Maths N2

ROSTEC TECHNICAL
FET COLLEGE MATN2

Department: Engineering Studies
RUSTENBURG CAMPUS
INTERNAL ASSESSMENT
MATHEMATICS N2
09:00 – 11:24
16 MARCH 2023
Duration: 2HRS 24 MINS Marks: 80
Assessor MR A MASIRAHA Assessment Task TWO

Moderator MR C SEBIDI ICAAS value 70%
This question paper consists of 3 printed pages and a 2 page formular sheet
INSTRUCTIONS TO CANDIDATES
1. Answer ALL the questions and submit answer script for marking on completion.
2. Read ALL the questions carefully.
3. Number the answers according to the numbering system used in this question
paper.
4. Write neatly and legibly.
Rating Code 1 3 4 8 7
Rating Distinction Pass Pass( Condoned) Fail Absent
Marks (%) 80-100 40-79 38-39 0-39 999
QUESTION 1
1.1 Simplify the following WITHOUT the use of a calculator:
1.1.1 ( )
× (3)
1.1.2 1
(log 27) + log
64 (3)
1
1.2 Solve for if log 9+ log 1 − log = 3
16 (4)
64
1.3 Solve for if = 256
16 (3)
1.4 Solve for a in the following equations:
1 𝑎−6
1.4.1 (32)2𝑎+1 × ( ) = (16)−4 (4)
2
1.4.2 [log(𝑎 − 1)]2 = log 10 (4)
1.4.3 𝑎 = log 64 8 (3)

[24]
QUESTION 2
2.1 Simplify the following algebraic fractions:
𝑎 𝑏 1
2.1.1 + + (6)
2𝑎2 − 3𝑎𝑏 + 𝑏 2 2𝑎2 + 𝑎𝑏 − 𝑏 2 𝑎 + 𝑏
4𝑝2 + 8𝑝𝑞 + 4𝑞 2 9𝑝2 − 6𝑝𝑞 − 3𝑞 2

2.1.2 ×
3𝑝2 − 3𝑞 2 4𝑝 + 4𝑞 (4)
2.2 Given the following algebraic expressions:
−2𝑛 − 2𝑙 − 2𝑛2 + 2𝑙 2 ;
−2𝑛 − 2𝑙 and
−2𝑛2 − 4𝑛𝑙 − 2𝑙 2
2.2.1 Factorise each expression completely. (7)
2.2.2 Determine the HCF and LCM of all three expressions. (3)
[20]
(1)
QUESTION 3
3.1 Solve for 𝑝 in the following equation by using the factorisation method:
−3𝑝2 + 𝑝 + 2 = 0 (3)
3.2 Solve for 𝑣 and 𝑤 in the following simultaneous equations:
5𝑣 − 2𝑤 − 6 = 0 and 6𝑤 − 3𝑣 − 30 = 0 (4)
3.3 A boy pays with R30 for 4 plums and 2 guavas and receives R2 change.
Calculate the price of a plum if a guava cost R2.50. (2)
5
√𝑡 3 − 𝑝3
3.4 Given: 𝑚𝑛 =
𝑚𝑞
3.4.1 Make 𝑝 the subject of the formula. (4)
3.4.2 Calculate the value of p if 𝑡 = 5,2; 𝑚 = 1,35; 𝑛 = 0,25 𝑎𝑛𝑑 𝑞 = 2,75 . (1)
[14]
QUESTION 4
4.1 Given the functions 𝑓(𝑥) = 6 + 𝑥 − 𝑥 2 𝑎𝑛𝑑 𝑔(𝑥) = 2𝑥 + 1
4.1.1 Calculate the equation of the axis of symmetry of 𝑓(𝑥) (1)
4.1.2 Calculate the 𝑦-ordinate of the turning point of 𝑓(𝑥). (1)
4.1.3 Use graph paper to draw the graphs of 𝑓(𝑥) and 𝑔(𝑥) on the same system
of axes. (5)
4.1.4 Use the graphs in QUESTION 5.1.3 to determine the values of 𝑥 for which
𝑔(𝑥) − 𝑓(𝑥) = 0.
[HINT: Use broken lines on the graph to read off the values of x ]. (2)
4.1.5 Use the graphs in QUESTION 5.1.3 to determine the values of 𝑥 for
which 𝑓(𝑥) = 4. (2)
[11]
(2)
QUESTION 5
5.1 Solve for all values of in the equation below if
tan = − 1; 0° ≤ ≤ 360° (3)
5.2 An artisan must determine lengths between several points on a floor plan. The
information available is limited and shown in FIGURE 2 below.
FIGURE 2
Determine the following:
5.2.1 The length of AB (3)
5.2.2 The length of BC (2)
5.3 Calculate the length of the chord of a circle of which the diameter is 42 mm, and the
height of the segment is 10 mm. (3)
[11]
(3)
MATHEMATICS N2
FORMULA SHEET
The right cone
𝑉𝑜𝑙𝑢𝑚𝑒 = ⅓𝜋𝑟 2 ℎ
𝑺𝒖𝒓𝒇𝒂𝒄𝒆 𝒂𝒓𝒆𝒂 = 𝜋𝑟√ℎ2 + 𝑟 2 + 𝜋𝑟 2

= 𝜋𝑟ℓ + 𝜋𝑟 2
The right pyramid
Volume = ⅓ (area of base) × (perpendicular height)
The prism
Volume = (area of base) × (perpendicular height)
The cylinder
𝑉𝑜𝑙𝑢𝑚𝑒 = 𝜋𝑟 2 ℎ
Surface area = 2𝜋𝑟 2 + 2𝜋𝑟ℎ
The sphere
4
V =  r 3 ; A = 4 r 2
3
Degrees and radians
180° = 𝜋 𝑟𝑎𝑑
𝑎𝑟𝑐
𝑆𝑒𝑐𝑡𝑜𝑟: 𝜃 = −; 𝐴 = ½𝑟 2 𝜃
𝑟𝑎𝑑𝑖𝑢𝑠
Angular velocity
Angular velocity: 𝑤 = 2𝜋𝑛
Circumferential velocity: 𝑣 = 𝜋𝐷𝑛
n = rotation frequency (r/s = revolution per second)
(4)
Mid-ordinate rule
A = ( distance between ordinates ) × ( sum of mid-ordinates )

1st ordinate + Last ordinate 
A=  + Sum of other ordinates   common distance between the ordinates
 2 
Graphs
Straight line: 𝑦 = 𝑚𝑥 + 𝑐
Parabola: 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
−b
Axis of symmetry: x =
2a
− b  b 2 − 4a
Roots: x =
2a
Trigonometry
90° <  < 180°
sin 𝜃 = sin(180° − 𝜃) cos 𝜃 = −cos (180° − 𝜃) tan 𝜃 = − tan(180° − 𝜃)
Segments of circles
Chord length = x Height of segment = h Diameter of circle = D
x2
D= h+
4h
Regular polygons
Angle subtended at centre of circumscribed circle by one side:
360
=
number of sides
R = radius of circumscribed circle
x = length of side
θ
x = 2R sin
2
(
Annulus: A =  R 2 − r 2 )
(5)

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ROSTEC TECHNICAL

FET COLLEGE MATN2

Duration: 2HRS 24 MINS Marks: 80

Assessor MR A MASIRAHA Assessment Task TWO

2. Read ALL the questions carefully.

4. Write neatly and legibly.

1.1 Simplify the following WITHOUT the use of a calculator:

1.4.2 [log(𝑎 − 1)]2 = log 10 (4)

1.4.3 𝑎 = log 64 8 (3)

2.1 Simplify the following algebraic fractions:

4𝑝2 + 8𝑝𝑞 + 4𝑞 2 9𝑝2 − 6𝑝𝑞 − 3𝑞 2

2.2 Given the following algebraic expressions:

2.2.1 Factorise each expression completely. (7)

3.2 Solve for 𝑣 and 𝑤 in the following simultaneous equations:

Calculate the price of a plum if a guava cost R2.50. (2)

3.4.1 Make 𝑝 the subject of the formula. (4)

4.1 Given the functions 𝑓(𝑥) = 6 + 𝑥 − 𝑥 2 𝑎𝑛𝑑 𝑔(𝑥) = 2𝑥 + 1

4.1.1 Calculate the equation of the axis of symmetry of 𝑓(𝑥) (1)

4.1.2 Calculate the 𝑦-ordinate of the turning point of 𝑓(𝑥). (1)

5.1 Solve for all values of in the equation below if

tan = − 1; 0° ≤ ≤ 360° (3)

Determine the following:

5.2.1 The length of AB (3)

5.2.2 The length of BC (2)

The right cone

𝑺𝒖𝒓𝒇𝒂𝒄𝒆 𝒂𝒓𝒆𝒂 = 𝜋𝑟√ℎ2 + 𝑟 2 + 𝜋𝑟 2

The right pyramid

Volume = ⅓ (area of base) × (perpendicular height)

Volume = (area of base) × (perpendicular height)

Surface area = 2𝜋𝑟 2 + 2𝜋𝑟ℎ

Degrees and radians

Angular velocity: 𝑤 = 2𝜋𝑛

Circumferential velocity: 𝑣 = 𝜋𝐷𝑛

n = rotation frequency (r/s = revolution per second)

A = ( distance between ordinates ) × ( sum of mid-ordinates )

90° <  < 180°

sin 𝜃 = sin(180° − 𝜃) cos 𝜃 = −cos (180° − 𝜃) tan 𝜃 = − tan(180° − 𝜃)

Chord length = x Height of segment = h Diameter of circle = D

Angle subtended at centre of circumscribed circle by one side:

R = radius of circumscribed circle

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