# Mathematics Grade 10 P1 National November 2018 QP (Eng)

> Grade 10 Mathematics Paper 1 question paper from the National November 2018 (English), 7 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/gr10-math-p1-english-november-2018-question-paper/cc7fff70-dc61-4042-9572-79f5ca9389ea
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 10
- Language: English
- Document type: Question paper
- Year: 2018
- Exam period: National November
- Paper: 1
- Curriculum: CAPS
- Pages: 7

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## About this document

Mathematics · Grade 10 · National November · 2018 · English. Question paper, 7 pages. Read online or download the PDF.

Read it free online on the page above; download the PDF from there.

## Document text

Text extracted from the PDF. Layout, diagrams and tables may not survive extraction.

### Page 1

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ie
=Ze basic education
a & Department:
(O): Basic Education
Sad REPUBLIC OF SOUTH AFRICA
NATIONAL
SENIOR CERTIFICATE
GRADE 10
gee TE SSS SSSR SRR R SSSR SSSR RRS SSSR RRR RRS ESSE
" MATHEMATICS P1 ‘
i NOVEMBER 2018 “
Me eee!
MARKS: 100

TIME: 2 hours

This question paper consists of 7 pages.

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— — = —=

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Mathematics/P1 2 DBE/November 2018

CAPS — Grade 10

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.

2.

This question paper consists of EIGHT questions.
Answer ALL the questions.

Clearly show ALL calculations, diagrams, graphs, etc. that you have used in
determining your answers.

Answers only will NOT necessarily be awarded full marks.

You may use an approved scientific calculator (non-programmable and non-
graphical), unless stated otherwise.

If necessary, round answers off to TWO decimal places, unless stated otherwise.
Diagrams are NOT necessarily drawn to scale.

Number the answers correctly according to the numbering system used in this
question paper.

Write neatly and legibly.

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Mathematics/P1 3 DBE/November 2018
CAPS —Grade 10

QUESTION 1
1.1 Factorise the following expressions fully:
1.1.1 4x—x? (2)
11.2 x? 4+15x-54 (2)
1.1.3 yrxytx-l (3)
1.2 Simplify the following expressions fully:
121  (x+2)(x? -x+3) (2)
1.2.2 oe
x+3 2-x (3)
123 221s"
3.5% (3)
1.3 Determine the value of p+q)’ if 9p? +q? =12 and pq=-3. (3)
[18]
QUESTION 2
2.1 Solve for x:
241 px+gx=a @)
212  2x?~5x4+2=0 (3)
2.13 (y" =32 GB)
2
2.2 Given: -11<3m-8<4
2.2.1 Solve for m. (2)
2.2.2 Hence, write down the number of integers that satisfy the inequality. (1)
2.3 Solve simultaneously for x and y if:
5x+4y=21 and 2x=3-y (4)
[15]

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Mathematics/P1 4 DBE/November 2018
CAPS — Grade 10
QUESTION 3
Consider the finite linear pattern: 20; 17; 14; ...; -103
3.1 Write down the 4" term of the pattern.
3.2 Determine the expression for the n™ term.
3.3 Calculate the number of terms in the sequence.
3.4 Which term is the first to have a negative value?
3.5 What is the value of the 19" even-valued term in the sequence?
QUESTION 4
Samantha is investigating a pattern of dots represented in the diagram below.
° e e
e e e e fo}
e @ @ e @ e
Pattern number: 1 2 3
Number of dots: Pel 14+3=2? =4 1434+5=3? =9
4l Write down:
4.1.1 The number of dots in the 4" pattern
4.1.2 The number of dots in the 13" pattern
4.1.3 A formula for the number of dots in the n™ pattern
4.2 Hence, or otherwise, calculate the value of:

14+34+54..443

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qd)
(2)
(2)
(3)

(2)
[10]

(1)
a)
(1)

(3)
[6]

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Mathematics/P1 5

CAPS — Grade 10

QUESTION 5

DBE/November 2018

Sketched below are the graphs of f(x) = ax® +q and g(x) = (3) -4.

A and B are the x-intercepts of f The graphs intersect at A and point E (1 ;3) lies on f.

C is the turning point of f and D is the y-intercept of g.

y

E(1 33)

5.1 Write down the:
5.1.1 Coordinates of D Q)
5.1.2 Range of g qd)
5.2 Calculate the:
5.2.1 Coordinates of A (2)
5.2.2 Values of a and g (4)
5.3 Determine the:
5.3.1 Length of CD (2)
5.3.2 Equation of a straight line through A and D G)
5.4 For which values of x is:
541 f(x) >0? Q)
5.4.2 Ff decreasing? 65)
[17]

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Mathematics/P1 6 DBE/November 2018

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CAPS - Grade 10

QUESTION 6

The equation of the function g(x)= a +q passes through the point (3;2) and has a range of
x

ye(-~; NUCL).

6.1 Determine the:
6.1.1 Equation of g
6.1.2 Equation of h, the axis of symmetry of g which has a positive gradient
6.2 Sketch the graphs of g and # on the same system of axes. Clearly show ALL the
asymptotes and intercepts with axes.
6.3 Write the equations of the asymptotes of f if f(x)=—g(x)+5.
QUESTION 7

Read the advertisement below.

7.1 Calculate the total amount to be paid over a period of 24 months.

72 The monthly instalment, quoted in the advertisement, is calculated on a hire purchase
agreement which charges interest of 7,5% p.a. on the cash price of the cellphone.
Show that the price of the cellphone is R4 779,13.

73 Calculate the total interest paid over a period of 24 months if the cellphone is bought
with this hire purchase agreement.

74 The cellphone is insured at 11,5% p.a of the cash price. The total insurance is
calculated and then split up over 24 months. It is then added to the monthly
instalment. Calculate the new monthly instalment if the customer wants to insure the
cellphone.

15 The cost of the cellphone is subject to inflation and increases to a cash price of
RS 100,00 after 2 years. Calculate the annual inflation rate.

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Buy a Samsung J5 for only
R229 per month.

You have 24 months to pay.
No deposit is required.

(3)
2)

(4)

@)
[12]

qd)

@)

()

G)

(4)
[14]

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Mathematics/P1 7 DBE/November 2018
CAPS — Grade 10

QUESTION 8
8.1 In a random physical sciences experiment, A and B are two different events. It was
found that:

5
P(A) = , PB’) == and P(A orB) =>

8.1.1 Calculate:

(a) P@) 2)
(b) P(Aand B) GB)
8.1.2 Hence, determine whether events A and B are mutually exclusive. Motivate
your answer. (2)
8.2 The Venn diagrams below represent different scenarios of events A and B.

Write down the probability of the shaded region for EACH of the diagrams below.

ee
e@

q)
8.2.3
QQ)
8.3 Which diagram(s) in QUESTIONS 8.2.1, 8.2.2 or 8.2.3 represent mutually exclusive
events? qd)
f14]

TOTAL: 100

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