# Mathematics Grade 10 September Test 2019 Paper & Memo

> Grade 10 Mathematics question paper and memo from the September Test 2019, 11 pages. Read online or get the free PDF download.

- Page: https://www.hlayiso.com/library/math-sept-qp-memo-2019-gr10/402fda76-7e3a-463c-bb93-c11ecab6eaa2
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 10
- Document type: Question paper and memo
- Year: 2019
- Exam period: September Test
- Curriculum: CAPS
- Pages: 11

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## About this document

Mathematics · Grade 10 · September Test · 2019. Question paper and memorandum, 11 pages. Read online or download the PDF.

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## Document text

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                    testpapers.co.za

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Mathematics 2 Common Test September 2019

INSTRUCTIONS AND INFORMATION
Read the following instructions carefully before answering the questions.

ip This question paper consists of 6 questions.

we

Answer ALL the questions.

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

4. Answers only will NOT necessarily be awarded full marks.

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

6. Hf necessary, round off answers correct to TWO decimal places. unless stated
otherwise.

qh Diagrams are NOT necessarily drawn to scale.
8. Write neatly and legibly.

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Mathematics 3 Common Test September 2019
NSC

QUESTION 1

1.1 Mrs. Reyem wants to buy herself a new laptop. After completing her monthly

budget she realises that she does not have the money to buy a new laptop right now.

Mrs. Reyem decides to buy a laptop on a hire purchase agreement from a computer
store that advertises the following special:

Cash Price: R 4 999
OR

Hire purchase: 12% Deposit and
24 equal monthly payments to
the value of R 6 598,68

1.1.1 Calculate how much Mrs. Reyem would pay for the deposit. (2)

1.1.2 Calculate how much Mrs. Reyem will have to pay as her monthly
instalment. (i)

1.1.3 Calculate the total amount that Mrs. Reyem will pay for her new laptop on
the hire purchase agreement. (2)

1.1.4 Calculate the yearly interest rate charged on the laptop hire purchase
agreement, if Mrs. Reyem had decided to pay a deposit of R600. (3)

1.2 The average price of a litre of petrol in the UK is now approximately £1.30.
In the United States a litre of petrol costs about $0,85 while in South Africa
we pay R16,57 per litre.

Country Currency Exchange Rate
United States (USA) Dollars ($) $1=R 14,75
United Kingdom (UK) Pounds (£) £1=R 18,77
Use the exchange rate table to calculate in which country the cost per litre 3
of petrol would be CHEAPEST. (3)
13 Amelia decides to invest some money at a compound interest rate of 14% p.a.
How much money (to the nearest rand) should be invested if she wants to receive a
final amount of R 85 000 in eight years time? (3)
1.4 The population of a city in South Africa increased by 5,25% for the year 2017.

At the beginning of 2018 the population of the city was 2 560 000.

Assuming that the population will continue to increase at a constant rate of 5,25%
each year, estimate the population of the city at the beginning of 2020.

Give your answer correct to the nearest whole number. (3)
17]

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Mathematics 4 Common Test September 2019
NSC

QUESTION 2

2.1 A bag contains red, green, blue and yellow balls. There are 5 of each colour,
numbered from | to 5. “The balls are placed in a bag and one is chosen at random.

211 Determine the probability that the ball selected is pink.
2.1.2 Determine the probability that the ball selected is blue.
2.1.3 Determine the probability that the ball selected is numbered 3.
22 The two events A and B are such that: P(A)=0,85 and P(B)=k.
Determine:
22) P(A and B). if A and B are mutually exclusive events.
2.2.2 P(A and B), if A and B are non-mutually exclusive, exhaustive cvents

and k=(),5.

28. Match the Venn diagrams in column A with the expressions in column B which best
represents the shaded area. In your answer book write down the question number and
the correct expression from column B only. e.g. 2.3.7) P(A or B)

COLUMN A COLUMN B
23]

A B

C0) a
23.2

A B

qe P(A and B)
235

A B

CQ) “ae®)
2.3.4

A B

CO) P(A and B)'

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(4)

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Mathematics 5 Common Test September 2019
NSC
24 Last year, there were 38 pupils in a grade 10 class. Of these pupils:

e 22 studied French (F)
e 8 studied German (G)
e 7 studied both French and German.

2.4.1 Represent the information above in a Venn diagram.

2.4.2 How many learners from the class studied neither French nor German?

2.4.3 Determine the probability that a learner selected at random from this
class:

(a) studied German ONLY

(b) did NOT study French.

QUESTION 3

Mr. Lembede asked each student in his Grade 10 Mathematics class how many minutes of
homework they do each day. He drew this box and whisker diagram for the information he
obtained.

a {———
0 20 40 60 80 100
Minutes

3.1 Using the box and whisker diagram determine:
3.1.1. the median for the data.

3.1.2 what percentage of these students do more than 50 minutes of homework
each day.

a2 Calculate:
3.2.1 the range for the data.

3.2.2 the interquartile range for the data.

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(3)

()

(1)

()
[18]

(1)

(2)

(2)

(2)

[7]

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Mathematics 6 Common Test September 2019

NSC

QUESTION 4

The frequency table and histogram below provide information from a survey about the

distances travelled by some teachers on a daily basis.

Use the information provided to answer the questions which follow.

Distance (x km) Frequency
0<x<10 15
10<x<20 a
20 <x S30 b
30< «S40 10
40 <x <50 10
Histogram showing distance travelled by a selection of
teachers on a daily basis
Bi ae Fa Bisa eal l] ii T i aaa ae
OH aaTOa tate MOTI ERT
ae i eunee
i
30 ELE dL
n |
¥ 25 ++ |
=) iste
B20}
Lal a a
ISHeEE
fanae
cr}
104
5
re
0) 10 20 30 40 50
DISTANCE (x km)
41 Is the above given data discrete or continuous? (1)
4.2 Determine the values of a@ and b from the frequency table. (2)
4.2 How many teachers participated in the survey? (1)
43 Identify the modal class for the data. (1)
4.4 Calculate an estimate the mean of the data. (3)
45 Calculate an estimate of the median daily distance travelled. (1)
[9]

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Mathematics 7 Common Test September 2019
: NSC

QUESTION 5

5.1 The diagram below shows a spotlight at point B, mounted 12 metres directly above

a point C at the front edge of a field.

The spotlight swings 44, 3° from the vertical to illuminate another point D, the

midpoint of AC.
B
: 12m
fn a m ia
A + D tt Cc
5.1.1 Calculate the length of DC. (3)
5.1.2 Calculate through how many more degrees the spotlight must swing in
order to illuminate point A (i.e. calculate @) (3)
2.2 The diagram below represents a pyramid with a square base of side 12 cm.

The diagonals QS and TR meet at M. N is vertically above M.and NR =9cm.

12cm

5.2.1 Calculate the length of TR. (Leave your answer in surd form.) (3)
5.2.2 Calculate the length of MN, the perpendicular height of the pyramid. (2)
5.2.3 Calculate the size of NTR . (3)

{14]

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Mathematics, 8 Common Test September 2019
NSC

QUESTION 6

6.1 The diagram below shows a sphere, with a diameter of 30cm, placed inside an

empty cylindrical tank of radius 45cm and height 80cm. The cylinder is then filled
with water.

4
Volume of sphere =F ar’
: 1,
-|80cem Volume of cone oe

Volume of a cylinder = 27h

6 i Calculate the volume of the metal sphere, indicated in the diagram as A, (2)
6.1.2 Calculate the volume of water required to fill the tank. (3)

6.1.3. The sphere is removed from the tank as seen in the diagram below.

Calculate /, the height of the water remaining in the tank. (3)
6.2 The sphere is then melted down and the metal is made into a solid cone of height
25cm. Calculate the radius of the cone. (2)
[10]
TOTAL: =

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education

Department:
Education

PROVINCE OF KWAZULU-NATAL

SENIOR CERTIFICATE

Pieter ee tt er ee

eueeuaees
otsssnaes are,

¢
Seessess

MARKS: = 75

TIME: 14 hours

SEPTEMBER 2019

MARKING GUIDELINE

NATIONAL

GRADE 10

+

MATHEMATICS

COMMON TEST

Sesseeeeessee eet

*
Peeeessesesseeees ess?

This marking guideline consists of 6 Pages.

Please turn over

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Mathematics 2 Common Test September 2019
NSC - MARKING GUIDELINE
QUESTION 1
a Deposit 12 4999
= =x
= 100
= R599,
R599,98 tay
1.1.2
Monthly instalment = amas
= R274,95 t15
113 Total paid =R 599,98 + R 6 598,68
= R7198,66
(2
114 A= R6598,68 |
P= — R4399,00
n=  2years
is?
A=P(+ixn)
an
i= P
”
6598.68 _
;- 4399
j=—4399__
2
i=0,25
-- interest rate = 25%
G3)
12 United States S1=R14,75
$0,85= R12,54 |
United Kingdom £1= R18,77
£1,30= 224,40 |
Petro! would be cheapest in the United States. By
13 A= R85000
P= ?
n= 8years
i= 14%
A=P(I+iy"
__A
ati”
_ _ 85000
(1+0,14)"
P=R29797,52 (3)
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Mathematics: ‘Common Test Sc oer 2019 Mathematics Common Test September 2019
NSC - naneke GUIDELINE NSC ~ anente GUIDELINE
14 ? 2.4.1
2560000 S, F
2 years
5,25%
A= P(1+i)"
(+1) 15
A= 2s60000( 1+ 525 sas)
100
A=2835856
(3)
) 242 | 15 leamers a)
2.43
an © | peGeman only) = = 0,0263=2,63% a
QUESTION 2 243 0
©) | paid NOT study French) = 6-5 0,42 42% a
2.1.1 Fipinkl =. Q)
[18]
212 P(blue)= <7 = 7 OR 25% OR 0,25 w QUESTION 3
2 4 =- yo see
2.13 P(numbered 3) = 55 = = OR 20% OR 0,2 a
ag. P(A and B)=0 ()
2223 Let P(A and By) =x _ 0
4 B 3.11 30 minutes: Q)
3.12 25% Q)
321 Range = 80-4
= 76 minutes (2)
3.22 IQR =50-20
= 30 minutes (2)
1
(0,85—x)+(x)+(0,5-x)=1
QUESTION 4
41 Continuous ()
42. a=20
‘Therefore P(A and B) = 0,35 b=30 (2)
(4)
fae “i 42 85 teachers a)
PA) (i) 43 20<x<30 ay
P(A and B)' a) 44 Estimated mean
P(A and B) ay _ (155) -+(20%15) + (30x25) + (10X35) +(10x45)
85
= 22,65
(3)
45 Estimated median = 25km ()
19

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Mathematics: Common Test September 2019
NSC - MARKING GUIDELINE
QUESTION 5
S11 DC
tan44,3° = m “tan ratio
DC =12tan44,3° = oannplification
DC=11,7lm YA (3)
3.1.2 AC =2xXDC = 23,42m
23,42
tan’ MABE => CA based on DC (5.1.1)
ABC = 62,87° CA value for ABC
£0 = 62,87°=44,3° =18,57° ¥CA ( ABC—44,3°)
therefore spotlight will need toswing 18,57° further (3)
5.2.1 TR°=TQ" + OR* (pythagoras)
TR=N12? +12°
TR =12V2.em 3
3.2.2 NM *=N&°-MR* — (pythagoras)
NM = (6)
NM =3em (2)
323 amNeae
6v2
NTR=19,47° Q)
{14
QUESTION 6
6.11 4_,
Volume of sphere 3
4 3
=—a(15)
5 (15)
=14137,17cm* 2)
6.1.2 Volume of water =Viinage ~ Vege
=nPh Sar
=(45)*(80)—14137.17
=498800,84cm* a

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Mathematics Common Test September 2019
NSC - Seam GUIDELINE
6.13 h _ Volume of water
ar
_ 498800,84
(45)
h = 78,41cm (3)
6.2 1a
V=—ar'h
3
@
{10}
TOTAL: 75

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