GRADE 11 LOCKDOWN HOLIDAY REVISION DOCUMENT 2020

HARRY GWALA DISTRICT FET MATHEMATICS GRADE 11 LOCKDOWN HOLIDAY LEARNER REVISION BOOKLET AUGUST 2020 Compiled by Harry Gwala FET Mathematics Advisors Mr. M. Govender, Mr. S. Ngubo, Mr. N. Gopichund

HARRY GWALA DISTRICT FET MATHEMATICS TABLE OF CONTENTS ASPECT PAGE INTRODUCTION 3 WEEK 1 : Algebra, Equations & Inequalities 4 WEEK 2 : Trigonometry 8 WEEK 3 : Euclidean Geometry 13 ANSWERS 27 Page 2 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS INTRODUCTION An unprecedented Pandemic of COVID19 has hit South Africa and the World. This has put the lives of learners and teachers at risk and has negatively affected the education system. In KZN Grade 11 learners were taught the First Term Content and then only returned to school for a few weeks in July 2020, before the NCCC closed schools again for learners for a period of four weeks (For Grade 11 learners) from the 27th July and will return on the 24th August. In an effort to assist teachers and learners to use this time away from school effectively, Harry Gwala FET Mathematics Advisors have decided to compile a booklet to enable learners to revise the important content that was already taught in Term 1 namely: Algebra Equations & Inequalities; Euclidean Geometry and Trigonometry. This booklet includes these sections and contains work to be done daily by learners for 3 weeks from the 3rd August to 21st August and utilizes the DBE Final Examination Papers for the past four years. In an effort to let learners work independently the answers (not solutions) are provided at the back. These answers are just a guideline and it is envisioned that learners will complete daily tasks where they will provide the complete solutions to educators. Their efforts must be submitted to educators via social media where a control could will be kept. In the event where learners cannot submit work daily then they should present hard copies of all work to the educator on returning to school on the 24th August. It is hoped that this booklet will allow teachers and learners to work in an effective and systematic way during the extended break so that when they return to school they will be ready to proceed with the remainder of the year’s work. In conclusion we would like to extend an earnest plea to all teachers and learners to abide by guidelines set by the NCCC and WHO to stay safe and prevent the spread of COVID19 . We pray for your health and safety and look forward to continuing to assist you when you return in the new term. God Bless. Kind regards, Mr. M. Govender, Mr. S. Ngubo & Mr. N. Gopichund (Harry Gwala FET Mathematics Advisors) Page 3 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS WEEK 1 (3rd – 7th AUGUST 2020) ALGEBRA, EQUATIONS AND INEQUALITIES MONDAY 3rd AUGUST DBE 2016 Page 4 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS TUESDAY 4TH AUGUST DBE 2017 Page 5 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS WEDNESDAY 5TH AUGUST DBE 2018 Page 6 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS THURSDAY 6TH AUGUST DBE 2019 FRIDAY 7TH AUGUST – REVISION & CONSOLIDATION OF WEEK’S WORK Page 7 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS WEEK 2 (10th – 14th AUGUST 2020) TRIGONOMETRY MONDAY 10TH AUGUST DBE 2016 Page 8 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS TUESDAY 11TH AUGUST DBE 2017 Page 9 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS Page 10 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS WEDNESDAY 12TH AUGUST DBE 2018 Page 11 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS THURSDAY 13TH AUGUST DBE 2019 FRIDAY 14TH AUGUST – REVISION & CONSOLIDATION OF WEEK’S WORK Page 12 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS WEEK 3 (17TH – 21ST AUGUST 2020) EUCLIDEAN GEOMETRY MONDAY 17TH AUGUST DBE 2016 Page 13 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS Page 14 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS Page 15 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS TUESDAY 18TH AUGUST DBE 2017 Page 16 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS Page 17 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS Page 18 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS WEDNESDAY 19TH AUGUST DBE 2018 Page 19 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS Page 20 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS Page 21 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS Page 22 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS THURSDAY 20TH AUGUST DBE 2019 Page 23 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS Page 24 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS Page 25 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS FRIDAY 21ST AUGUST – REVISION & CONSOLIDATION OF WEEK’S WORK Page 26 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS ANSWERS TO QUESTIONS WEEK 1 MATHEMATICS PAPER 1 (DBE NATIONAL PAPER (2016) Algebra, Equations and Inequalities 1.1.1 x = 1.85 or x = - 0,18 1.1.2 x = 4 or x = 2 1.1.3 x < 0 or x > 2 1.1.4 2 𝑥=3 1.1.5 𝑥 ≠ 5 𝑜𝑟 𝑥 = 10 1.2 y = 8 or y = - 7; x = - 3 or x = 2 1.3 Proof 2.1.1 1 5 2.1.2 1 −2 2.2 Proof MATHEMATICS PAPER 1 (DBE NATIONAL PAPER (2017) Algebra, Equations and Inequalities 1.1.1 x = 1.5 or x = - 7 1.1.2 x = - 0. 79 or x = 0, 36 1.1.3 x = 5 only 1.1.4 x < - 3 or x > 6 1.2 y = 1 or y = - 1 ; x = 3 or x = - 1 1.3 k = +/- 0,5 2.1 1 2.2.1 1 16 2.2.2 x = 1 2.3 24,5 2.4 120 MATHEMATICS PAPER 1 (DBE NATIONAL PAPER (2018) Algebra, Equations and Inequalities 1.1.1 x = 0 or x = - 1 2 1.1.2 x = 0,91 or x = - 1,31 1.1.3 𝑥 ≤ − 1 𝑜𝑟 𝑥 ≥ 2 2 1.1.4 x = - 2 1.2 y = - 2 or y = 3; x = 4 or x = - 1 1.3 1<𝑚<4 1.4 max = 4 2.1 −47 2 2.2.1 x = 2 2.2.2 x = 0 or x = 3 Page 27 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS 2.2.3 x = 2 5 2.3 (p + q )3 MATHEMATICS PAPER 1 (DBE NATIONAL PAPER (2019) Algebra, Equations and Inequalities 1.1.1 x = 0 or x = 3 1.1.2 x = 1,54 or x = - 0,87 1.1.3 1≤𝑥≤4 1.1.4 x = 1 𝑥 ≠ −4 1.2 y = - 3 or y = 7; x = 10 or x = - 10 1.3 Roots are non-real 1.4 𝑝 = ±1 2.1 15 2.2.1 x = - 5 2.2.2 x = 1 8 2.2.3 No solution or x = 1 2.3 2 + √3 Page 28 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS WEEK 2 MATHEMATICS PAPER 2 (DBE NATIONAL PAPER (2016) Trigonometry 5.1.1 t = - 15 5.1.2 (a) 8 − 17 5.1.2 (b) 32 17 5.2.1 5.2.2 √1 − 𝑎2 5.2.3 2a 2 5.4 Proof MATHEMATICS PAPER 2 (DBE NATIONAL PAPER (2017) 5.1 -1 5.2 − √2 3 5.3.1 Tan ∝ = 3 4 5.3.2 − 3 5 5.3.3 P (- 8; - 6) 5.4 Proof 6.1 𝑥 = 40° + 𝑘. 120° 𝑜𝑟 𝑥 = −120° + 𝑘. 360° MATHEMATICS PAPER 2 (DBE NATIONAL PAPER (2018) 5.1.1 x = - 8 5.1.2 𝑇𝑎𝑛𝜃 = 15 −8 5.1.3 8 17 5.1.4 225 289 5.1.5 15 a= 4 5.2 3 −4 5.3 Proof 5.4 𝑥 = 0° + 𝑘. 360° 𝑜𝑟 𝑥 = 180° + 𝑘. 360° 𝑜𝑟 𝑥 = 48,19° + 𝑘. 360° 𝑜𝑟 𝑥 = 311,81° + 𝑘. 360° 𝑘 ∈ 𝑍 Page 29 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS MATHEMATICS PAPER 2 (DBE NATIONAL PAPER (2019) 5.1.1 k = - 7 5.1.2 𝑇𝑎𝑛𝜃 = − 24 7 5.1.3 24 𝑠𝑖𝑛𝛼 = − 25 5.1.4 527 − 635 5.2 −2 5.3 Proof 5.4 𝑥 = 270° + 𝑘. 360° 𝑜𝑟 𝑥 = 90° + 𝑘. 180° 𝑜𝑟 𝑥 = 45° + 𝑘. 360° 𝑜𝑟 𝑥 = 135° + 𝑘. 360° 𝑘 ∈ 𝑍 WEEK 3 MATHEMATICS PAPER 2 (DBE NATIONAL PAPER (2016) 9.1 Equal to twice the angle subtended by the arc at the circumference 9.2.1 𝑅̂ = 30° 9.2.2 𝑁𝑆̂𝑇 = 30° 10.1 170° − 2𝑥 10.2 110° 11.1 42,83° 11.2 8 units 12.1 Proof 12.2.1 Proof 12.2.2 Proof 12.2.3 Proof MATHEMATICS PAPER 2 (DBE NATIONAL PAPER (2017) 9.1 Proof 9.2 3 Units 10.1 𝑅̂2 = 55° 10.2 𝑄̂1 = 35° 10.3 𝑂̂2 = 110° 11.1 Proof 11.2 𝐶̂ = 90° 12.1 𝑃̂1 ; 𝐶̂2 ; 𝐸 & 𝑃̂5 12.2 Proof 12.3 𝑥 + 𝑦 = 60° Page 30 of 31 Govender, Ngubo, Gopichund 2020

HARRY GWALA DISTRICT FET MATHEMATICS MATHEMATICS PAPER 2 (DBE NATIONAL PAPER (2018) 9.1.1 𝑂̂1 = 78° 9.1.2 𝑂̂2 = 78° 9.2 x = 84° 9.3 Proof 10.1 Proof 10.2.1 (a) 𝑄̂1 = 24° 10.2.1 (b) 𝑅̂ = 24° 10.2.1 (c) 𝑀̂1 = 48° 10.2.2 Proof 11.1 Proof 11.2 Proof MATHEMATICS PAPER 2 (DBE NATIONAL PAPER (2019) 9.1.1 𝑄̂ = 35° 9.1.2 𝑅̂ = 35° 9.1.3 𝑃̂2 = 𝑅̂ = 35° 9.2 Proof 10.1 Proof 10.2.1 𝑂̂1 = 102° 10.2.2 ̂2 = 39° 𝐴 10.2.3 𝐷̂ = 61° 10.2.4 𝐴𝐶̂ 𝑂 = 22° 11.1 𝐶̂3 = 𝑥 11.2 Proof 11.3 Proof 11.4 𝐴𝐵̂ 𝐷 = 180° − 2𝑥 11.5 𝑅̂2 = 180° − 2𝑥 ALL DBE November National Papers from 2016 – 2019 were utilized when compiling this document. Page 31 of 31 Govender, Ngubo, Gopichund 2020