Mathematics Grade 11 Paper 2 North West June 2017 Memo

GRADE 11 MATHEMATICS P2 MEMORANDUM JUNE 2017 MARKS: 100 This marking guideline consists of 12 pages.

Mathematics / P2 NSC – Grade 11 Memorandum NW/June 2017 QUESTION 1 1.1 (1) ✓ answer 1.2 (3) ✓ correct substitution ✓ 10 ✓ conclusion 1.3 (2) ✓ 16 ✓ 11 1.4 (3) ✓ substitution ✓ ✓ answer 1.5 (2) ✓ ✓ 1.6 (2) ✓ correct substitution ✓ answer 1.7 (5) ✓ correct substitution ✓ ✓ ✓ ✓ [18] 2

Mathematics / P2 NSC – Grade 11 Memorandum NW/June 2017 QUESTION 2 2.1.1 (4) A ✓ correct diagram x ✓ substitution ✓ selecting ✓ answer 2.1.2 (2) ✓ correct substitution ✓ answer 2.2.1 (2) ✓ ✓ answer 3

Mathematics / P2 NSC – Grade 11 Memorandum NW/June 2017 2.2.2 (3) 1 p 61 ✓ correct diagram ✓ ✓ answer OR ✓ ✓ ✓ answer 2.3 (4) ✓ ✓ for ✓ ✓ [15] 4

Mathematics / P2 NSC – Grade 11 Memorandum NW/June 2017 QUESTION 3 3.1 (6) ✓ ✓ ✓ ✓ ✓ ✓ answer 3.2 (6) ✓ factors ✓✓ ✓✓ ✓ OR ✓ factors ✓ ✓ ✓ ✓ ✓ [12] 5

Mathematics / P2 NSC – Grade 11 Memorandum NW/June 2017 QUESTION 4 4.1 (4) ✓ OR ✓ ✓ correct substitution ✓ OR 4.2 (1) ✓ answer Period of 4.3 (1) ✓ answer Amplitude of 6

Mathematics / P2 NSC – Grade 11 Memorandum NW/June 2017 4.4 (5) ✓ for ✓ factors ✓ ✓ ✓ 4.5 (2) ✓ correct boundaries ✓ correct notation [13] 7

Mathematics / P2 NSC – Grade 11 Memorandum NW/June 2017 QUESTION 5 5.1 (5) Q N 1 O 2 P  correct construction 2 x K L M Construction : Draw diameter LOQ and join QP or Join OL and OP STATEMENT REASON Let angle subtended by  S/R the diameter LM OL, tan – radius  S/R Sum of the angles of a  S triangle Subtended by the same chord LP  S/R 8

Mathematics / P2 NSC – Grade 11 Memorandum NW/June 2017 5.2.1 (2)  S R (a) ^ 1 = 40 ° R [ at centre at circumference] (b) (2)  S R [tan chord theorem] (c) (4)  S R [tan radius]  S R [chord subtends equal ‘s ] 5.2.2 (3)  S R [line from centre to midpt of chord]  conclusion TN // PM [corr. s equal ] 5.2.3 [Pyth] (3) ✓ SR [given, TK = KN] ✓ S ✓ SR [OT = OM, radii] [19] 6.1.1 diameter (1) 6.1.2 (1) Supplementary 9

Mathematics / P2 NSC – Grade 11 Memorandum NW/June 2017 6.2 6.2.1 ^ A 2 = 40 ° [tan chord theorem] (5)  S R ^ A 5 = 40 ° [vert. opp. angles]  SR ^ [tan chord theorem]  S R P 2 = 40 ° 6.2.2 P ^ 2 = = 40 ° but these are alt. angles (5) S ∴ PN ∥ TQ  conclusion ^ 1= ^ P A4 given but these are alt. angles  S ∴ PT ∥ NR  conclusion ∴ PNRT is a parallelogram [2 pairs of opp.sides ∥ ]  S/R 10

Mathematics / P2 NSC – Grade 11 Memorandum NW/June 2017 6.3 A 1 B 1 11 1 1 F C D E 6.3.1 B ^ E D= ^ B1 = x [alt. angle, AB∥ EC] (6) S/R ^ ^ D=x A2 = B E [angle in same segment] S R ^2= E ^ [tan. chord] S R B A B=x+ y ^+^ C B 2 = 180 ° [co-int. angles, AB ∥ EC] B1 + ^  S/R ^ = 180 ° - 2 x - y ∴C 6.3.2 B F ^ D =2 x [ext. angle of ∆ FED ] (5)  S R ^ = 180 ° - 2 x - y C [proven] B^ FD +C ^ = 180 ° - 2 x - y + 2 x = 180 ° - y S ∴B ^ ^ ≠ 180 ° F D +C [opp. angles not suppl.] S ∴ Becky is correct. S [23] TOTAL: [100] 11