MEMORANDUM ISEBE LEMFUNDO LEMPUMA KOLONI EASTERN CAPE EDUCATION DEPARTMENT OOS-KAAP ONDERWYSDEPARTEMENT

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1 MATH MEMORANDUM ISEBE LEMFUNDO LEMPUMA KOLONI EASTERN CAPE EDUCATION DEPARTMENT OOS-KAAP ONDERWYSDEPARTEMENT IIMVIWO ZEBANGA LESHUMI ELINANYE GRADE EXAMINATIONS GRAAD -EKSAMEN NOVEMBER 008 MATHEMATICS SECOND PAPER This memrandum cnsists f pages.

2 MATHEMATICS SECOND PAPER (MATH) (MEMO /08) QUESTION. AB ( x x) + (y y) frmula. ( ) + ( y y Gradient f AB x x 8 ( ) - ) () frmula (). tan m ,80,6. Equatin f AB : y y m(x x ) y ( -) - ( x ) y + - x + 8 y - x - tan ref. angle () frmula (). Crdinates f C: ( 0;- 8 ) ().6 Midpint f AB + 8 ; The crdinates f C x + x y + y ; ; 8 0; ; C is nt the midpint f AB frmula ; cnclusin () [8]

3 (MEMO /08) MATHEMATICS SECOND PAPER (MATH) QUESTION x + x y + Midpint f PR : M ( ; ) + + M ; m PR y x - - y x - - (-) y M (- ; ) - (-) 6 mmq mpr. mmq ( - ) - PR QM Prduct f gradients - 6 Area bh Area f RMQ ( PR MQ) PR ( ) + ( ) MQ 0 0 Area f RMQ unit ( ) + ( + ) () - - cnclusin () PR 0 MQ 0 (). y x y x - gradient f the line gradient f the parallel line is Equatin f the parallel line is y y m( x x ) Substituting ( ; - ) y + ( x - ) y x - 7. m AB m BC OR M AB ½ 0 ( -) p 0 y ½ (x+) --(-) ( -) y ½ x+ p p Subst (;p) p ½ + gradient gradient f parallel line (; -) () m AB m BC () [8]

4 MATHEMATICS SECOND PAPER (MATH) (MEMO /08) QUESTION C (-;9) B (-6; 8) A (-; ) G(-;0) E(-;-) C(;9) 9 B(6; 8) A(; ) F(0;-) F A (-;) B (-6;8) C (-;9) ().. E(-;- ) F(0;-) G(- ;0) ().. D(-8;-6) ().. Rtatin clckwise arund rigin thrugh 90 clckwise arund rigin rtatin 90 ().. (-;-) ().. Scale factr ().. P ; Q ; R 7 ; () [7]

5 (MEMO /08) MATHEMATICS SECOND PAPER (MATH) QUESTION.. OP (-) OP Applying Pythagras therem (). tan(80 + α ) tan α -.. β α - 90 sin β sin (α -90 ) sin (-(90 - α )) - sin(90 - α ) - cs α - ( - ) tan α () β α sin(90 - α ) - cs α ().. LHS sin x. cs x. sin x cs x sin x cs x RHS sin x cs x sin x - cs x ().. RHS sin y cs y cs y cs y ( + cs y)( - cs y) - cs y + cs y LHS cs y factrs simplificatin () []

6 6 MATHEMATICS SECOND PAPER (MATH) (MEMO /08) QUESTION. (- sin θ)(- sin θ) ( - sin θ) tan θ - sin θ sinθ csθ - cs θ - sin θ - sin θ - sin θ tan θ sinθ csθ (6). (- sin0 ) ( - cs 0 ) tan sin 0 ( - sin 60 ) ( - ) - - sin 60. cs0.. OR OR sin 60 cs0 - cs 0 sin 0 - sin (8) [] QUESTION 6 6. tan θ 6 tan θ θ ,9, 6. sin x 0 r cs x - x k x k r x k x k cs x - where k ε Z x k r x k tan θ reference angle ,9 () sin x 0 r cs x - x k x k x k x k x k x k k ε Z (9)

7 (MEMO /08) MATHEMATICS SECOND PAPER (MATH) p () 6.. x -90 ; 0 ; 90 ; 80 mark per values () 6.. Minimum value f f(x) - () [7] QUESTION 7 7. PR S 80 -,,9 and RP S,7 In PRS: PS RS sin,9 sin,7 RS.sin,9 PS sin,7,7.sin,9 sin,7 0,9 km 7. Height f the muntain is PQ PQ sin, PS PQ PS.sin, 7. 0,9.sin,,7 km Area f PRS. RS. PS.sin, 7 (,7)(0,9) sin,7 7,8km,9 and,7 applying sine rule () PQ sin, PS area rule () () []

8 8 MATHEMATICS SECOND PAPER (MATH) (MEMO /08) QUESTION 8 8. Slant height: H h + r H 98, mm Using Pythagras therem () 8. Exterir surface area r + rh x 9 x 9 + x 9 x, 9,6mm Ttal exterir surface area x 9,6 79mm using frmula 9,6mm () 8. Vlume f the cne π r h frmula π 9 9 0,7mm Vlume f sand after minutes,7mm 66,7mm,7mm divisin by () []

9 (MEMO /08) MATHEMATICS SECOND PAPER (MATH) 9 QUESTION Mde 9 () 9.. Arithmetic mean ,8 0 () rder Median , 9.. Lwer quartile(q ) 9 Upper quartile (Q ) () Range , 8 Skewed t right / mre spread ut n right bx whiskers cmment () () () []

10 0 MATHEMATICS SECOND PAPER (MATH) (MEMO /08) QUESTION 0 0. MARKS TALLY FREQUENCY CUM. FREQ. 0-9 //// 0-9 //// //// //// /// //// //// 0 Tally Frequency Cumm. Frequency () 0. Ogive representing marks Cummulative frequency axes Pltting pints shape () Marks 0. x x 90 9 n 0 x x - x (x - x ) Variance n i ( x x) 0 0 Standard deviatin,9 {Answer nly (using calculatr) Full marks} i n 90 x (x - x ) frmula fr variance S.D var iance (6) []

11 (MEMO /08) MATHEMATICS SECOND PAPER (MATH) QUESTION. Gals Scatter plt Match axes and labels pltting pints (). Linear (). See graph drawing (). 9 accrding t candidate s graph () [6] Ttal: 0