72) Stalware Simdliitie Stet Maigate Building». burban + A0O%:> , ony. sewlal@kuneto OOOH FAK 427 031-391 GO18 + Bie Jobrwuw.keneducation.goviid. \

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Marks: 100 Time: 2 hours Copyright Reserved : Dawnloaged Om nia e Om Education KwaZulu-Natal Department of Education REPUBLIC OF SOUTH AFRICA SRR GSR RRR SRS SS ES EGS SSR SSR SESE SSRE SERS R HERES MATHEMATICS hoses COMMONTEST = =————~«<‘“ . a MARCH 2017 oo . NATIONAL SENIOR CERTIFICATE N.B. This question paper consists of 8 pages and an information sheet. Please Turn Over NTT NUCL

Downloaded from hlayiso.com , , - 2 Mathematics March 2017 Common Test NSC INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 8 questions. 2. Answer ALL questions. 3. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers. 4, Answers only will not necessarily be awarded full marks. 5. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise. 6. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise. 7. Diagrams are NOT necessarily drawn to scale. 8. Number the answers correctly according to the numbering system used in this question paper. Write neatly and legibly. Copyright Reserved Please Turn Over

Downloaded from hlayiso.com Mathematics 3 March 2017 Common Test NSC QUESTION 1 1.1 Determine the derivative of f(x) =x +3x from first principles. (5) 1.2 Evaluate: | | 1.2.1 ® ip ya3x? 2 8x" (4) dx | x? -5x? +4x 1.2.2 f'(x)if f@)=—— x#4 (5) x- | [14] Copyright Reserved Please Turn Over

Downloaded from hlayiso.com 4 Mathematics March 2017 Common Test NSC QUESTION 2 21 Determine co-ordinates of the points on the curve y= 4 where the gradient of the x tangent to the curve is— 1. (5) 2.2. The graph ofa cubic function with equation f(x) =x° + ax? +6x-+c¢ is drawn. » fY=fA=0 » J has a local maximum at B and a local minimum at x = 4. y B ro) T cy 2.2.1 Show that a =-9, b= 24 andc =-16. (4) 2.2.2 Calculate the coordinates of B. (5) 2.2.3 Write down the value(s) of k for which f(x) = k has negative roots only. (2) 2.2.4 Determine the value(s) of x for which fis concave up. (3) [19] Copyright Reserved Please Turn Over

Mathematics NSC. QUESTION 3 A rectangular box has a length of 5x units, breadth of (9 - 2x) units and its height of x units. (9 —2x) 5x 3.1 Show that the volume (V) of the box is given by V=45x?—10x° . 3.2 Calculate the value of x for which the box will have maximum volume. QUESTION 4 In the figure below, A (-1; 3) , B (3; -1) and C (-p; q) are vertices of A ABC. Area of A ABC = 12 square units. CDis L AB. yA ACA;8) D < Q Rg A B(3;-1) ce | 4.1 Determine the coordinates of D, the midpoint of AB 4.2 Show thatp = ¢ 4.3 If p ; q <0, determine the co-ordinates of C. Copyright Reserved Downloaded from hlayiso.com Match 2017 Common Test (2) 6) [7] (2) (5) (5) [12] Please Turn Over

Mathematics QUESTION 5 Downloaded from hlayiso.c 6 NSC om March 2017 Common Test In the accompanying diagram alongside, P(3; 2) lies on the circumference of a circle with centre M. The circle also passes through the origin. Q is the intercept of the circle with the x-axis. Determine: y cS P(3;2) 5.1 the co-ordinates of M. M 5.2 the gradient of OP. « Q_, 5,3. the equation of the circle M. 6) x 5.4 the co-ordinates of Q. 5.5 the equation of the line through Q, parallel to OP. v QUESTION 6 y 6. In the diagram alongside, REJp : Jp -3) is a point R-alp ; Jp-3) ina Cartesian plane, ROX = 0 6.1 Express cos”@ in terms of p. 6.2 Hence, for which real values of p is cos’@ defiried? 6.3 Determine cos a Copyright Reserved in terms of p if a and @ are supplementary. 2) qd) (3) (4) (3) [13] (5) (2) (2) 19] Please Turn Over

Mathematics NSC QUESTION 7 71 7.2 73 Simplify WITHOUT the use of a calculator cos 225° . sin (135°) - sin 330° tan 225° Prove the identity: tan x — sin x _ 1 sin? x cos x (I + cos x) Determine the general solution of cos 2x +cosx —2=0 Copyright Reserved Downloaded from hlayiso.com 7 March 2017 Common Test (6) G) G) [16] Please Turn Over

Downloaded from hlayiso.cen NSC Mathematics QUESTION 8 8.1 Given A KMN, with N obtuse, as shown in the diagram below: K sin M _ sin N m n Prove that 8.2 In the diagram below, S,Q and R are points in the same plane. PS is a vertical telephone mast. The angle of elevation of P from Q is 9. SOR = x, SRQ = y, QR = 10m, 8.2.1 Express PS in terms of QS and 0 10 sin y 8.2.2 Show that QS = ————*+~ sin (x +y) Copyright Reserved 2017 Common Test 4) (2) 4) [10] TOTAL: 100 Please Turn Over

| parley =I i ey — fam L+A)- F(X) | 2) = jim h d=) -x%) +0,-y,) Downloaded from hlayiso.com Mathematics 9 March 2017 Common Test NSC INFORMATION SHEET _ abt vb? ~4ac 2a A= P(l+ni) A= P(|—ni) A= P(1-i)" A=P(+i)" n T, =at+(n—-ld 8, = 5 a+ @—Dd] T, =ar™" Ss _ ate" -1) ir#1 8, =—-;-ler<l | 1-r pe sl") L xX, +X. + u( 2.41 22) 2 2 y=mxte y-y, =m(x-x,) a2 m= tan@ Xq xy (ca) +(y~b) =r? inaasce: = 4 Pt a =b? +c —2be.cos A area AABC = 5abasinC sin(a + 8) = sina.cos B + cosazsin B cos(a + £) = cos @.cos 8 —sina.sin B cos’ a—sin? a cos 2@ =41~-2sin? a 20s? @-1 Copyright Reserved sin(o.— B)=sin o.cos$ —cos asin cos(a - 8) = cosa. cos B +sina.sin B sin 2o = 2sina.cosa A y (x; 7 xy ist n a= P(A or B) = P(A) + P(B) ~ P(A and B) ja at HV- I) di@-xy

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