PAST EXAM PAPER & MEMO N4

1 Website: Email: PAST EXAM PAPER & MEMO N4 ABOUT THE QUESTION PAPERS AND ONLINE INSTANT ACCESS: THANK YOU FOR DOWNLOADING THE PAST EXAM PAPER AND ITS MEMO, WE HOPE IT WILL BE OF HELP TO YOU. SHOULD YOU NEED MORE QUESTION PAPERS AND THEIR MEMOS PLEASE SEND US AN EMAIL TO INFO@ AND WE WILL SEND YOU A FULL DOWNLOAD VERSION OF THESE THOUGH A FULL DOWNLOAD COMES AT A COST. ALTERNATIVELY YOU CAN PURCHASE THEM ONLINE FROM OUR WEBSITE TO AVOID DELAYS AND YOU FOLLOW ALL THE NEEDED STEPS TO GET INSTANT DOWNLOAD. WITH ONLINE PAYMENT YOU CAN GET INSTANT DOWNLOADS OF YOUR PURCHASE. WE SELL PREVIOUS PAPERS AND MEMOS FOR THE SUBJECTS MENTIONED AND THE PAPERS ARE BETWEEN 2014-2019. THE PAPERS ARE IN PDF FORM AND EACH PDF HAS A MINIMUM OF SEVEN DIFFERENT PAPERS. THE YEARS FOR THE PAPERS YOU ARE PURCHASING ARE ALSO INCLUDED ON THE WEBSITE.

2 PRICE OF THE PAPERS AT A BIG DISCOUNT Previous papers are very important in ensuring you pass your final exams . The actual value of the papers we are making you access is way more than R1 000 and we are making these very cheap as we have you in mind. For a small amount you can have these papers. THE COST PER SUBJECT IS R300. Website: Email: info@ CELL: 073 770 3028 (16030164) -1- (E)( )T Copyright reserved T960(E)(A7)T APRIL EXAMINATION NATIONAL CERTIFICATE MATHEMATICS N4 (16030164) 7 April 2016 (X- PAPER ) 09:00 12:00 Scientific calculators may be used. This question PAPER consists of 5 pages and 1 formula sheet. (16030164) -2- T960(E)(A7)T Copyright reserved Please turn over DEPARTMENT OF HIGHER EDUCATION AND TRAINING REPUBLIC OF SOUTH AFRICA NATIONAL CERTIFICATE MATHEMATICS N4 TIME: 3 HOURS MARKS: 100 INSTRUCTIONS AND INFORMATION 1.

3 2. 3. 4. 5. 6. 7. 8. Answer ALL the questions. Read ALL the questions carefully. Number the answers according to the numbering system used in this question PAPER . Show ALL intermediate steps and simplify where possible. ALL final answers must be rounded off to THREE decimal places (unless indicated otherwise). Questions may be answered in any order, but subsections of questions must be kept together. Use only BLUE or BLACK ink. Write neatly and legibly. (16030164) -3- T960(E)(A7)T Copyright reserved Please turn over QUESTION 1 Draw the graph of 20,cos20 xecxy (3) Is the graph of ecxycos2 in QUESTION above a function or a relation? (1) Is the graph of ecxycos2 in QUESTION above symmetrical or asymmetrical about the X-axis?

4 (1) Draw the graph of the inverse of xy11 (3) What is the domain of the graph of the inverse of xy11 in QUESTION above? (2) Given: acbbcacba 2323 Solve the value of 'a' by using Cramer's rule only. (8) Given: 311021 Calculate the value of the determinant. (2) [20] QUESTION 2 Calculate the value of A2sin if 2524cos A and A is in the first quadrant. (3) Solve for the value of 'A' if: 001800;cos342cos5 AAA (5) Prove that: AAAAsec2sincos1sin2 (3) (16030164) -4- T960(E)(A7)T Copyright reserved Please turn over Simplify: aaaaaa (2) If 53cos x and 1312sin y and both 'x' and 'y' are acute angles, determine without the use of a calculator the value of yx cos.

5 (4) Prove that: AAcos22cos22 (3) [20] QUESTION 3 The perimeter of a field in the form of a right-angled triangle is 60 m. The length of the hypotenuse is 25 m. Calculate the lengths of the other two sides. (5) Solve for 'x' if: x (3) Make 'c' the subject of the formula if: Rctei10 (3) Solve for 'x' if: 057 xx (4) Rationalise: sincos1j (3) Given: 63jz Convert z into polar form. The argument may only be positive. (2) [20] (16030164) -5- T960(E)(A7)T Copyright reserved QUESTION 4 Determine the following limit: 121lim33xxxx (4) Given: 251 xxy Calculate, using differentiation, the co-ordinates of the maximum and minimum turning points. (7) Differentiate with regard to 'x': xexxxy2cos3lncot26 (5) Use the quotient rule to differentiate the following: 4 xxy (4) [20] QUESTION 5 Simplify: dAAA22sincos (3) Evaluate: dxx 4213ln (3) Sketch and indicate clearly the area enclosed by the graph of 22 xy, 0 x and 2 x.

6 Also indicate the representative strip used to calculate the indicated area. (3) Calculate, using integration, the magnitude of the area indicated in QUESTION above. (4) Integrate: dxxaxxxx 433cos3132cos2sin (7) [20] TOTAL: 100 (16030164) T960(E)(A7)T Copyright reserved FORMULA SHEET MATHEMATICS N4 babaxxloglog n x = logex (r | )n = rn | n a + bj = c + dj a = c and b = d sin(a b) = sina cosb sinb cosa sin2x + cos2x = 1 cos(a b) = cosa cosb sina sinb 1 + cot2x = cosec2x 1 + tan2x = sec2x tan (a b) = btanatan1btanatan y dy dx axn naxn-1 y = u(x) v(x) xvxuxvxudxdy11 )()(=xvxuy 211xvxvxuxuxvdxdy dxdududydxdy = kax kax na k nx xk sin x cos x cos x -sin x tan x sec2x cot x -cosec2x sec x sec x tan x cosec x -cosec x cot x Cnaxdxaxnn 11 cnxadxxa cnakadxkaxx buoxydxA sin xdx = -cosx + c cos xdx = sinx + c tan xdx = nsec x + c sec xdx = n(sec x + tan x)

7 + c Copyright reserved Please turn over NATIONAL CERTIFICATE APRIL EXAMINATION MATHEMATICS N4 7 APRIL 2016 This marking guideline consists of 8 pages. MARKING GUIDELINE MARKING GUIDELINE -2- T960(E)(A7)T MATHEMATICS N4 Copyright reserved Please turn over QUESTION 1 ecxycos2 2 labelling shapes (3) Function (1) Symmetrical (1)

8 Yx11 shape yx11 labelling (3) Rxxx ,1: (2) y x 2 -2 x y 1 MARKING GUIDELINE -3- T960(E)(A7)T MATHEMATICS N4 Copyright reserved Please turn over 09,15,5663123121310131210131211113211011 3113215312121111121211121211111211111211 1 aDaDo (8) (2) [20] MARKING GUIDELINE -4- T960(E)(A7)T MATHEMATICS N4 Copyright reserved Please turn over QUESTION 2 AAA (3) 010022537,10151cos1806051cos21cos01cos51 cos201cos3cos1004cos31cos25 AAAjAAAAAAA (5) AAAAAAAAAAA seccos1secsin21cos1sin2seccossin2cos1sin 2 (3) aaaaaa (2) yxyxyx (4) AAAAAAAAcos2cos2cos2cos4cos22cos42cos21c os222222 (3) [20] MARKING GUIDELINE -5- T960(E)(A7)

9 T MATHEMATICS N4 Copyright reserved Please turn over QUESTION 3 203515:153520:2152,200152003003562535336 252351ln251602211122222 yyyyyynxxxxxxxxnyxyxzzyx (5) 429,14ln25,7ln25,7ln4ln xxx (3) 000000000lnlnlnln1 IiIRtcIiIRCtIiIeIiIeIieRCtRCtRCt (3) MARKING GUIDELINE -6- T960(E)(A7)T MATHEMATICS N4 Copyright reserved Please turn over 2352352352745507521122jxjxxxxx (4) sincossincossincossincossincossincossinc ossincossincossincos122222jjjjjjjjxj (3) 0122435,632tan708,6456363 rrjz (2) [20] MARKING GUIDELINE -7- T960(E)(A7)T MATHEMATICS N4 Copyright reserved Please turn over QUESTION 4 73121211212111111121lim222 xxxxxxxxxxx (4) 0,5&32,10,50,118602551519532251151915105 1056151832222222322312122 MmMdxydxmdxydxxdxydyyxxxxxxxxdxdy (7) 2220tansec36cos2xxxxxecdxdy (5) ;421.

10 XxxxvuvuvdxdyvxvxuxuLet (4) [20] MARKING GUIDELINE -8- T960(E)(A7)T MATHEMATICS N4 Copyright reserved QUESTION 5 cAdAA 22sin2cos (3) 504, xx (3) 22 xy shape shaded area rep. strip (3) 23203202667,602232232uxxdxxAox (4) cxaxxxxx 433sin934cos24 (7) [20] TOTAL: 100 y x y dx 2 2 Website: Email: THANK YOU FOR DOWNLOADING PAST EXAM PAPER & MEMO FOR N4 IF YOU NEED MORE PAPERS WE SELL THEM FOR R300 VISIT OUR WEBSITE AT OR SEND US AN EMAIL AT AND WE WILL GLADLY HELP YOU.