Province of the EDUCATION Steve Vukile Tshwete Education Complex Zone 6 Zwelitsha 568 Private Bag X3 Bhisho 565 REPUBLIC OF SOUTH AFRICA CHIEF DIRECTORATE CURRICULUM MANAGEMENT GRADE LEARNER SUPPORT PROGRAMME REVISION AND REMEDIAL TEACHING INSTRUMENT: ANSWERS SUBJECT: MATHEMATICS THIRD PAPER June 9 This document consists of 8 pages. Strictly not for test/examination purposes
MATHEMATICS THIRD PAPER (MATH) (MEMO 6/9) QUESTION. T n T n and 4 T ; ; 8 3 () for first three terms. 5 ; 8 ; 3 ; ;... for sequence T n Tn + Tn or Tn Tn + T for + + n recursive formula [5] QUESTION. Cellphone company A R,57 Cellphone company B R,6 Cellphone company A offers better value for money. () both averages. Cellphone company A R,7 Cellphone company B R,7 The tariffs of the two cellphone companies are the same. () correct explanation.3 If the tariffs of the new cellphone company are the same or more expensive, the subscribers will remain. If the tariffs offer better value for money, subscribers will join new company. ANY CONCLUSION BY CANDIDATE THAT MAKES SENSE. () [6]
(MEMO 6/9) MATHEMATICS THIRD PAPER (MATH) 3 QUESTION 3 NOTE: According to the NCS the solutions to data-handling problems should be done with the use of a calculator. The alternative is to use the pen and paper method as indicated below. 3. Speed interval (km/h) Midpoint of interval (x) Frequency ( f ) f x ( x x) f ( x x) 98 3 3 84,96 554,88 3 7 5 9 945 73,96 665,64 8 4 54,96 8,44 3 7 5 9 35,96 7,64 8 9 8 4,96 36,64 3 7 5 5 9,96 59,9 8 3 3 6 68,96 537,9 33 37 35 7 457,96 95,9 SUM 5 568 3494 ( f x) 3.. Mean n 568 5 3,6 3.. Standard deviation 3494 5 f ( x x) 8,4 () 3..3 Interval [5,; ] () : 34 cars n () (CA) Standard deviation 3. 3.. 6 cars (accept 6 8) () 3.. Approximately 6 km/h (accept: between 59 6 km/h) ()
4 MATHEMATICS THIRD PAPER (MATH) (MEMO 6/9) 3.3 3.3. Not much change. Only increase from 3% to 33%. () 3.3. That there is a steep increase in popularity. Achieved by large vertical scale. () explanation QUESTION 4 3.3.3 Using graph to create false impression and can discourage voters or can fool voters. () [6] 4. 4.. P(Kwesi passes and Emma fails),8 x,,8 () 4.. P(only one of Kwezi or Emma passes) (Kwezi passes and Emma fails OR Emma passes and Kwezi fails),8 +,9 x,,8 +,8,6 S, +,9 x, 4. 4.. M P 3 3 x x x 5 x x intersecting parts rest of diagram 6 A 4.. 3 + 3 x + + x + x + 5 x + 6 x x 34 4 x () Equation Answer 8 4..3 P(not A, M and Ph) Answer
(MEMO 6/9) MATHEMATICS THIRD PAPER (MATH) 5 4..4 P(A) x P(Ph) 5 P(A and Ph) 39 54,74,36 Conclusion: not independent events/s different calculation and calculation and 4.3 4.3. x 3 6 combinations () 4.3. P(wearing something blue) 6 4 () [9] QUESTION 5 5. 5.. Mass (in grams) Length of spring (in cm) 5 5 8, () 3,8 (4) 6, (6) () completing the table (accept values in brackets) 5.. Equation: y 7,75 +, 4x (Accept variations due to different values in 5.. CA) (4) a or b a or b equation 5..3 Positive, strong positive / () strong 5..4 Length of spring 3 cm () 5..5 r,998 (using calculator) CA applies 5.. Option best describes the relationship between the max temperature and electricity used because r,978 is closer to. [5] option explanation * FOR QUESTIONS 6 TO 9 FOLLOW CANDIDATE S REASONING *
6 MATHEMATICS THIRD PAPER (MATH) (MEMO 6/9) QUESTION 6 6. Â Ĉ ( alt ' s : AP // BC ) Â ABˆ C ( Tan Chord Thm Ĉ ABˆ C ABC is an isosceles triangle ) ( base ' s ) (5) [5] & & QUESTION 7 7. MN ( x ) x + ( x ) + x + x x x + () 7. EP ( x ) + ( 5 x ) x + x + 5 x + x (5 x) x 3x + 5 () 7.3 x x + x 3x + 5 x 5 x, 5 units () [6] QUESTION 8 8. Ŷ x (Tan Chord Thm ) Xˆ x ( Isosceles triangle ) Qˆ x ( Alternate ' s ) Ŷ x ( ' s on same chord ) (6) 8. Tˆ Ŷ + Ŷ x + x ( Alternate x Tˆ ' s )
(MEMO 6/9) MATHEMATICS THIRD PAPER (MATH) 7 8.3 PTˆQ 3x 9 Tˆ 3 x 3 ( in semi circle) () 8.4 Ŝ Rˆ 4 Xˆ + XŶS 3 9 + 6 ( Co Interior ' s : XY // TR ) SORT is a cyclic quad. 9 ( Ext. opp.int ) 8.5 OR TQ ( Rˆ 9 ) TR RQ (line fromcentreof circle perpendicular to chord,bisects thechord.) [7] Ŝ 4 9 Rˆ 9 QUESTION 9 9. In SRQ and QRM Qˆ Mˆ [ Qˆ Tˆ ( alt. ' s ) & Tˆ Mˆ ( ' s subtended by same chord ) Rˆ is common Ŝ MQˆ R [ Third angle] SRQ /// QRM (,, ) 9. In QRM and PXM M iscommon. R X ( corresponding ' s ; PT / / QR ) 3 QRM / / / PXM (,, ) (4) Third angle or (A,A,A)
8 MATHEMATICS THIRD PAPER (MATH) (MEMO 6/9) 9.3 From 9. it follows that QR RM SR QR QR SR RM RM QR MX QR In MRQ; RM MX PX PX MX QR QR SR PX SR MX QR PX (5) [] simplification Note NO MARK for, since it is given. TOTAL: