Mathematics Grade 9 ANA 2011 Memo (English)

Downloaded from hlayiso.com basic education ANNUAL NATIONAL ASSESSMENTS 2010 GRADE 9 MATHEMATICS - ENGLISH Department: Basic Education FORM B REPUBLIC OF SOUTH AFRICA MEMORANDUM Important Information This is a marking guideline. In instances where learners have used different but mathematically sound strategies to solve the problems they (learners) should be credited. Unless stated otherwise, learners who give a correct answer only, should be awarded full marks. QUESTION 1 111A 12 |B 1.3 14 1C 15 |C Give 1 mark for each correct 1 answer. . 16 |C 17 |C¢ 18 19 |¢ 1.10 | ¢ [10] QUESTION 2 2.4.4 x 4dr t dex? 4243 vy Distributive law: 2 marks =6x+7 Answer: 1 mark (3) 2.1.2 4y2 vv 4:1 mark xv y? 1 mark x: 1 mark (3) 2.1.3 VV Vv Vv 2 Simplifying each term of fraction: 3 marks Bxt + 4x-1 4x41 expanding the bracket: 1 mark Answer: 1 mark (5) =8x v 2.2.1 Yvv Each correct term: 1 mark =9a? -6a-3 (3) 2.2.2 a> 2a? +4a+2a7-4a+8 Expanding: 2 marks =a+8 vv Answer: 1 marks (3) 2.3.1 Vv v 2xy: 1 mark 2xy(xy — 2x + 5y) (x ) -2x+5y): 1 mark (2) 2.3.2 Yoev Each correct bracket: 1 mark (2) (x + y)Gx- y) 2.3.3 v v v Common factor: 1 mark (3) 2x(x? — 4) = 2x(x + 2)(x- 2) difference of two squares: 1 mark

Downloaded from hlayiso.com Page 2 of 6 2.4 3 1089 3 363 11 121 11 11

factorising correctly: 2 marks 1

Answer: 2 marks 1089 = 3 2 . 11 2 = 3 × 11 = 33 (4) 2.5.1 3x − 3 − 4 x = 5 − 2 x − 2
Expanding: 1 mark ∴ − x − 3 = −2 x + 3 Simplifying x : 1 mark
∴x = 6
Answer = 6: 1 mark (3) 2.5.2 2 x − 3 = 3x
Multiply by 3: 1 mark ∴ x = −3

Answer: 2 marks (3) 2.5.3 Multiply by 12: 1 mark 3( x − 2) − 4( 4 x + 1) = x − 2
∴ 3x − 6 − 4 x − 4 = x − 2
Simplifying correctly: 1 mark − x − 10 = x − 2

Further Simplifying: 2 marks − 8 = 2x
Answer: 1 mark ∴ x = −4 (5) [39] QUESTION 3 P.n.r SI =
3.1 100 Formula: 1 mark Substitution: 2 mark = ( R5400)(4)6) Answer: 1 mark 100

(4) = R1296 n  r  3.2 A = P 1 + 
 100  Formula: 1 mark ( R8 000)(1,05)3 Substitution: 3 marks =


100 Answer: 1 mark = R9 261 (5)
Amount to be paid = R9 261 3.3.1 inverse proportion
Answer: 1 mark (1) 3.3.2 Let time taken = t hours Equation: 1 mark Then 16 t = 40 hours
∴ t = 2,5 or 2 hours 30 minutes
Answer: 1 mark (2) 2

Downloaded from hlayiso.com Page 3 of 6 3.4 Cost of 4,5 kg = R36 Work out cost of 1 kg: 1 mark Cost of 1 kg: R36 ÷ 4,5 = R8
∴ Cost 2,5 kg = 8 × 2,5 = R20

Cost of 2,5 kg: 2 marks 4,5 36 = 2,5 x or ⇒ 4,5 x = 2,5 × 36 = 20 (3) [15] QUESTION 4

4.1 17; 21 Each term: 1 mark (2) 4.2
Add 4 to get to the next number. Answer: 1 mark (1)

4.3 4n + 1 Answer : 1 mark (2) 4.4 4n + 1 = 101

Equation: 2 marks 4n = 100 n = 25

Answer : 2 marks (4) Therefore T25 = 101 [9] QUESTION 5 5.1 5.1.1 c 5.1.2 a 1 mark each (2) 5.2 y=2−x x -2 -1 0 1 y 4 3 2 1 y = 2x − 3 Note: learners can choose other x–values in the table below. x -1 0 1 y -5 -3 -1 3

Downloaded from hlayiso.com Page 4 of 6 y = −x + 2 Y 4 points plotted: 1 mark 12 Labelling: 10 1 mark Shape 8 (separate points): 6 1 mark y = −x + 2 4 2 X -14 -12 -10 -8 -6 -4 -2 2 4 6 8 10 12 14 -2 y = 2x − 3 -4 plot chosen points (two) correctly: -6 2 marks y = 2x − 3 -8 correct labelling: 1 mark -10 Shape (straight line): -12 1 mark (7) [9] 4

Downloaded from hlayiso.com Page 5 of 6 QUESTION 6 6.1.1
parallelogram: 1 mark A parallelogram – both pairs of opposite sides equal
reason:1 mark (2) 6.1.2 Area trap. APCD = (PC + AD).h

Recognising APCD is a trapezium: 1 mark 2 Formula: 1 mark (16 + 24).12 = 2 cm2
Substitution: 1 mark = 240 cm2
Answer: 1 mark (4) 6.1.3 Opposite sides of rectangle APTC Answer: 1 mark (1) 6.1.4 In ∆ ABP and ∆ CDT 1. AP = TC (opp. sides of rect. APTC)
Correct statement: 1 mark 2. BP = TD = 8 cm
Correct statement: 1 mark Correct statement: 1 mark 3. P̂1 = T̂1 = 90°
∆ ABP ≡ ∆ CDT (S, <, S)
Correct case: 1 mark (4) 6.2 In ∆ ABC Aˆ1 + Bˆ = 140° (sum of < s of ∆)

Correct statement and reason: 2marks ° But Â1 = B̂ = 70 (angles opp. equal sides of a ∆)

Correct statement and reason: 2 marks Ĉ 2 = Â1 = 70° (Alt < s; AB || DC)

Correct statement and reason: 2 marks  2 = Ĉ1 = 40 ° (Alt < s; AD || BC)

Correct statement and reason: 2 marks ∴ BÂD = 110°
Answer: 1 mark (9) 6.3.1 ∆ ABE Answer: 1 mark (1) AB BE AE = = (proportional sides of similar ∆’s)

Proportional sides: 2 marks 6.3.2 AC CD ED 9 3 substitution: 1 mark =
AC 8 AC = 24 cm
AC = 24 : 1 mark ∴ BC = 24 − 9 Answer: 2 marks = 15 cm

(6) 6.4.1 Volume = Area ∆ ABC x h
formula: 1 mark 5(12) substitution: 1 mark = × 20 m3
2 = 600 m3
Answer: 1 mark (3) 5

Downloaded from hlayiso.com Page 6 of 6 6.4.2 In ∆ ABC: BC2 = 25 + 144 m2 (Pythagoras.)

= 169 m2
Using Pythagoras to get BC: 4 marks Therefore BC = 13 m
Formula: 1 mark
Surface Area = 2 x Area ∆ ABC + (AB+AC+BC) x AD 5(12) Substitution: 2 marks = 2 + (30)(20) m2

2 = 60 + 600 m2 = 660 m2
Answer : 1 mark (8) [38] QUESTION 7 7.1 Stem Leaf Stem Leaf 2 marks for each plot 3 8 1 3 1 8 4 5 7 9 4 5 7 9 5 2 2 5 8 5 2 2 5 8 6 8 4 6 4 8 7 4 2 7 2 4 8 1 4 8 1 4 (4) 7.2.1 Range = 84 – 31 = 53

Correct answer: 2 marks (2) 7.2.2 Mode = 52
Correct answer: 1 mark (1) 7.2.3 Median = 55

Correct answer: 2 marks (2) 7.2.4 870 Correct answer: 3 marks (3) Mean = = 58


15 7.3 7 learners

Correct answer: 2 marks (2) [14] QUESTION 8 8.1 P(> 6) = 2 = 1 Answer: 2 marks 8 4

(2) 8.2 P (prime number) = 4 = 1

Answer: 2 marks 8 2 (2) 8.3 4 1 P (a factor of 8) = = Answer: 2 marks 8 2

(2) [6] Total [140] 6