# Mathematics Grade 10 P1 2020 QP (Eng) > Grade 10 Mathematics Paper 1 question paper from the Mpumalanga National Exemplar Exam (NSC) 2020 (English), 7 pages. Read online or download the free PDF. - Page: https://www.hlayiso.com/library/maths-p1-gr10-qp-nov2020-english/d2bd4731-0cb0-4bd1-b830-03dc2554a962 - Updated: 2026-09-27 - Subject: Mathematics - Grade: Grade 10 - Language: English - Document type: Question paper - Year: 2020 - Exam period: Mpumalanga National Exemplar Exam (NSC) - Paper: 1 - Curriculum: CAPS - Pages: 7 Breadcrumbs: [Home](https://www.hlayiso.com/) › [Library](https://www.hlayiso.com/library) › [Grade 10](https://www.hlayiso.com/library/grade-10) › [Mathematics](https://www.hlayiso.com/library/grade-10/mathematics) › [Mathematics Grade 10 P1 2020 QP (Eng)](https://www.hlayiso.com/library/maths-p1-gr10-qp-nov2020-english/d2bd4731-0cb0-4bd1-b830-03dc2554a962) ## About this document Mathematics · Grade 10 · Mpumalanga National Exemplar Exam (NSC) · 2020 · English. Question paper, 7 pages. Read online or download the PDF. Read it free online on the page above; download the PDF from there. ## Matching paper and memo - [MATHS P1 GR10 MEMO NOV2020 Afr+Engl](https://www.hlayiso.com/library/maths-p1-gr10-memo-nov2020-afr-engl/64cff9d8-8481-482f-aea1-c19731dab929) — Memo · 2020 · Eng ## Document text Text extracted from the PDF. Layout, diagrams and tables may not survive extraction. ### Page 1 NATIONAL SENIOR CERTIFICATE GRADE 10 NOVEMBER 2020 MATHEMATICS P1 (EXEMPLAR) MARKS: 100 TIME: 2 hours This question paper consists of 7 pages, including a 1-page diagram sheet. ### Page 2 2 MATHEMATICS P1 (EC/NOVEMBER 2020) INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of SEVEN questions. 2. Answer ALL the questions. 3. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers. 4. You may use an approved scientific calculator (non-programmable and non- graphical), unless stated otherwise. 5. Answers only will NOT necessarily be awarded full marks. 6. If necessary, round off answers to TWO decimal places, unless stated otherwise. 7. Diagrams are NOT necessarily drawn to scale. 8. Number the answers correctly according to the numbering system used in this question paper. 9. Write neatly and legibly. Copyright reserved Please turn over ### Page 3 3 MATHEMATICS P1 (EC/NOVEMBER 2020) QUESTION 1 1.1 Factorise the following expressions fully: 1.1.1 4𝑦 2 − 16 (1) 1.1.2 𝑥3 − 1 𝑥2 + 𝑥 + 1 (2) 1.1.3 𝑥 − 1 + 𝑦 − 𝑥𝑦 (2) 1.2 Simplify the following expressions fully: 1.2.1 3 − 3𝑥 𝑥 2 − 3𝑥 + 2 (3) 1.2.2 16−𝑥 .12𝑥+1 3𝑥 .4 −𝑥 (3) 1.3 Given that: 𝑚 = 𝑥(𝑥 − 𝑦 )2 Determine the value of m if x𝑦 2 = 4 and 𝑥 3 – 2𝑥 2 y = 3 (3) [14] QUESTION 2 2.1 Solve for 𝑥 without the use of a calculator: 2.1.1 𝑥 3 = 9𝑥 (3) 3 2.1.2 𝑃 = 𝑥(𝑃𝑄 2 − 𝑃𝑞 2 ) 2 (4) 3 2.1.3 3𝑥 4 = 81 (2) 2.2 Solve for 𝑥 if: 2.2.1 3(2 – 3𝑥) ≥ 15 (3) 2.2.2 Hence, represent your answer to QUESTION 2.2.1 on a number line. (1) 2.3 Solve simultaneously for 𝑥 and 𝑦: 3𝑥 + 2𝑦 = 13 and 3𝑥 = 2 – 𝑦 (4) [17] Copyright reserved Please turn over ### Page 4 4 MATHEMATICS P1 (EC/NOVEMBER 2020) QUESTION 3 Given the linear pattern: 2𝑥 + 2 ; 3𝑥 + 4 ; 5𝑥 + 6 ; … 3.1 If 𝑥 = 0, calculate the numerical value of the fourth term. Hence determine the nth term of the sequence. (4) 3.2 Calculate the value of the 18th term. (2) 3.3 Which term in the sequence will be equal to 108? (2) 3.4 Determine the largest value of 𝑛 for which 𝑇𝑛 < 166. (3) 3.5 The following values are the multiples of five from the number pattern: 5; 10; 15; 20; … Determine the 16th even number of this pattern. (3) [14] QUESTION 4 4.1 Sylvia wants to buy a Defy dishwasher which is priced at R9 899 by means of a hire purchase agreement. The conditions of the hire purchase agreement are as follows: • Sylvia must pay a 30% deposit of the purchase price • Interest is charged at 12% per annum simple interest on the balance • Compulsory monthly insurance premium of R65,30 • The balance must be paid in monthly instalments • Account should be settled in 36 months 4.1.1 Calculate the balance after Sylvia has paid the deposit. (2) 4.1.2 Calculate her monthly instalment, if the settlement must be settled in 36 months. (5) 4.2 The table below shows the exchange rate of the British pound and the US dollar in South African rand. COUNTRY UNIT EXCHANGE RATE USA Dollar ($) R16,24 England Pound (£) R27,63 4.2.1 George, a visitor from England, saw an industrial textile machine on sale for $6 800. This machine is suitable for his business back at home. The cost for a similar machine in England is £4 600. Calculate in which country will it be cost saving for George to buy the machine. (3) 4.2.2 To install an outdoor swimming pool will cost you £800 in England. How much will it cost you to install a swimming pool of the same capacity in South African rand? (2) [12] Copyright reserved Please turn over ### Page 5 5 MATHEMATICS P1 (EC/NOVEMBER 2020) QUESTION 5 𝑎 The equation of the function 𝑔(𝑥) = 𝑥 + 𝑞 is shown below. It passes through the point (4 ; 2) on the graph of g and has a range of 𝑦 ∈ (−∞; 1) ∪ (1; ∞). 5.1 Determine the: 5.1.1 Equation of 𝑔 (3) 5.1.2 Equation of ℎ, the axis of symmetry of 𝑔 which has a positive gradient (2) 5.2 Sketch the graph of ℎ on the provided diagram sheet. Clearly show ALL the asymptotes and intercepts with the axes. (4) 5.3 Write the equations of the asymptotes of 𝑓 if 𝑓(𝑥) = −𝑔(𝑥) + 3. (3) 5.4 Use the graphs to determine the value(s) of 𝑥 for which: 5.4.1 𝑔(𝑥) = ℎ(𝑥) (2) 5.4.2 𝑔(𝑥) ≤ ℎ(𝑥) where (𝑥 < 0) (2) [16] Copyright reserved Please turn over ### Page 6 6 MATHEMATICS P1 (EC/NOVEMBER 2020) QUESTION 6 1 Given: 𝑓(𝑥) = 3𝑥 − 1 and 𝑔(𝑥) = 𝑥+1 6.1 Sketch the graphs of 𝑓 and 𝑔 on the same set of axes, using the provided diagram sheet. Clearly indicate all intercept points with the x-axis and the y-axis as well as any asymptotes. (6) 6.2 Using your graph, write down the coordinates of the point of intersection of 𝑓 and 𝑔 (where 𝑥 > 0). (2) 6.3 What is the range of 𝑓? (1) 6.4 Write down the domain of 𝑔. (2) 6.5 Write down the equation of the asymptotes of 𝑔. (2) 6.6 Determine the values of 𝑥 where 𝑔(𝑥) ≤ 0 where 𝑥 < −2 (2) [15] QUESTION 7 7.1 An entire sample space is made up of two complementary events, S and T, where P(S') = 0,33. 7.1.1 Complete the statement: P(S) + P(T) = … (1) 7.1.2 Write down the value of P(T). (1) 7.2 A survey was conducted among 180 residents of a small town to establish how many people contracted tuberculosis (TB) and/or human immunodeficiency virus (HIV) during the last 5 years. The results were as follows: • 𝑥 people were diagnosed with TB • 30 people were diagnosed with both TB and HIV • 69 people were HIV positive • 51 people did not have either disease 7.2.1 Represent the information above in a Venn diagram. (4) 7.2.2 How many people contracted TB only? (3) 7.2.3 Calculate the probability that a person selected at random: (a) Will only have been diagnosed with TB (2) (b) Will not have any of the two diseases (1) [12] TOTAL: 100 Copyright reserved Please turn over ### Page 7 7 MATHEMATICS P1 (EC/NOVEMBER 2020) NAME OF LEARNER: CLASS: DIAGRAM SHEET QUESTION 5.2 (4) QUESTION 6.1 (6) Copyright reserved Please turn over ## Related documents - [Gr10 Math P1 (English) 2020 Exemplars Question Paper](https://www.hlayiso.com/library/gr10-math-p1-english-2020-exemplars-question-paper/158652c3-9dc3-4e0d-abd5-566d18b569f0) — Mathematics · QP · 2020 · Eng - [MATHS P1 GR10 QP NOV2019 English](https://www.hlayiso.com/library/maths-p1-gr10-qp-nov2019-english/36d84e45-25a0-456c-992b-77ebd9f12143) — Mathematics · QP · 2019 · Eng - [MATHS P2 GR10 QP NOVEMBER 2020 English](https://www.hlayiso.com/library/maths-p2-gr10-qp-november-2020-english/ccd33a44-d5d3-48e2-a62d-9a45bc8b0426) — Mathematics · QP · 2020 · Eng - [Gr10 Math P2 (English) 2020 Exemplars Question Paper](https://www.hlayiso.com/library/gr10-math-p2-english-2020-exemplars-question-paper/ead91564-3a75-49e3-bceb-18e02947fc17) — Mathematics · QP · 2020 · Eng - [MATHS P2 GR10 QP NOV2019 English](https://www.hlayiso.com/library/maths-p2-gr10-qp-nov2019-english/595f8054-31b9-4b5f-9f68-cabef8ef98a1) — Mathematics · QP · 2019 · Eng - [Gr 10 Mathematics P1 (English) November 2022 Question Paper](https://www.hlayiso.com/library/gr-10-mathematics-p1-english-november-2022-question-paper/9fd7fdac-14c6-44f7-b7d1-0903e3efa9a2) — Mathematics · QP · 2022 · Eng ## More from Grade 10 Mathematics - [Grade 10 Mathematics P2 November 2026 Mock Memo](https://www.hlayiso.com/library/grade-10-mathematics-2026-november-mock-exam-memorandum-paper-2/ce3b0a71-94ab-4e5e-8316-cc54779fc61a) — Memo · 2026 · Eng - [Gr 10 Maths ATP 2023-24](https://www.hlayiso.com/library/gr-10-maths-atp-2023-24/80c1c337-e011-4b8b-a37b-d2e0df9daaf6) — ATP - [KZN Maths Grade 10 June 2025 P1 and Memo](https://www.hlayiso.com/library/kzn-maths-grade-10-june-2025-p1-and-memo/dc5ae33f-46ec-4eae-b577-25a82956eaec) — QP + Memo · 2025 - [KZN Maths Grade 10 March 2025 QP and Memo](https://www.hlayiso.com/library/kzn-maths-grade-10-march-2025-qp-and-memo/bc27cbbf-ec6d-4c60-bf7e-25a154d363e4) — QP + Memo · 2025 - [KZN Maths Grade 10 November 2025 P1 and Memo](https://www.hlayiso.com/library/kzn-maths-grade-10-november-2025-p1-and-memo/ece9abee-2009-4e22-8de3-34ccb229e5cb) — QP + Memo · 2025 - [KZN Maths Grade 10 November 2025 P2 and Memo](https://www.hlayiso.com/library/kzn-maths-grade-10-november-2025-p2-and-memo/417e9b18-c39d-4fb2-9e32-c089e8fbfd22) — QP + Memo · 2025 ## Collection - [Grade 10 past papers](https://www.hlayiso.com/grade-10/past-papers) --- Hlayiso: free CAPS and IEB past papers, memos, notes and study guides for South African learners. 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