PAST EXAM PAPER & MEMO N3 ABOUT THE QUESTION PAPERS:

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1 EKURHULENI TECH COLLEGE. N. 3 Mgale Square, Krugersdrp. Website: www. ekurhulenitech.c.za inf@ekurhulenitech.c.za TEL: CELL: / PAST EXAM PAPER & MEMO N3 ABOUT THE QUESTION PAPERS: 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 TO INFO@EKURHULENITECH.CO.ZA AND WE WILL SEND YOU A FULL DOWNLOAD VERSION OF THESE. HOWEVER PLEASE NOTE THAT THESE ARE SOLD FOR A SMALL AMOUNT OF R300 PER DOWNLOAD PER SUBJECT. ABOUT REGISTERING WITH OUR COLLEGE CONSIDER REGISTERING WITH OUR COLLEGE AND WE HAVE THE FOLLOWING TYPES OF LEARNING: ONLINE OR CORRESPONDENCE LEARNING. THIS IS THE MOST PREFARED ONE BY THOUSANDS PART-TIME CLASSES DURING SATURDAYS IF NEAR OUR OFFICES IN KRUGERSDORP FULL-TIME CLASSES IF NEAR OUR CLASSES IN KRUGERSDORP ABOUT EXTRA TEXTBOOKS IF LOOKING FOR TEXBOOKS FOR CERTAIN SUBJECTS I N-N6 ENGINEERING STUDIES PLEASE SEND US AN ON INFO@EKURHULENITECH.CO.ZA ABOUT VIDEO MATERIAL WE HAVE VIDEO MATERIAL FOR EXTRA UNDERSTANDING ON CERTAIN ENGINEERING FOR A FEE. REQUEST A QUOTE. SEND US AN ON INFO@EKURHULENITECH.CO.ZA Website: inf@ekurhulenitech.c.za

2 T950(E)(A)T APRIL EXAMINATION NATIONAL CERTIFICATE (603043) April 06 (X-Paper) 09:00 :00 This questin paper cnsists f 6 pages and frmula sheet f pages.

3 (603043) -- T950(E)(A)T DEPARTMENT OF HIGHER EDUCATION AND TRAINING REPUBLIC OF SOUTH AFRICA NATIONAL CERTIFICATE TIME: 3 HOURS MARKS: 00 INSTRUCTIONS AND INFORMATION Answer ALL the questins. Read ALL the questins carefully. Number the answers accrding t the numbering system used in this questin paper. Questins may be answered in any rder but subsectins f questins must NOT be separated. Shw ALL the calculatins and intermediary steps. ALL final answers must be accurately apprimated t THREE decimal places. ALL graph wrk must be dne in the ANSWER BOOK. Graph paper is NOT supplied. Diagrams are NOT drawn t scale. Write neatly and legibly.

4 (603043) -3- T950(E)(A)T QUESTION. Factrise the fllwing epressins as far as pssible in prime factrs:.. (3 ) y(3y ).. 4p p 4n 3n (). Factrise the fllwing epressin cmpletely: 3 5 (5).3 Simplify the fllwing epressin: (6) [7] QUESTION. Simplify the fllwing: 3 3. Use lgs t the base and simplify the fllwing WITHOUT using a calculatr: lg0,58.3 Slve fr : (lg ) lg( ) 0 ( 4) (8) [6]

5 (603043) -4- T950(E)(A)T QUESTION 3 3. Slve fr by cmpleting the square: Make 'b ' the subject f the frmula: b D b 3.3 Make ' w ' the subject f the frmula: lge t lge p lge w ds (3) 3.4 Ale paid a depsit f R3 fr a cmputer. He paid the rest in 9 mnthly instalments. He paid a ttal f R33. What is the payment f each mnthly instalment in terms f. [5] QUESTION 4 4. Cnsider FIGURE A belw. ABC is an issceles triangle with AB BC and vertices A(;), B(4;5) and C(0;k). FIGURE A

6 (603043) -5- T950(E)(A)T 4.. Find the length f AB. () 4.. Determine the value(s) f k Shw that AB is perpendicular t BC if k 7. (3) 4..4 Calculate the area f ABC when k 7. (3) 4. P ( ; ) and Q (4;7) are pints in the plane with M as the midpint f PQ. Determine the equatin f the line parallel t the y-ais and passing thrugh the pint M. 4.3 Cnsider FIGURE B belw. The lines BA and CA with equatins y and y 3 3 respectively, intersect at A. Determine the size f BAC ˆ where B and C are the intercepts n the -ais as shwn. FIGURE B (5) []

7 (603043) -6- T950(E)(A)T QUESTION 5 5. Draw the graph defined by the equatin: 3 3y 7 () 5. Given : 3 y Make use f differentiatin t determine the crdinates f the turning pints f the given equatin. (5) 5.. Draw the graph f the given functin. Shw ALL values at the pints f intersectin with the system f aes and the c-rdinates f the turning pints. (3) 5.3 Determine dy d if y. Leave the answers with psitive indices and in surd frm. [4] QUESTION 6 6. Prve the fllwing trignmetric identity: sin A tan A cs A sec A 6. Calculate the value(s) f which will satisfy the equatin if 0 70 : sin cs (5) 6.3 Cnsider FIGURE C belw. An bserver, standing at a pint A is watching the tp f a vertical twer BC. The angle f elevatin f the tp f the twer, BC, is 5 and the angle f depressin f the ft f the twer is 0. If the height f the twer BC is knwn t be 30 m, determine the fllwing: 6.3. The distance between the bserver at A and the pint B. (3) 6.3. The distance between the tw twers. (3)

8 (603043) -7- T950(E)(A)T FIGURE C 6.4 Cnsider FIGURE D belw. The sketch represents the graph f f ( ) asin p where 0. Determine the values f a and p. FIGURE D () [7] TOTAL: 00

9 (603043) -- T950(E)(A)T FORMULA SHEET Any applicable frmula may als be used.. Factrs. Lgarithms a 3 - b 3 = (a - b)(a + ab + b ) lg ab lg a lg b a 3 + b 3 = (a + b)(a - ab + b ) lg a b lg a lgc a 3. Quadratic frmula lgb a lgc b lg b b b 4ac lg a m m lg a a 4. Parabla lgb a lga b y a b c lg a a n e 4ac y 4a b a b a lg a t t e n m m 5. Circle 6. Straight line y r y y m( ) D h 4h 4Dh 4h Perpendicular: m m Parallel lines: m m Distance: D ( ) (y y ) Midpint: P ; y y Angle f inclinatin: - θ tan m

10 (603043) -- T950(E)(A)T 7. Differentiatin dy d lim h 0 f h f h d d n - n n Ma/Min Fr turning pints: f ' 0 8. Trignmetry sinθ csθ tanθ y r r y csecθ secθ ctθ sin θ cs θ tan θ sec θ ct θ csec θ tanθ sinθ csθ csθ ctθ sinθ sina a sinb b sinc c a b c bc csa Area f ABC = ½ ac sin B

11 MARKING GUIDELINE NATIONAL CERTIFICATE APRIL EXAMINATION APRIL 06 This marking guideline cnsists f 0 pages.

12 MARKING GUIDELINE -- T950(E)(A)T QUESTION... (3 ) y(3y ) 3 3y y 3( y ) ( y) 3( y)( y) ( y) ( y)[3( y) ] ( y)[3 3y ].. 4p p 4n 3n p p ( n )(4n ) (). 3 f ( ) 5 f 3 () () () 5() = 5 =0 - is a factr f f ( ) ( ) ( )( 3 ) f = ( )( )( ) (5)

13 MARKING GUIDELINE -3- T950(E)(A)T.3 3) )( ( = 3) )( ( 7 7 ) )( ( 3) )( ( = 3) )( ( ) )( ( 3) ( 5 (6) [7]

14 MARKING GUIDELINE -4- T950(E)(A)T QUESTION. 3. 0, lg lg8 lg lg lg 7 7lg lg TEST : If then LHS=RHS=5.3. (lg ) lg( ) 0 lg 0 r lg( ) 0 lg = [6]

15 MARKING GUIDELINE -5- T950(E)(A)T QUESTION D b b

16 MARKING GUIDELINE -6- T950(E)(A)T 3.3 lg e tw ds p tw e p ds w p t ds e (3) 3.4 Depsit is R3 Ttal price is R33 Ttal amunt fr 9 instalments= R Each mnthly instalment = R R 9 3 [5]

17 MARKING GUIDELINE -7- T950(E)(A)T QUESTION y y AB = 4 5 = 4 6 = 0 = 5 () 4.. BC= 5 k k 5 = 0 k 5 = 4 k 5 = k 5 r k 5 k 7 k M AB M CB 0 4 MAB MCB therefre CB AB (3) 4..4 Area f ΔABC = base height = AB BC = 0 0 =0 units (3)

18 MARKING GUIDELINE -8- T950(E)(A)T 4. y y crdinates f M ; 4 7 = ; =(;3) Equatin = 4.3 MAB MAC 3 tan tan =3 =45 =7,565 BAC ˆ = = 7, = 6,565 (5) [] QUESTION y 7 Y X -3 ()

19 MARKING GUIDELINE -9- T950(E)(A)T y 6 9 dy d Let y ( 4 3) 0 ( )( 3) 0 r 3 f f 3 ( ) ( ) 6( ) 9( ) 4 3 ( 3) ( 3) 6( 3) 9( 3) 0 Turningpints ( 3;0) and ( ; 4) (5) 5.. (3) 5.3 y y dy (0,5) d dy d [4]

20 MARKING GUIDELINE -0- T950(E)(A)T QUESTION sin cs sin sin sin sin 0 sin (sin ) 0 sin 0 r sin r 80 0 r 90 (5) In ABC : AB 30 sin 70 sin 45 30sin 70 AB sin 45 39,868m (3) 6.3. In ABD : AD cs 5 AB AD AB cs 5 39,868cs 5 36,33m (3)

21 MARKING GUIDELINE -- T950(E)(A)T 6.4 a p () [7] TOTAL: 00

22 EKURHULENI TECH COLLEGE. N. 3 Mgale Square, Krugersdrp. Website: www. ekurhulenitech.c.za inf@ekurhulenitech.c.za TEL: CELL: / REGISTERING WITH OUR COLLEGE CONSIDER REGISTERING WITH OUR COLLEGE AND WE HAVE THE FOLLOWING TYPES OF LEARNING: ONLINE OR CORRESPONDENCE LEARNING. THIS IS THE MOST PREFARED ONE BY THOUSANDS PART-TIME CLASSES DURING SATURDAYS IF NEAR OUR OFFICES IN KRUGERSDORP FULL-TIME CLASSES IF NEAR OUR CLASSES IN KRUGERSDORP ABOUT EXTRA TEXTBOOKS IF LOOKING FOR TEXBOOKS FOR CERTAIN SUBJECTS I N-N6 ENGINEERING STUDIES PLEASE SEND US AN ON INFO@EKURHULENITECH.CO.ZA ABOUT VIDEO MATERIAL WE HAVE VIDEO MATERIAL FOR EXTRA UNDERSTANDING ON CERTAIN ENGINEERING FOR A FEE. REQUEST A QUOTE. SEND US AN ON INFO@EKURHULENITECH.CO.ZA Website: inf@ekurhulenitech.c.za