Mathematics Grade 9 Paper 2 Free State November 2022 Memo

Grade 9 FS/ November 2022 Mathematics Paper 2 English Marking Guideline GRADE 9 MATHEMATICS PAPER 2 ENGLISH MARKING GUIDELINE NOVEMBER 2022 This mathematics marking guideline consist of 13 pages Copyright reserved 1 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 English Marking Guideline QUESTION 1 1.1 G ሺ2𝑥 − 9ሻ0 H 𝑥 F Statement Reason Statement: 1 mark (3) 𝑥= 900 + 90 Compl. angles add up to 900 Reason: 1 mark 3 Answer: 1 mark = 330 1.2 H A F B 𝑚 C D 2𝑝 + 300 E G Statement Reason Statement: 1 mark (3) 𝑝= 1100 −300 Corr, angles AB ‖ CD Reason: 1 mark 2 Answer: 1 mark = 400 Copyright reserved 2 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 English Marking Guideline 1.3.1 U Q 800 𝑎 𝑏 1200 S V 600 R T Statement Reason Statement: 1 mark (4) 𝑎 = 800 Vert. opp angles Reason: 1 mark 𝑏 = 600 Alt. angles, ST‖QR OR Statement: 1 mark 𝑏 = 600 Angles on a str. line Reason: 1 mark 1.3.2 A B 1050 a C D E Statement Reason Statement: 1 mark (2) 𝑎 = 750 Co-int, angles, AB‖CD Reason: 1 mark Copyright reserved 3 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 English Marking Guideline 1.3.3 E F 1060 𝑥 G H Statement Reason Statement: 1 mark (2) 𝑥 = 1060 alt, angles, EF‖GH Reason: 1 mark 1.3.4 𝑎 430 Statement Reason Statement: 1 mark (2) 𝑎 = 2ሺ430 ሻ = 860 Ext. angle of ∆=twice int. angle Reason: 1 mark of a ∆ [16] Copyright reserved 4 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 English Marking Guideline QUESTION 2 2.1 𝑦 380 𝑥 Statement Reason Statement: 1 mark (4) 𝑥 = 520 Int. angles of a ∆ add up Reason: 1 mark 1800 Statement: 1 mark 𝑦 = 52 0 Alt, angles, ‖ lines Reason: 1 mark 2.2 𝑦 𝑥 Statement Reason Statement: 1 mark (4) 𝑥 = 900 Diag. bisect each other ⟂ Reason: 1 mark 𝑦 = 450 Diag. bisect the corners Statement: 1 mark Reason: 1 mark [8] Copyright reserved 5 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 English Marking Guideline QUESTION 3 3.1 i. SSS or ii. AAS or iii. SAA or iv. RHS One answer: 1 mark (1) 3.2 R Q U T S In ∆QRU and ∆TSU Statement Reason 𝐓𝐒̂𝐑 : 1 mark (3) ̂ T = QT RQ ̂S alt angle, QR ‖ ST Reason: 1 mark ̂S QR = 𝐓𝐒̂𝐑 alt angle, QR ‖ ST ̂ 𝐑 : 1 mark 𝐐𝐔 ̂𝐑 𝐐𝐔 = ̂S TU vert. opp. angles ∴ ∆QRU ⫼∆TSU equal angles or AAA Copyright reserved 6 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 English Marking Guideline 3.3 B A D C E Statement Reason Statem & Reason: 1 (4) mark In ∆ABD and ∆CED Statem & Reason: 1 AD = DC given mark ̂ B = CD AD ̂E Vert. opp. angles Statem & Reason: 1 mark ̂ D = EĈD BA Alt. angles, AB‖EC AAS: 1 mark ∆ABD ≡ ∆CED AAS [8] Copyright reserved 7 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 English Marking Guideline QUESTION 4 4.1.1 Answer/ translate: 1 (1) mark • • 4.1.2 Aሺ4 ; 0ሻ Answer: 1 mark (1) 4.2.1 Answer: 1 mark (1) Aሺ−3; 5ሻ • •Bሺ−6; 3ሻ • • Cሺ−2; 3ሻ • A′ ሺ−2; 0ሻ • B ′ ሺ−3; −4ሻ •C′ ሺ1; −4ሻ Copyright reserved 8 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 English Marking Guideline 4.2.2 Answer: 1 mark (1) A′ ሺ3 ; 5ሻ • • • • •′ • B′ ሺ6 ; 3ሻ C ሺ2 ; 3ሻ 4.3 𝐂′ ሺ4 ; 10ሻ 𝐂ሺ𝟐 ; 𝟓ሻ 𝐀′ ሺ4 ; 2ሻ 𝐁′ ሺ10 ; 2ሻ 𝐀ሺ𝟐 ; 𝟏ሻ 𝐁ሺ𝟓 ; 𝟏ሻ Determine the coordinates of the vertices of ∆A′ B′ C′ 4.3.1 A′ ሺ4 ; 2ሻ Answer: 3 marks (3) B ′ ሺ10 ; 2ሻ C ′ ሺ4 ; 10ሻ Copyright reserved 9 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 English Marking Guideline 4.3.2 Determine the lengths of the sides of ∆A′ B′ C′ . Each side: 1 mark (3) A′ B′ = 6 units OR (count the blocks) A′ C′ = 8 units OR (count the blocks) ሺB′ C′ ሻ2 = ሺ6ሻ2 + ሺ8ሻ2 (Pythagoras) = 36 + 64 = 100 √ሺB′ C′ ሻ2 = √100 BC = 10 units [10] QUESTION 5 5.1 22 𝑚 15 𝑚 − 𝟗 𝒎 = 6 𝑚 9𝑚 15 𝑚 𝟔𝒎 𝟏𝟒 𝒎 8𝑚 22 𝑚 − 𝟖 𝒎 = 𝟏𝟒 𝒎 This is irregular shape 6 m + 14 m: 1 mark (2) P = 22 𝑚 + 15 𝑚 + 9 𝑚 + 𝟔 𝒎 + 𝟏𝟒 𝒎 + 8 𝑚 Answer: 1 mark = 74 𝑚 Copyright reserved 10 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 English Marking Guideline 5.2 11 𝑐𝑚 9 𝑐𝑚 8 𝑐𝑚 17 𝑐𝑚 1 Area (answer): 1 (2) 𝐴𝑟𝑒𝑎 = 2 ሺ𝑎 + 𝑏ሻ × 𝐻 mark 1 ሺ11 𝑐𝑚+17 𝑐𝑚ሻ × 8 𝑐𝑚 Area = 2 ሺ11 cm + 17 cmሻ × 8 𝑐𝑚 OR Perimeter (answer): 2 1 mark = 28 𝑐𝑚 × 4 𝑐𝑚 = 112 𝑐𝑚2 P = 9 𝑐𝑚 + 17 𝑐𝑚 + 9 𝑐𝑚 + 11 𝑐𝑚 = 46 𝑐𝑚 5.3 Not drawn to scale. Formula: 1 mark (3) ሺ2𝑥 + 5ሻ 𝑐𝑚 Subst: 1 mark Simplify: 1 mark ሺ𝑥 + 6ሻ 𝑐𝑚 Answer: 1 mark If a learner did not write the formula, give 2 marks for P= 46 cm showing distributive law OR simplifying 𝐴𝑟𝑒𝑎 = 𝑙 × 𝑏 = [ሺ2𝑥 + 5ሻሺ𝑥 + 6ሻ]𝑐𝑚2 = 2𝑥ሺ𝑥 + 6ሻ + 5ሺ𝑥 + 6ሻ]𝑐𝑚2 = ሺ2𝑥 2 + 12𝑥 + 5𝑥 + 30ሻ𝑐𝑚2 = ሺ2𝑥 2 + 17 𝑐𝑚 + 30ሻ𝑐𝑚2 Copyright reserved 11 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 English Marking Guideline 5.4 1 𝑘𝑚2 = 1 000 000 𝑚2 (1) ∴ 1,12 𝑠𝑞𝑢𝑎𝑟𝑒 𝑘𝑖𝑙𝑜𝑚𝑒𝑡𝑟𝑒 ሺ𝑘𝑚2 ሻ = 𝟏 𝟏𝟐𝟎 𝟎𝟎𝟎 𝒎𝟐 = 1,12 × 1 000 000 𝑚2 Answer: 1 mark = 1 120 000 𝑚2 5.5 Not drawn to scale 10 𝑐𝑚 20 𝑐𝑚 30 𝑐𝑚 back end base end 20 𝑐𝑚 front 10 𝑐𝑚 10 𝑐𝑚 top 20 𝑐𝑚 30 𝑐𝑚 Area of base = ሺ30 × 20ሻ𝑐𝑚2 (3) = 600 𝑐𝑚2 Area of each end = ሺ10 × 20ሻ 𝑐𝑚2 = 200 𝑐𝑚2 Area of front = ሺ10 × 30ሻ𝑐𝑚2 = 300 𝑐𝑚2 Total surface area = 2ሺ600 + 200 + 300ሻ𝑐𝑚2 = 2 × 1 100 𝑐𝑚2 = 2 200 𝑐𝑚2 OR 𝑆𝐴 = 2ሺ𝑙 × 𝑏ሻ + 2ሺℎ × 𝑏ሻ + 2ሺℎ × 𝑙ሻ = 2ሺ30 × 20ሻ + 2ሺ10 × 20ሻ + 2ሺ10 × 30ሻ = 2ሺ600 + 200 + 300ሻ = 1 200 + 400 + 600 = 2 200 𝑐𝑚2 Copyright reserved 12 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 English Marking Guideline 5.6 A cylinder has a radius of 7 𝑐𝑚 and height of 10 𝑐𝑚. Not drawn to scale 7 𝑐𝑚 10 𝑐𝑚 5.6.1 Volume of cylinder = 𝜋𝑟 2 𝐻 22 = 7 × 7 × 7 × 10 𝑐𝑚 Formula: 1 mark (2) = 1 540 𝑐𝑚2 Answer: 1 mark 5.6.2 TSA = 2𝜋𝑟ℎ + 2𝜋𝑟 2 Formula: 1 mark (3) 22 22 = ሺ2 × 7 × 7 × 10ሻ + ሺ2 × 7 × 7 × 7ሻ Subst: 1 mark = 440 + 308 Answer: 1 mark 2 = 748𝑐𝑚 5.6.3 Doubled Answer: 1 mark (1) [17] TOTAL [60] Copyright reserved 13 Please turn over