# Mathematics Grade 10 P1 National November 2016 QP (Eng)

> Grade 10 Mathematics Paper 1 question paper from the National November 2016 (English), 8 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/gr10-math-p1-english-november-2016-question-paper/2d489251-2f4f-4ac5-b478-e23f3e54a781
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 10
- Language: English
- Document type: Question paper
- Year: 2016
- Exam period: National November
- Paper: 1
- Curriculum: CAPS
- Pages: 8

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## About this document

Mathematics · Grade 10 · National November · 2016 · English. 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

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### Page 1

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basic education

WE

ulahys Department:

i) A A) Basic Education

RX REPUBLIC OF SOUTH AFRICA

NATIONAL
SENIOR CERTIFICATE
GRADE 10
MATHEMATICS P1 :
F: NOVEMBER 2016 “

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SRR COCOOOOOCOCOCOCO OCC CCC ee eee eee eee eee eee eee ee ee |

SECC CORE CC CREE OCC CREO OC CORE CC CREE OCC ROE EO 8 eee

MARKS: 100

TIME: 2 hours

This question paper consists of 8 pages.

III)

*K6*
GAUTENG Please turn over

Copyright reserved

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Mathematics/P1 2 DBE/November 2016

CAPS — Grade 10

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.

2.

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

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 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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DBE/November 2016

Mathematics/P1 3

QUESTION 1
11 Factorise the following expressions fully:
11.1 x =x
1.1.2 3x? +3 px —2mx—2mp
1.1.3 2p? —2p-12
1.2 Simplify the following:
a+l a-l
1.2.1 ue
7
122 x? -x41 2x
~ xt] | 2x42
QUESTION 2
2.1 Solve for x:
2.1.1 x(x—-1)=20
2.1.2 3x2 ay
2.2 Given: -4s-dm<5 where meER
2.2.1 Solve for m.
2.2.2 Write the answer to QUESTION 2.2.1 in interval notation.
2.3 Given: 4x” —y? =171 and 2x-y=9

CAPS — Grade 10

2.3.1 Calculate the value of 2x+y.

2.3.2 Solve simultaneously for x and y.

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Please turn over

(1)
(3)

(3)

(3)

(4)
[14]

(4)

(G3)

(3)
(1)

(2)

G3)
[16]

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Mathematics/P1 4 DBE/November 2016
CAPS — Grade 10

QUESTION 3

Dark tiles (D) and light tiles (L) are used to create patterns on a floor. The first four patterns are
shown below. For the patterns that follow the tiles are arranged in a similar manner.

sa

Pattern 1 Pattern 2 Pattern 3 Pattern 4
3.1 How many dark tiles were used in pattern 5? (1)
3.2 How many light tiles were used in pattern 6? qd)
3.3 Write down the general term (D,) for the number of dark floor tiles used in each
pattern. (2)
3.4 Write down the general term (L,) for the number of light floor tiles used in each
pattern. (2)
3.5 Which pattern will have exactly 64 light floor tiles? (3)
3.6 Each dark tile is 0,3 m wide and 0,6m long. Calculate the total area covered by
all the dark tiles in the first 100 patterns. (3)

[12]

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Mathematics/P1 5 DBE/November 2016
CAPS — Grade 10

QUESTION 4

4.1 Mary wants to buy a fridge that costs R15 550. She has to pay a deposit of 15% of

the cost and the balance by means of a hire-purchase agreement. The rate of interest
on the loan is 16,25% p.a. simple interest. The repayment period of the loan is
54 months. In addition to the hire-purchase agreement, an annual insurance premium
of 1,5% of the total cost of the fridge should be added. The annual insurance

premium should be paid in monthly instalments.

4.1.1 Calculate the value of the loan that Mary will take.
4.1.2 Calculate the total amount that must be repaid on the hire-purchase
agreement.
4.1.3 Calculate the monthly repayment, which includes the monthly insurance
premium.
4.2 The table below shows the rand equivalent of one British pound and one US dollar.
COUNTRY CURRENCY RATE OF EXCHANGE
OF THE RAND
Britain (United
Kingdom) Pound (£) 21,41
United States
of America Dollar ($) 13,45
A South African nurse works in the United States of America.
4.2.1 The nurse saves the equivalent of R4 800 per month. Calculate the

amount, in US (American) dollars, that she saves per month.

4.2.2 She ordered a book from the United Kingdom (Britain) and paid $85
for it. Calculate the price of the book in pounds (£).

43 A sum of money doubles in 5 years when the interest is compounded annually.

Calculate the rate of interest.

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(2)

(3)

GB)

(2)

(3)

(3)
[16]

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Mathematics/P1 6 DBE/November 2016
CAPS — Grade 10

QUESTION 5

The graphs of f(x)=x?—4 and g(x)=—x+2. are sketched below. A and B are the
x-intercepts of f/ C and D are the y-intercepts of f and g respectively. K isa point on g
such that BK || x-axis. f and g intersect at A and E.

x
Cc

5.1 Write down the coordinates of C. qd)
5.2 Write down the coordinates of D. qd)
5.3 Determine the length of CD. qd)
5.4 Calculate the coordinates of B. (3)
5.5 Determine the coordinates of E, a point of intersection of f and g. (4)
5.6 For which values of x will:

5.6.1 fo) < gx) Q)

5.6.2 — f(e.g(x)20 (2)
5.7 Calculate the length of AK. (4)

[18]

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Mathematics/P1 7 DBE/November 2016
CAPS — Grade 10

QUESTION 6

The graph of g(x)=-2*+8 is sketched below. A and B are the y- and x-intercepts
respectively of g.

g
fa) B \

6.1 Write down the range of g. ()

6.2 Determine the coordinates of B. (3)

6.3 If g is reflected over the x-axis to form a new graph h, determine the equation of h. (2)

6.4 Explain why the x-intercepts of g and h are both at B. (2)
[8]

QUESTION 7

A hyperbola, h, is described with the following characteristics:

e The equation of the vertical asymptote is x = 0

e The range of / is (2 33)UG; oo)

e The x-intercept of h is (2; 0)

Determine the equation of h. [4]

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Mathematics/P1 8 DBE/November 2016
CAPS — Grade 10

QUESTION 8
8.1 In a certain class of 42 boys:

27 play hockey (H)

32 play soccer (S)

7 do not play hockey or soccer

An unknown number (x) play both hockey and soccer

eecee

The information is represented in the Venn diagram below.

HW Ss
8.1.1 Calculate the value of x. (2)
8.1.2 If a boy from the class is chosen at random, calculate the probability
that he:
(a) Does not play hockey or soccer qd)
(b) Plays only soccer (2)
8.2 A bag contains 3 blue balls and x yellow balls.
8.2.1 Write down the total number of balls in the bag. qd)
8.2.2 If a ball is drawn from the bag, write down the probability that it is blue. (2)
8.3 8.3.1 Complete the following statement:

If A and B are two mutually exclusive events, then

P (A and B)=... qd)
8.3.2 Given that A and B are mutually exclusive events. The probability that
event A occurs is 0,55. The probability that event B does not occur
is 0,7.
(3)
Calculate P (A or B). [12]

TOTAL: 100

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