MATHEMATICS P2 COMMON TEST JUNE 2014 NATIONAL SENIOR CERTIFICATE

Transcription

1 Mathematics/P Jue 04 Cmm Test MATHEMATICS P COMMON TEST JUNE 04 NATIONAL SENIOR CERTIFICATE GRADE Marks: 5 Time: ½ hurs N.B. This questi paper csists f 9 pages, diagram sheets ad ifrmati sheet.

2 Mathematics/P Jue 04 Cmm Test INSTRUCTIONS AND INFORMATION Read the fllwig istructis carefully befre aswerig the questis.. This questi paper csists f SIX questis.. Aswer ALL the questis.. Clearly shw ALL calculatis, diagrams, graphs, et cetera that yu have used i determiig yur aswers. 4. Aswers ly will t ecessarily be awarded full marks. 5. Yu may use a apprved scietific calculatr (-prgrammable ad -graphical), uless stated therwise. 6. If ecessary, aswers shuld be ruded ff t TWO decimal places, uless stated therwise. 7. A diagram sheet fr aswerig QUESTION 4., QUESTION 5., QUESTION 6., QUESTION 6. ad QUESTION 6. is attached at the ed f this questi paper. Write yur ame these diagram sheets i the spaces prvided ad isert the diagram sheets iside the back cver f yur ANSWER BOOK. 8. Diagrams are NOT ecessarily draw t scale. 9. A ifrmati sheet with frmulae is icluded at the ed f this questi paper. 0. Number the aswers crrectly accrdig t the umberig system used i this questi paper.. Write eatly ad legibly.

3 Mathematics/P Jue 04 Cmm Test QUESTION. A(; 4), B( ; ) ad C(4; ) are vertices f ABC i the cartesia plae as shw i the figure belw. M is the midpit f AB. y A(; 4) M C(4; ) x B(, ).. Calculate the legth f AC (leave the aswer i simplified surd frm) ().. Determie the c-rdiates f M. ().. Fid the equati f the perpedicular bisectr f AB. (4). The equati f a circle is give as (x ) + (y + ) = (x y)... Write dw the equati f the circle i the frm x a y b r. (4).. Hece, write dw the c-rdiates f the cetre ad the legth f the radius f the circle. () [5]

4 Mathematics/P 4 Jue 04 Cmm Test QUESTION. I the diagram belw, J ( ; ), K(p; 4), L(5; 0) ad M(; ) are vertices f trapezium JKLM. Als JK // ML. y M( ; ) J( ; ) x L(5 ; 0) x K(p ; 4).. Shw that p =. (4).. Calculate JK: LM i the simplest frm. (5).. Q (x; y) JK is such that JQLM is a parallelgram, determie the c-rdiates f Q. (5)..4 Determie the equati f the lie passig thrugh K ad M. ()..5 Write dw the value f, the icliati f lie KM. ()..6 If pits, R (; k), J ad L are clliear, calculate the value f k. (4)

5 Mathematics/P 5 Jue 04 Cmm Test. I the diagram algside, cetre Q f the circle lies the straight lie x + 4y + 7 = 0. The straight lie cuts the circle at W ad Z ( ; ). The circle tuches the y - axis at P (0 ; ). W Q P (0; ) y x Z ( ; ).. Determie the equati f the circle i the frm x a y b r (5).. Determie the legth f diameter WZ. () [7] QUESTION. Shw withut usig a calculatr that: 6 si 5 () 4. Write the fllwig as a sigle trigmetric rati: si ta 80. cs cs 90 cs 540.cs (9) (5). Prve that: si 45 x.si 45 x cs x si cs.4 Shw = (6) si cs tax.5 Determie the geeral sluti f the equati: 0 ta 4 (5) [8]

6 Mathematics/P 6 Jue 04 Cmm Test QUESTION 4 4. Give FGH with Ĝ btuse. F Use the abve diagram t prve that: G si G g H si H (5) h 4. I the diagram algside, P, Q ad R are pits the same hriztal plae. W WP is a vertical telephe mast. The agle f elevati f W frm Q is. PQˆ R y, QR = 5 metres. PRˆ Q x ad P Q y 5 m x R 4.. Express PW i terms f PQ ad. () 5 si y Hece, shw that PR (4) si x y If x = y, shw that PW ta 7,5 () cs y [4]

7 Mathematics/P 7 Jue 04 Cmm Test QUESTION 5 5. Cmplete the fllwig therem statemet: Oppsite agles f a cyclic quadrilateral are () 5. I the figure algside, RS ad RNP are tagets t the circle with cetre O at the pits S ad N. Radius NO is prduced ad cuts the circle at M ad meets RS prduced at T. T S 4 M O R N P 5.. Why is R ŜO = 90? () 5.. Prve that RNOS is a cyclic quadrilateral. (4) 5.. If Ŝ x, determie, with reass, FOUR ther agles i the figure which are equal t x. (8) 5..4 Prve that Ŝ Ô (4) [8]

8 Mathematics/P 8 Jue 04 Cmm Test QUESTION 6 6. Give ABC with DE // BC as shw i the figure belw: A D E B C Prve that: AD AE (6) DB EC 6. I the diagram belw, M is the midpit f QR i PQR. T is a pit PQ such that PM ad TR itersect at G. GH PQ with H QR. PG : PM = :. P T G Q H M R Determie, with reass, the umerical value f: QH HM RG RT () (5)

9 Mathematics/P 9 Jue 04 Cmm Test 6. I the diagram belw, the chrd XY is prduced by its w legth t A, ad taget AZ is draw t tuch the circle at Z. XZ is prduced t meet the lie perpedicular t XA at B ad AZ = AB. X Y A Z B 6.. Prve that Ẑ = 90. (5) 6.. Prve that AXZ AZY () 6.. Prve that AZ = AY. XA. () [] TOTAL: 5

10 Mathematics/P 0 Jue 04 Cmm Test INFORMATION SHEET: MATHEMATICS INLIGTINGSBLAD: WISKUNDE b b 4 ac x a A P( i) A P( i) A ) P( i A P( i) T a ( ) d S a ( d ) T ar ar S x i F i f '( x) lim h 0 f ( x h) f ( x) h r ; r x[ ( i) ] P i ( ) ( ) x d x x y y M x y y ; y mx c y y m x ) x a y b r IABC: si cs ( x S a ; r r y y m m ta x x a b c a b c bc. cs A area ABC ab. si C si A si B si C si.cs cs. si si si.cs cs. si cs.cs si. si cs cs.cs si. si cs si cs si si si. cs cs xi x i fx x ( A) P( A) P (A r B) = P (A) + P (B) P (A ad B) S yˆ a bx b x ( x x) x ( y y)

11 Mathematics/P Jue 04 Cmm Test NAME: DIAGRAM SHEET QUESTION 4. F G H PLEASE TEAR ON DOTTED LINES QUESTION 5. S 4 T M O P QUESTION 6. A D E B C

12 Mathematics/P Jue 04 Cmm Test NAME: DIAGRAM SHEET QUESTION 6. P T G Q H M R QUESTION 6. X Y A Z B