# Mathematics Grade 12 P2 NSC Supplementary 2018 QP (Eng)

> Grade 12 Mathematics Paper 2 question paper from the NSC Supplementary Exam 2018 (English), 14 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/mathematics-p2-feb-march-2018-eng/5e82dde6-557e-4aa5-bf11-e1c8b132bce5
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 12
- Document type: Question paper
- Year: 2018
- Exam period: NSC Supplementary Exam
- Paper: 2
- Curriculum: CAPS
- Pages: 14

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## About this document

Mathematics · Grade 12 · NSC Supplementary Exam · 2018. Question paper, 14 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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ae. basic education

- Department:
) / Basic Education

KO
,
WI REPUBLIC OF SOUTH AFRICA

NATIONAL

SENIOR CERTIFICATE

GRADE 12

Pe

" MATHEMATICS P2 a

u

ly ii

i: FEBRUARY/MARCH 2018 "

eee eer er err rr rr rrr Ter rrrrrrrerrTrrrt rrr ert fs
MARKS: 150
TIME: 3 hours

This question paper consists of 13 pages, 1 information sheet
and an answer book of 27 pages.

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Mathematics/P2 2 DBE/Feb.—Mar. 2018

NSC

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.

2.

This question paper consists of 10 questions.
Answer ALL the questions in the ANSWER BOOK provided.

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.
An information sheet with formulae is included at the end of the question paper.

Write neatly and legibly.

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Mathematics/P2 3 DBE/Feb.—Mar. 2018
NSC

QUESTION 1

An organisation decided that it would set up blood donor clinics at various colleges. Students
would donate blood over a period of 10 days. The number of units of blood donated per day by
students of college X is shown in the table below.

DAYS 1 2 3 4 5 6 7 8 9 10
UNITS OF
BLOOD 45 | 59 | 65 | 73 | 79 | 82 | 91 | 99 | 101 | 106

1.1 Calculate:

11.1 The mean of the units of blood donated per day over the period of 10 days (2)
1.1.2 The standard deviation of the data (2)
1.1.3 How many days is the number of units of blood donated at college X
outside one standard deviation from the mean? (G3)
12 The number of units of blood donated by the students of college X is represented in

the box and whisker diagram below.

e————_________ |
T T
A B
1.2.1 Describe the skewness of the data. qd)
1.2.2 Write down the values of A and B, the lower quartile and the upper
quartile respectively, of the data set. (2)
1.3 It was discovered that there was an error in counting the number of units of blood
donated by college X each day. The correct mean of the data is 95 units of blood.
How many units of blood were NOT counted over the ten days? qd)

[14]

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DBE/Feb.—Mar. 2018

Mathematics/P2

QUESTION 2

4
NSC

The table below shows the number of hours that a sales representative of a company spent with
each of his nine clients in one year and the value of the sales (in thousands of rands) for that

client.
NUMBER OF HOURS 30 50 80 | 100 | 120 | 150 | 190 | 220 | 260
VALUE OF SALES
(IN THOUSANDS OF RANDS) 270 | 275 | 376 | 100 | 420 | 602 | 684 | 800 | 820
SCATTER PLOT
900 = ~

oo
2
6

~
9
3

a

Q

6
nl

wu
fo}
6

b

fo}

a
f,

w
S
r=)

N
°
oO

Value of sales (in thousands of rands)

e
2
o

0 + =p ee 1 —
(e) 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300
Number of hours

21 Identify an outlier in the data above. ql)
2.2 Calculate the equation of the least squares regression line of the data. (3)

2.3 The sales representative forgot to record the sales of one of his clients. Predict the

value of this client's sales (in thousands of rands) if he spent 240 hours with him
during the year. (2)
2.4 What is the expected increase in sales for EACH additional hour spent with a client? (2)
[3]

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Mathematics/P2 3 DBE/Feb.—Mar. 2018
NSC

QUESTION 3

In the diagram, P, Q(-7 ; -2), R and S(3 ; 6) are vertices of a quadrilateral. R is a point on
the x-axis. QR is produced to N such that QR=2RN. SN is drawn. PTO =71,57° and

SRN =0.

8(3 ; 6)

T/71,57° D :

oO R *
QC7 ; -2)
Determine:
3.1 The equation of SR (1)
3.2 The gradient of QP to the nearest integer (2)
3.3 The equation of QP inthe form y=mx+ce (2)
3.4 The length of QR. Leave your answer in surd form. (2)
3.5 tan@0°— 6) GB)
3.6 The areaof ARSN, without using a calculator “
[16]

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Mathematics/P2 6 DBE/Feb.—Mar. 2018
NSC

QUESTION 4

In the diagram, PKT is a common tangent to both circles at K(a ; 6). The centres of both
circles lie on the line y = > The equation of the circle centred at O is x? +y* =180.

The radius of the circle is three times that of the circle centred at M.

X

4.1 Write down the length of OK in surd form. qd)
4.2 Show that K is the point (—12 ; -6). (4)
43 Determine:

43.1 The equation of the common tangent, PKT, in the form y=mx+c (3)

4.3.2 The coordinates of M (6)

4.3.3 The equation of the smaller circle in the form (x-—a)? +(y—b)? =r? (2)
4.4 For which value(s) of r will another circle, with equation x’ + y? =r’, intersect the

circle centred at M at two distinct points? (GB)
45 Another circle, x? + y* +32x+16y+240=0, is drawn. Prove by calculation that

this circle does NOT cut the circle with centre M(-16 ; -8). i

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Mathematics/P2 7 DBE/Feb.—Mar. 2018
NSC
QUESTION 5
5.1 If cos20= -2, where 20 €[180°;270°], calculate, without using a calculator,
the values in simplest form of:
5.1.1 sin20 (4)
5.1.2 sin’ 0 (3)
5.2 Simplify sin(180° — x).cos(—x) + cos(90° + x).cos(x—180°) to a single trigonometric
ratio. (6)
5.3 Determine the value of sin3x.cos y+cos3x.siny if 3x+y=270°. (2)
5.4 Given: 2cosx =3tanx
5.4.1 Show that the equation can be rewritten as 2sin? x+3sinx—2=0. (3)
5.4.2 Determine the general solution of x if 2cosx =3tan x. (5)
5.4.3 Hence, determine two values of y, 144°<y<216°, that are solutions of
2cos5y =3tan5y. (4)
5.5 Consider: g(x) =—4cos(x + 30°)
5.5.1 Write down the maximum value of g(x). qd)
5.5.2 Determine the range of g(x) + 1. (2)

5.5.3 The graph of g is shifted 60° to the left and then reflected about the
x-axis to form a new graph A. Determine the equation of hin its
simplest form. G3)
[33]

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Mathematics/P2 8 DBE/Feb.—Mar. 2018
NSC

QUESTION 6

PQ and AB are two vertical towers.
From a point R in the same horizontal plane as Q and B, the angles of elevation to P and A
are @ and 20 respectively.

AQR =90°+6, QAR =6 and QR=x.

6.1 Determine in terms of x and 0:
6.1.1 QP Q)
6.1.2 AR (2)
6.2 Show that AB = 2xcos? @ 4
AB
Determine — if @=12°.
6.3 termine OP i (2)

[10]

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Mathematics/P2 9

NSC

QUESTION 7

DBE/Feb.—Mar. 2018

In the diagram, PQRT is acyclic quadrilateral in a circle such that PT = TR. PT and QR are
produced to meet in S. TQ is drawn. SQP = 70°

7A

7.2

Calculate, with reasons, the size of:

TAA f,

71.2 Q,

If it is further given that PQ || TR:

7.2.1 Calculate, with reasons, the size of T,

722 Prove that IX _RQ
TS RS

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(2)

(2)

(2)

2)
[8]

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Mathematics/P2 10 DBE/Feb.—Mar. 2018
NSC

QUESTION 8

In the diagram, PR is a diameter of the circle with centre O. ST is a tangent to the circle
at T and meets RP produced at S. SPT=x and §=y.

Determine, with reasons, y in terms of x. [6]

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Mathematics/P2 i DBE/Feb.—Mar. 2018
NSC

QUESTION 9

In the diagram, DEFG is a quadrilateral with DE=45 and GF = 80. The diagonals GE and
DF meetin H. GDE=FEG and DGE=EFG.

D
45
G E
H
80
F
9.1 Give a reason why ADEG ||| AEGF. (1)
9.2 Calculate the length of GE. (3)
9.3 Prove that ADEH ||| AFGH. (3)
9.4 Hence, calculate the length of GH. (3)

[10]

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Mathematics/P2 12 DBE/Feb.—Mar. 2018
NSC

QUESTION 10

10.1 In the diagram, O is the centre of the circle with A, B and C drawn on the circle.

Prove the theorem which states that BOC = 2A. (5)

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Mathematics/P2

10.2 In the diagram, the circle with centre F is drawn. Points A, B, C and D lie on the
circle. Chords AC and BD intersect at E such that EC =ED. K is the midpoint

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13 DBE/Feb.—Mar. 2018

NSC

of chord BD. FK, AB, CD, AF, FE and FD are drawn. Let B=x.

10.2.1

10.2.2

10.2.3

10.2.4

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Determine, with reasons, the size of EACH of the following in
terms of x:

(a) F,
) ¢é

Prove, with reasons, that AFED is a cyclic quadrilateral.

Prove, with reasons, that F, = x.

If area AAEB = 6,25 x area ADEC, calculate ~.

TOTAL:

Q)
2)
(4)
(6)

G)
[24]

150

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Mathematics/P2 DBE/Feb.—Mar. 2018
NSC

INFORMATION SHEET: MATHEMATICS

_ —b+y52 ~4ac

2a
A= P(+ni) A=P(-ni) A=P(1-i)" A=P(l+i)"
T, =a+(n—N)d S, =F ea+(n—vd]
T, =ar™! s, -ae"=!) sr#l S,=—);-ler<l

r-l I-r

pa 2+ =I) p2l-d+97")

i i

im FET f@)

I'@)=
x, +x. ¥, +y.
Pe es rroees M| 12
2 2
= _y= _ YT =
y=mxt+e yy, =m(x-x,) m= m=tan@
%y 7%
(x-a) +(y-by =r?
InAABC: ab _-¢
sinA sinB sinC
a® =b* +¢7 -2be.cosA
area N\ABC = 5 absinc
sina +f) =sina.cosf +cosa.sinB sin(a— B) =sina.cosf —cosa.sinB
cofat B) =cosa.cosf-sina.sing cofa— B) =cosa@.cosf+sina.sin£
cos’ a@—sin> a
cos2a =41-2sin’@ sin2a@ = 2sina.cosa
2cos’?a—1
n 2
zeke >@-»)
ye o ==
An
" (A) =
P(A)= 78) P(A or B) = P(A) + P(B) — P(A and B)
(x-¥y-9)
paatbx Y@-z

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