# Mathematics Grade 10 P1 National November 2015 QP

> Grade 10 Mathematics Paper 1 question paper from the National November Exam 2015, 8 pages. Read online or get the free PDF download, memo linked when available.

- Page: https://www.hlayiso.com/library/maths-p1/a2771707-eff7-49d5-91cd-ca5631bacb0e
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 10
- Document type: Question paper
- Year: 2015
- Exam period: National November Exam
- Paper: 1
- Curriculum: CAPS
- Pages: 8

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## About this document

Mathematics · Grade 10 · National November Exam · 2015. Question paper, 8 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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basic education

Department:
Basic Education
REPUBLIC OF SOUTH AFRICA

NATIONAL

SENIOR CERTIFICATE

GRADE 10
SESS SSH SSST SSSR RRR SSH RSS SES SRS SSE S SSSR RR EES
a MATHEMATICS P1 4
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a
" NOVEMBER 2015 "
OS eee ee eee eee”

MARKS: 100

TIME: 2 hours

Copyright reserved

This question paper consists of 7 pages.

TL

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Mathematics/P 1 2 DBE/Noveinber 2015

CAPS — Grade 10

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.

2.

3,

This question paper consists of 8 questions.
Answer ALL the questions.

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

Clearly show ALL calculations, diagrams, graphs et cetera 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 off answers to TWO decimal places, unless stated otherwise.
Diagrams are NOT necessarily drawn to scale.

Write neatly and legibly.

Corie reserves HOMAGE Nese ove
EASTERN CAPE

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Mathematics/P 1 3 DBE/November 2015
CAPS — Grade 10

QUESTION 1
1 Factorise the following expressions fully:
Ll x! 81 (2)
112 6x? y —1Oxy +15x—25 re)
12 Simplify the following expressions fully:
1.2.1 3, 2 ; 21 (5)
a-4 at+3 a’-a-12
102°*7,4 bx
12.2 a5he (4)
13 Consider the following numbers: 427 ; ¥—27 ; /—27.
Which ONE of these numbers is:
13.1 Irrational (3)
1.3.2 Non-real qd)
[16]
QUESTION 2
2.1 Solve for x:
2.1.1 15x? -8= 14x (4)
2.1.2 5* -1 2
~ 125 2)
2.2 The following inequality is given: 3(x + 7) < oH
2.2.1 Solve for x in the inequality. (3)
2.2.2 Represent your answer to QUESTION 2.2.1 on a number line, qd)
2.3 Mary gave one third of her money to Nazeem and one fifth of her money to Elwethu.
Elwethu received R28 less than Nazeem. How much money did Mary have
originally? (4)
[14]

coset LAE

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Mathematics/P | 4 DBE/November 2015
CAPS — Grade 10

QUESTION 3

3.1 Given the linear number pattern: 8 ; 3 ;-2;...
3.1.1 Write down the NEXT TWO terms of the pattern. (2)
3.1.2 Determine the n” term of the pattern. Q)
3.1.3 Calculate T,,, the thirtieth term of the pattern. (2)
3.1.4 Which term of the pattern is equal to 492? (2)

3.2 The first four terms of PATTERN A and PATTERN B are shown in the table below:

Position of term (#) 1 2 3 4 ;
PATTERN A 1 3 5 7 (
PATTERN B 1 9 25 49
3.2.1 Determine a general formula for the n” term of PATTERN A. (2)
3.2.2 Hence, or otherwise, determine a general formula for the n” term of
PATTERN B. q)
3.2.3 Hence, determine a general formula for the pattern 0 ;-6 ; -20;-42....
Simplify your answer as far as possible. (4)
[15]
QUESTION 4
f(x) =-2x? +2 and g(x) =2* +1 are the defining equations of graphs f and g respectively. (
4.1 Write down an equation for the asymptote of g. qQ
42 Sketch the graphs of f and g on the same set of axes, clearly showing ALL
intercepts with the axes, turning points and asymptotes. (6)
43 Write down the range of f (1)
4.4 Determine the maximum value of h if A{x)=3/), Q)
4.5 What transformation does the graph of y= /' (x) undergo in order to obtain the
raph of p=2x?-2? Q)
grap! y {12]

Conia reserva UUM
EASTERN

CAPE

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Mathematics/P 1 5 DBE/November 2015
CAPS — Grade 10

QUESTION 5

The sketch below shows f and g, the graphs of f(x) at -1 and g(x) =ax+q respectively.
x

Points AC-1 ;—4) and BQ ; 4) lie on the graph g.
The two graphs intersect at points C and D.
Line BE is drawn parallel to the y-axis, with E on f

5.1 Show that a=2 and g=-2. (2)
5.2 Determine the values of x for which /(| (x) = a(x). (4)
5.3 For what values of x is g(x) > f(x)? Q)
5.4 Calculate the length of BE. (3)
55 Write down an equation of h if A(x)= f(x)+3. by
QUESTION 6

Given: —_ ffx) =ax’ +e

J passes through the x-axis at (¢—5) and (d—1), where deR.
6.1 Determine the value of a. (2)

6.2 Determine the values of a and ¢ ifitis also given that f(1)=—9. (4)
[6]

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EASTERN CAPE

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Mathematics/P1

QUESTION 7

6
CAPS — Grade 10

DBE/November 2015

Zach likes to travel. He has saved R5 000 as spending money for his vacation in Australia at

the end of 2015.

7A Zach looks up the exchange rate on the Internet. Using the information in the table
below, calculate how many Australian dollars Zach can buy for R5 000.

SOUTH AFRICAN RAND RATES TABLE

FOREIGN EQUIVALENT RAND vont
CURRENCY VALUE OF RI CURRENCY

US dollar 0,083130 12,029313

Euro 0,074048 13,504730

British pound 0,053877 18,560961

Australian dollar 0,105058 9,518569

72 Zach plans to make another trip to Australia at the end of 2018,

7.21 Assume that the average annual rate of inflation in South Africa will be
6,1% over the next 3 years. In 2018, what amount of money will be
equivalent to the value of R5 000 now?

72.2 Zach plans to invest equal amounts into a savings account on

1 December 2016 and on 1 December 2017 to have accumulated an
amount of R5 980 by 1 December 2018. If this account earns interest at
9% p.a. compounded annually, how much money should Zach deposit
into the account on each occasion?

Copyright reserved

NA 040

Please turn over

2)

GB)

(4)
9)

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Mathematics/P1 7 DBE/November 2015
CAPS — Grade 10

QUESTION 8

8.1 At a certain school there are 64 boys in Grade 10. Their sport preferences are
indicated below:

© 24 boys play soccer

¢ 28 boys play rugby

* 10 boys play both soccer and rugby

* 22 boys do not play soccer or rugby

8.1.1 Represent the information above in a Venn diagram,

8.1.2 Calculate the probability that a Grade 10 boy at the school, selected at
random, plays:

(a) Soccer and rugby
(b) Soccer or rugby

8.1.3 Are the events a Grade 10 boy plays soccer at the school and a Grade 10
boy plays rugby at the school, mutually exclusive? Justify your answer.

8.2 One moming Sarnuel conducted a survey in his residential area to establish how many
passengers, excluding the driver, travel in a car. The results are shown in the table
below:

Number of passengers,
excluding the driver 0 ; 2 3 4
Number of cars 7 11 6 5 1

Calculate the probability that, excluding the driver, there are more than two
passengers in a car.

8.3 If you throw two dice at the same time, the probability that a six will be shown on one

of the dice is x and the probability that a six will be shown on both the dice,

is = . What is the probability that a six will NOT show on cither of the dice when

you throw two dice at the same time?

TOTAL:

Copsighreserved UAT AT

6)

@
(1)

2)

3)

G)
[15]

100

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