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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
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TABLE OF CONTENTS
ASPECT PAGE
INTRODUCTION 3
WEEK 1 : Algebra, Equations & Inequalities 4
WEEK 2 : Trigonometry 8
WEEK 3 : Euclidean Geometry 13
ANSWERS 27
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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)
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WEEK 1 (3rd – 7th AUGUST 2020)
ALGEBRA, EQUATIONS AND INEQUALITIES
MONDAY 3rd AUGUST
DBE 2016
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TUESDAY 4TH AUGUST
DBE 2017
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WEDNESDAY 5TH AUGUST
DBE 2018
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THURSDAY 6TH AUGUST
DBE 2019
FRIDAY 7TH AUGUST – REVISION & CONSOLIDATION OF WEEK’S WORK
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WEEK 2 (10th – 14th AUGUST 2020)
TRIGONOMETRY
MONDAY 10TH AUGUST
DBE 2016
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TUESDAY 11TH AUGUST
DBE 2017
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WEDNESDAY 12TH AUGUST
DBE 2018
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THURSDAY 13TH AUGUST
DBE 2019
FRIDAY 14TH AUGUST – REVISION & CONSOLIDATION OF WEEK’S WORK
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WEEK 3 (17TH – 21ST AUGUST 2020)
EUCLIDEAN GEOMETRY
MONDAY 17TH AUGUST
DBE 2016
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TUESDAY 18TH AUGUST
DBE 2017
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WEDNESDAY 19TH AUGUST
DBE 2018
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THURSDAY 20TH AUGUST
DBE 2019
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FRIDAY 21ST AUGUST – REVISION & CONSOLIDATION OF WEEK’S WORK
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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
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2.2.3 x=
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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
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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
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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°
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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.
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