# Mathematics Grade 12 P2 North West Mock 2016 Question Paper

> Grade 12 Mathematics Paper 2 question paper from the North West Mock Exam 2016, 11 pages. Read online or get the free PDF download, memo linked when available.

- Page: https://www.hlayiso.com/library/2016-grade-12-math-trial-exam-paper-2-nw/35cfa34f-270f-43be-8cb3-910dadc31a79
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 12
- Document type: Question paper
- Year: 2016
- Exam period: North West Mock Exam
- Paper: 2
- Curriculum: CAPS
- Pages: 11

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## About this document

Mathematics · Grade 12 · North West Mock Exam · 2016. Question paper, 11 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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Education and Sport Development

Department of Education and Sport Development
Departement van Onderwys en Sportontwikkeling
Lefapha la Thuto le Tihabololo ya Metshameko

NORTH WEST PROVINCE

NATIONAL
SENIOR CERTIFICATE

BO ee ee ae Ge a eed he apc en rd
# — MATHEMATICS P2 __

* ss SEPTEMBER 2016

i. 2 ‘

AS

MARKS: 150

TIME: 3 hours

This question paper consists of 9 pages, 1 information sheet and
a 20-pages answer book.

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Mathematics/P2 2 NW/September 2016
NSC

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1. This question paper consists of 10 questions.

2. Answer ALL the questions in the SPECIAL ANSWER BOOK provided.

3 Clearly show ALL calculations, diagrams, graphs, et cetera that you used to
determine the answers.

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

5. If necessary, round off answers to TWO decimal places, unless stated otherwise.

6. Diagrams are NOT necessarily drawn to scale.

7. ‘You may use an approved scientific calculator (non-programmable and non-

graphical), unless stated otherwise.
8. An INFORMATION SHEET with formulae is included at the end of the question
paper.

9. Write neatly and legibly.

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Mathematics/P2

QUESTION 1

A Mathematics teacher wants to create a model by which she can predict a learner’s

3

NSC

final marks. She decided to use her 2015 results to create the model.

NW/September 2016

Preparatory | 55 | 35 | 67 |85|91| 48 | 78 | 72 | 15 | 75 | 69|37
exam (x)
ana 57 | 50 | 74 | 80}92] 50 | 80 | 81 | 23 | 80 | 75} 42

gl Determine the equation of the least squares regression line in the form

y=atbx.

1.2 Use the equation of the regression line to predict the final exam mark for a
learner who attained 46% in the preparatory examination.

1.3 Could you use this equation to estimate the preparatory exam mark for a

learner who attained 73% in the final exam? Give a reason for your answer.

1.4 Show that the point (x ; y) lies on the regression line.

1.5 Determine the correlation coefficient of the data.

1.6 Describe the correlation between preparatory and final exam results.

QUESTION 2

G3)

(2)

Q)
@)
qd)

(2)
{14]

The table below shows the results from a survey of cellphone expenditure for 100 learners
from a secondary school in Rustenburg.

Expenditure (in rand) | Frequency Cumulative frequency
50 < x <100 24
100 < x <150 52
150 < x <200 14
200 < x <250 a
250 < x <300 4

21 Determine the value of a.

2.2 Complete the cumulative frequency table in the ANSWER BOOK.

2.3 Draw an ogive (cumulative frequency graph) for the data.

24 What is the modal class for the data?

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q)
(2)
(3)

qd)
[7]

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Mathematics/P2

4 NW/September 2016

NSC

QUESTION 3

In the diagram below, A(4 ; 5) , B(-3 ; -2 ) and C(6 ; —5) are the vertices of AABC.
AD is drawn perpendicular to BC.

3.1
3.2
3.3
3.4

3.5

3.6

y

Z

A(4; 5)

BC-3 ; -2,

Calculate the length of BC.
Determine the equation of BC.
Determine the equation of AD.

Determine the coordinates of D.

Calculate the size of B AD 7

CO ;-5)

(2)
(3)
(3)
3)
(5)

Calculate the coordinates of a point E if the area of AEBC = area of AABC

and E is a point on the positive x axis.

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(4)
[20]

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Mathematics/P2 > NW/September 2016
NSC

QUESTION 4

In the diagram below, O(0; 0) and N(2; y) are two points on the circumference of a circle
with centre M(4 ; 2). The tangents at O and N meet at R.

Jy
| NQsy
R
-M(4; 2)
>
(0) x
4.1 Determine the equation of the circle. (3)
42 Calculate the value of y (4)
4.3 Determine the equation of OR. (3)
4.4 — Calculate the coordinates of R. (6)
4.5 Determine, with a reason, the type of quadrilateral represented
by MNRO. (2)
[18]
QUESTION 5
0 -t ° — x). sin2(90° — :
5.1. Determine the value of cos(180°+ x) an(360 2).sin (00° =) + sin? x (6)
sin(180° — x)
52 5.2.1 Prove the identity: cos(A —B) — cos(A + B) = 2sin A sinB (3)
5.2.2 Hence calculate, without using a calculator, the value of
cos 15° — cos 75° (4)

5.3 Find the value of tan 0, if the distance between A(cos 6 ; sin 0) and B(6 ; 7)
is 86. (4)

(17]

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Mathematics/P2 6 NW/September 2016
NSC

QUESTION 6
Consider: f(x) = cos(x— 45°) and g(x) = tan x for xe [-180° ; 180°]

6.1 Use the grid provided to draw sketch graphs of f and g on the same set of axes
for xe [-180° ; 180°]. Show clearly all the intercepts on the axes,

the coordinates of the turning points and the asymptotes. (6)

6.2 Use your graphs to answer the following questions for xe [—180° ; 180°]

6.2.1 Write down the solutions of cos(x — 45°) =0 (2)
6.2.2 Write down the equations of asymptote(s) of g. (2)
6.2.3 Write down the range of f. (1)

6.2.4 How many solutions exist for the equation cos(x — 45°) = tan x u

6.2.5 For what value(s) of xis f(x).g(x) >0 (3)

[15]
QUESTION 7

In the diagram below, ABCD is a cyclic quadrilateral with DC = 6 units, AD = 10 units,
ADC = 100° and CAB = 40°

_
Calculate the following, correct to ONE decimal place:

7A The length of BC (6)
72 The area of AABC (3)
[9]

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Mathematics/P2 7 NW/September 2016
NSC

Give reasons for ALL statements in QUESTIONS 8, 9 and 10

QUESTION 8
8.1 Complete the following statement:
8.1.1 The angle subtended at the circle by a diameter is «0.0.0.4... qd)

8.1.2 The angle between a tangent to a circle and a chord drawn from
the point of contact is equal tO... eects qd)

8.2 In the diagram below, ED is a diameter of the circle with centre O.
ED is produced to C and CA is a tangent to the circle at B. AO intersects BE at F.

BD||AO.
Let E =x
Cc

8.2.1 Write down, with reasons, THREE other angles each equal to x. (6)
8.2.2 Determine, with reasons, CBE interms of x. (3)
8.2.3. Prove that F is the midpoint of BE. (4)
8.2.4 Calculate the length of the diameter if it is further given that

EB =8cm and OF =3 cm. (4)

[19]

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Mathematics/P2 8 NW/September 2016
NSC

QUESTION 9

In the diagram below, CE is a common chord of the circles ACE and CBDE. CD is a tangent
to circle ACE at C and AEH is a tangent to circle CBDE at E. ACB and BDH are straight
lines. AC =ED.

9.1 Prove that AB||ED. (5)

9.2 What type of quadrilateral is ACDE? Give reasons. (2)

9.3 Prove that af = BE (4)
CB EA

{11]

QUESTION 10

10.1 In the diagram alongside, AABC and ADEF are given.
Prove the theorem which states that:

A
If A=D, B=E andC=F
hen ee
DE DF
E F
Cc

B

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Mathematics/P2 9 NW/September 2016
NSC

)

10.2 In the diagram below, PQRS is a cyclic quadrilateral. PS and QR are produced
to meet at T. RE is a tangent to the circle at R, with E on PT and RE | Qs.

Prove that:
10.2.1 QR = RS (4)
10.2.2 ARST ||| APQT (4)
10.2.3 EOE SE (5)
PT ET
[20]
TOTAL: 150

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Mathematics/P2 NW/September 2016
NSC

INFORMATION SHEET

pe bt Vb? —4ac

7 2a
A=P(i+ni) A=P(l-ni) A=P(-i)" A= P(1+i)"

T,=at+(n-ld_ S, = 5a +(n-1a]

¢7 pl l-r
eee ali)" -1| p-alna+)")
L t

fat+h)- fa)

Oe) =i
Fe) 30

h
xX, +x. y, +y.
d=y (x, -x,)7 +0, -9,)7 M| 12-1 2
2 2
y=mx+e y-y, =m(x-x,) m=22 1 m=tand
02) acs
(x-a) +(y-by =r
In AABC: = = a = a a? =b2 +¢7 ~2be.cos A
sinA sinB_ sinC
area AABC =F absin€
sin(a + B) = sina.cos B + cosa.sin B sin(a — 8) = sina.cos B — cosaz.sin B
cos(a+ B)=cosa.cos # -sina.sin B cos(a— 8) = cos@.cos # + sina.sin B
cos’ a@—sin’ @
cos2a@=41—2sin? a sin 2@ = 2sina.cosa@
2cos* a-1
- Dre > Xx, -x)
x= et o = ___
n n
n(A)
P(A)= AS) P(A or B) = P(A) + P(B) — P(A and B)
n
x-x\(y-y
jsatbe pau! \o-y)

Si@-x)y

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