Mathematics Grade 9 ANA Exemplars 2013 Memo

Downloaded from hlayiso.com Page 1 of 12 ANNUAL NATIONAL ASSESSMENT 2013 GRADE 9 MATHEMATICS EXEMPLAR MEMORANDUM KEY M Method mark CA Consistent Accuracy mark A Accuracy mark 1. MULTIPLE CHOICE QUESTIONS 1.1 B 1.2 D 1.3 C 1.4 C 1.5 D Give 1 mark for each 1. correct answer. 1.6 C 1.7 D 1.8 D 1.9 D 1.10 A [10] 1 Grade 9 Mathematics Exemplar Memorandum

Downloaded from hlayiso.com Page 2 of 12 2. NUMBERS, OPERATIONS AND RELATIONS 2.1.1 0,0067  A 1 mark (1) 2.1.2 −16 − 12 − 18 + 2 = −44 Substitution: 1 mark Simplifying: 2 marks Answer: 1 mark (4) 2.2 7,125 ÷ √25 = 7,125 ÷ 5  M 5: 1 mark = 1,425  CA Answer: (2) 1 mark 2.3 96:120 = 8:10 8:10: = 4:5A 1 mark (2) Answer: 1 mark 2.4 =  M formula: 1mark 80 =  M substitution: = 240 CA 1 mark = Answer for 50 = M : 1 mark = 4,8ℎ CA or 4 hours 48 minutes substitution: 1mark Answer for : 1mark (5) 2.5 = (1 + )  M formula: 1mark = 6 500(1 + 0,075) M substituting: 1mark = 8 074,93 CA Answer for A: 1 mark or Calculating interest: 1 mark Year 1: 6 500 × 7,5% = 487,50 Answer: 1 mark Year 2: 6 987,50 × 7,5% = 524,06 Year 3: 7 511,56 × 7,5% = 563,37 M The amount will be R8 074,93 CA Interest = R8 074,93 − R6 500M = 1 574,93 CA (5 ) 2 Grade 9 Mathematics Exemplar Memorandum

Downloaded from hlayiso.com Page 3 of 12 2.6.1 20% = 35 000 = 35 000  M = 3500: 1 mark = 175 000 CA Answer: 1 mark (2) 2.6.2 Amount still to be paid = 175 000 − 35 000 = 140000 A Answer: 1 mark (1) 2.6.3 = (1 + )  M formula: 1mark = 140 000(1 + 0,1 × 4) M substituting = 4: 1mark = 196 000  CA substituting = 0,1: 1mark ∴ monthly installment = 196 000 ÷ 48  M Answer for A: 1 mark = 4 083,33 CA Dividing A by 48: 1 mark Answer: 1 mark or 14 000: 1 mark 10% of 140 000 = 14 000  M × 4 years: 1 mark 14 000 × 4 years = 56 000 M 56 000: 1 mark 140 000 + 56 000 = 196 000M Answer for A: 1 mark 196000 ÷ 48 ℎ = 4083,33 ℎ M/ CA Dividing A by 48: 1 mark Answer: 1 mark (6) 2.7 5 8 Answer: 2 marks ∶ = 5 ∶ 8 3 3 (2) 2.8 Amount = 155,50 ×  Calculation:2 marks = 93,30 Answer: 1 mark (3) 2.9 . . =  Formula: 1 mark 3000( )(0,8) = 960  =4  or Substitution: 1mark Answer: 1 mark = (1 + ) 3960 = 3000(1 + 0,08 ) 0,32 = 1 + 0,08 0,32 = 0,08 (3) = 4 2.10 = (1 + )  Formula: 1 mark = 10 000(1 + 0, 1)  Substitution: 1mark (3) = R13 310,00 Answer: 1 mark 3 Grade 9 Mathematics Exemplar Memorandum

Downloaded from hlayiso.com Page 4 of 12 3. PATTERNS, FUNCTIONS AND ALGEBRA 3.1.1 (2 ) + 3 =4 +3  M 4 : 1 mark = 7  CA Answer: 1 mark (2) 3.1.2 2 × Numerator: 1 mark Denominator: 1 mark =  A (2 ) 3.1.3 ( ) =  M 4 : 1 mark = 4  CA 4 : 1 mark Answer: 1 mark = 64  A (3) 3.2.1 3 (3 − 4 − ) 1 mark for each term =9  − 12 −3 A (3) 3.2.2 (2 − 3)( + 1) Answer: 2 marks = 2 − − 3 A (deduct a mark for each error) (2 ) 3.2.3  . : 1 mark =  Answer:1 mark (2) 3.3.1 10 − 5 5 : 1 mark = 5 (2 − 1)  A 2 − 1: 1 mark (2) 3.3.2 81 − 100 9 − 10 : 1 mark = (9 − 10 )(9 + 10 )A 9 + 10 : 1 mark (2 ) 3.4.1 2 − 5 = 5 + 16 −3 : 1 mark −3  = 21  M 21: 1 mark = −7  A Answer:1 mark (3) 3.4.2 ( − 2) (2 + 1) 5 + = 4 3 3 × 12 12 + 12( ) = 12 × 3( − 2): 1 mark 3( − 2) + 4(2 + 1) = 4 × 5 M 4(2 + 1): 1 mark 3 − 6 + 8 + 4 = 20  M 4 × 5: 1 mark 11 = 22 Simplifying: 1 mark =2 A Answer: 1mark (5 ) 3.5 −16 − 12 − 18 + 2 = −44 Substitution: 1 mark Simplifying: 2 marks (4) Answer: 1 mark 3.6 20 +8 − 12  20 : 1 mark 8 : 1 mark −12 :1 mark (3) 3.7.1 ( )( )=  ( ): 1 mark : 1 mark (2) 4 Grade 9 Mathematics Exemplar Memorandum

Downloaded from hlayiso.com Page 5 of 12 3.7.2 +  Answer: 2 marks (2 ) 3.7.3  Simplifying: 2 marks Answer: 1 mark = 8  (3) 3.7.4 −2 −3 Simplifying: 4 marks – 2 3 Answer: 1 mark ( ) ( ) =  =  =  (5 ) =  3.7.5 × =  Simplifying: 1 mark Answer: 1 mark (2) 3.7.6 ( )( ) Difference of two ( )  squares: =  1 mark Common factor: 1 mark Answer: 1 mark (3 ) 3.8.1 3 ( − 3 − 2) Common factor3 : 1 mark (2 ) Factor − 3 − 2: 1 mark 3.8.2 ( + )(4 − ) Common factor: 2 = ( + )(2 + )(2 − ) marks Difference of two squares: (4 ) 2 marks 3.9.1 8 + 3 = 3 − 22 Simplifying:1 mark 8 − 3 = −22 − 3 Answer: 1 mark 5 = −25 = −5 (2) 3.9.2 −1 Multiplying by 2: 1 − =3 mark 2 2 − + 1 = 6 Simplifying:1 mark + 1 = 6 Answer: 1 mark (3 ) = 5 3.9.3 3 =3  Applying exponential + 1 = 4 law: 2 marks = 3 Answer: 1 mark (3 ) 3.10.1 13A , 17A 1 mark per term (2) 5 Grade 9 Mathematics Exemplar Memorandum

Downloaded from hlayiso.com Page 6 of 12 3.10.2 The number of sides increase by 4 to get the next diagramA Correct deduction: 1 mark (1) 3.10.3 = 4 + 1A 4 :1 mark +1: 1 mark (2) 3.11.1 Answer: 2 marks 1 2 3 6 9 12 15 matches  (2) 3.11.2 Tn = 3n + 3 3n: 1 mark 3:1 mark (1 mark per term) (2) 3.11.3 = 3(20) + 3 = 63 Substitution: 1 mark Answer :1 mark (2) 3.12 = 2 −3 +5 = 2(−1) − 3(−1) + 5M substitution: 1 mark = 10CA Answer: 1 mark (2) 3.13.1 = 2A Answer: 1 mark (1) 3.13.2 = 2 A Answer: 2 marks (2) 3.13.3 (2; −2)A 2: 1 mark −2: 1 mark (2) 6 Grade 9 Mathematics Exemplar Memorandum

Downloaded from hlayiso.com Page 7 of 12 3.14.1 y=3x+1 y=3x-2 . .4 .3 = 3 + 1 .2 = 3 − 2 .1 -5 -4 -3 -2 -1 .0 1 2 3 4 5 1 2 .-1 3 3 .-2 .-3 .-4 .-5 X-intercept: 1 mark per graph+A Y-intercept: 1 mark per graph+A Correct labelling of graph: 1 mark per graph +A (6) 3.14.2 The lines are parallel or the lines will never cut.A (1) 3.15 (3; 3) Answer: 1 mark (1) 3.16.1 = = −2 = −2 + −2 : 1 mark 4:1 mark 4 4 = = −2 −2 = −2 − 4 −2 : 1 mark −4:1 mark (4) 3.16.2 AD || BC  AD || BC : 1 mark (because the Gradient of AD = Gradient of BC) Reason :1 mark (2) 7 Grade 9 Mathematics Exemplar Memorandum

Downloaded from hlayiso.com Page 8 of 12 4. SPACE AND SHAPE 4.1 = 95° − 30° (ext. ∠ of ∆ ) M/ A correct statement with reason:1 mark = 65° A Answer for : 1 mark or = 180° − 95° (ext. ∠ of ∆ ) = 85° + 85° + 30° = 180° (sum of ∠s of ∆= 180°) M/ A + 115° = 180° = 65° A correct statement with reason:1 mark + = 180° (co - interior <s AB || CD) M/ A Answer for : 1 mark (4) = 115° A 4.2 In ∆ ∆ = (Common) A correct statement with reason:1 mark = = 90° (Given) A correct statement with reason:1 mark = (Given) A correct statement with reason:1mark ∴∆ ≡∆ (90°Hyp S) A correct deduction and reason:1 mark (4) 4.3.1 + + + = 180° (co-int ∠ ; || ) A Correct statement with reason: 1 mark But = and = (given) A Correct statement with reason: 1 mark Correct deduction: 1 mark ∴2 + 2 = 180°A Simplification: 1 mark + = 90°A Correct deduction with reason: 1 mark = 90°(sum of ∠ of ∆= 180°) (5) 4.3.2 ∆ ||| ∆ ( )A Correct statement with reason: 2 marks (2) 4.3.3 = = (prop. sides of similar ∆ ) A Correct statement with reason: 1 mark Correct statement with reason: 1 mark Answer: 1 mark = ( =2 ) A 1 4 = 2 (3) =8 A 8 Grade 9 Mathematics Exemplar Memorandum

Downloaded from hlayiso.com Page 9 of 12 4.4.1 (−5; 4) A Correct pair of co – ordinate:1 mark each (−4; 2)A (2) 4.4.2 A B B’ A’ D C C’ D’ correct shape: 1 mark A correct coordinates of the image: 1 mark A (2) 4.4.3 (5; 4)  1 mark per co - ordinate (4; 2)  (2) 4.5 No .of faces : 5A 1 mark per correct answer No. of vertices : 6A (3) No. of edges : 9A 4.6 In ∆AEW : + = 110° (sum of <s of ∆ = 180°) but = (angles opp. equal sides of ∆) Statement with reason: 1 mark Statement with reason:1 mark = 55° Statement with reason:1 mark (3) = = 55° (alt <s ; CS || HW) 9 Grade 9 Mathematics Exemplar Memorandum

Downloaded from hlayiso.com Page 10 of 12 4.7.1 In ∆ ABD and ∆ ACD statement with reason: 1 mark AB = AC (given)  statement with reason: 1 mark statement with reason: 1 mark BD = CD (given) Correct case: 1 mark AD = AD ( common side) ∴∆ ABD ≡ ∆ AC (s,s,s) (4) 4.7.2 = (corr<s of congruent ∆s) Correct statement with reason:1 mark DA bisects BÂC Conclusion:1 mark (2) 4.8 + 50° + 2 − 20° = 180° Statement with reason: 1 mark Statement with reason:1 mark (co-interior<e; AB || CD) 3 + 30° = 180° : 1 mark 3 = 150° : 1 mark = 50°  + + 50° = 180° (co-interior <e; AC || BD) + 100° = 180° = 80° (4) 5. MEASUREMENT 5.1 Surface area = 6 M/ A = 6(6 ) Formula/ substitution: 1 mark = 216 A Answer: 1 mark (2) 5.2.1 Volume of cylinder = ℎM Formula: 1 mark = × 9 × 100 M Substitution: 1 mark = 25 446,90 CA Answer: 1 mark (3) 5.2.2 Volume of rectangular = ℎ M Formula: 1 mark = 30 × 14 × 8 M Substitution: 1 mark = 3 360 CA Answer: 1 mark (3) 5.2.3 Number of rectangular prisms = M , Formula: 1 mark = M Substitution: 1 mark = 7,573 … = 7 CA Answer: 1 mark (3) 10 Grade 9 Mathematics Exemplar Memorandum

Downloaded from hlayiso.com Page 11 of 12 5.3 = 12 + 5 ( ℎ) Formula/substitution: = 169  1 mark = 13  Calculation: 1 mark Answer: 1 mark (3) 5.4 Volume = 5000 Formula:1 mark ℎ = 5000 Substitution: 1 mark (20) ℎ = 5000 Answer: 1 mark ℎ = 4,0  (3) 6. DATA HANDLING 6.1.1 24 passengers A Answer: 1 mark (1) 6.1.2 Range = (70 − 1) = 69 A Answer: 1 mark (1) 6.1.3 Mean age = Formula/ ( ) substitution: = M 1 mark = M Calculations: 1 mark = 26,71 Answer: 1 mark = 27 CA (3) 6.2.1 Amount = 19% of 105 = × 105 M × 105 : 1 mark Answer: 1 mark (2) = 19,95 CA 6.2.2 Percentage = 17% + 14% = 31% A Answer: 1 mark (1) 6.2.3 Amount = (19% + 11%) of 105 = 30% of 105 M 30% of 105 : 1 mark = 31,5 A Answer: 1 mark or or Amount = 19% of 105 + 11% of 105 19% of 105 + 11% of = 11,55 + 19,95 M 105 : 1 mark = 31,5 A Answer: 1 mark (2) 6.3.1 Stem Leaves 0 3 5 6 7 9 A 1 0 1 1 1 3 3 4 5 7 A 2 0 1 2 3 3 6 A (3) 6.3.2 Range = 26 − 3 = 23 A Answer: 1 mark (1) 11 Grade 9 Mathematics Exemplar Memorandum

Downloaded from hlayiso.com Page 12 of 12 6.3.3 Median mark = 13 A Answer: 1 mark (1) 6.3.4 Modal mark = 11 A Answer: 1 mark (1) 6.4.1 Win (W) Draw (D ) Loss (L ) Win WW WD WL A Draw DW DD DL A Loss LW LD LL A (3) 6.4.2.1 A Answer: 1 mark (1) 6.4.2.2 A Answer: 1 mark (1) 6.4.2.3 A Answer: 1 mark (1) 6.5.1 For each correct Class-interval Tally marks Frequency interval: 2 marks 140-144 |||| 4 145-149 ||| 3 150-154 |||| |||| 9 155-159 |||| | 6 160-164 |||| |||| 10 165-169 |||| 5 170-174 ||| 3 (14) 6.5.2 Range = 174 − 140  Answer:2 marks = 34 (2) 6.5.3 160 − 164 (2) Answer: 2marks 6.5.4 < < Answer: 2marks Class-interval 155 - 159 (2) 7. PROBLEM SOLVING A : B : C : Total 4 : 3 4 : 3 16 : 12 : 9 : 37 A’s share = × 148 = 64 A Each correct statement: 1 mark B’s share = × 148 = 48  C’s share = × 148 = 36  or C’s share = R148 − R112 = R36 (3) END 12 Grade 9 Mathematics Exemplar Memorandum