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MTCG1016 Basic Mathematics Page 1 of 15
MILITARY TECHNOLOGICAL COLLEGE
ACADEMIC YEAR
GENERAL FOUNDATION PROGRAMME
SAMPLE EXAMINATION PAPER
Instructions:
Write the information required on the front page. Use blue / black ink or ball-point pen.
Students should not keep any helping / study materials with them. Copying, cheating and any kind
of malpractice in the examination are strictly prohibited.
Use of only non- programmable calculators is allowed.
Answer the questions in the space provided. Extra sheets will not be allowed or provided.
All necessary solutions should be shown completely in Section B and Section C, otherwise marks
for method will be lost.
The figures shown, if any, are only for illustration.
Do not open this question paper until the invigilator has told you to do so. ----------------------------------------------------------------------------------------------------------------------
MARK DISTRIBUTION
Section No. of Questions Γ Marks per Question =
Total Marks Allocated 1st Marking 2nd Marking
A 10 Γ 2 = 20 Marks
B 6 Γ 2 = 12 Marks
C 6 Γ 3 = 18 Marks
Total = 50 Marks /50 /50
Final Marks /50
Final Marks in %
1st Marker 2nd Marker
Name and Signature Name and Signature
Module Name & Code GFP Basic Mathematics - MTCG1016
ID Number Duration of Exam Exam Seat number
90 Minutes
MTCG1016 Basic Mathematics Page 2 of 15
Section A
Part-I: Answer the following 20 questions. Each question carries 1 mark.
[Total Marks 20]
Circle the correct answer of the following questions
1. The percentage of 8 out of 32 is β¦..
a) 25%
b) 75%
c) 66%
2. If β2π₯ > 8, then β¦β¦.
a) π₯ > β4
b) π₯ < β4
c) π₯ = β4
3. If π₯
10=
2
5, then π₯ =β¦β¦.
a) 5
b) 4
c) 10
4. The inequality notation for (β1, 0] is
a) β1 β€ π₯ β€ 0
b) β1 β€ π₯ < 0
c) β1 < π₯ β€ 0
5. Which property is shown by π Γ π = π Γ π ?
a) Distributive
b) Commutative
c) Associative
a)
MTCG1016 Basic Mathematics Page 3 of 15
6. If βπ₯ = 7, then π₯ = β¦β¦
a) 49
b) 7
c) β7
7. The value for β²πβ² in π£ = π’ + ππ‘ isβ¦β¦.
a) π =π’βπ£
π‘
b) π =π£+π’
π‘
c) π =π£βπ’
π‘
8. Which number is an odd number?
a) 1 b) 22
c) e
9. The two consecutive numbers are β¦β¦..
a) 51, 41
b) 24, 25
c) 10, 14
10. If 8 is added to 4 times a number, the result is 28 then the number is β¦β¦β¦
a) 11
b) 5
c) 12
MTCG1016 Basic Mathematics Page 4 of 15
11. 5600 πππ‘πππ = _____ππ
a) 56
b) 0.56
c) 5.6
12. 2.64 πππππ£πππ‘π = _____πππππ£πππ‘π
a) 2640
b) 0.00264
c) 26400
13. The following graph is symmetric about the β¦.
a) x-axis
b) y-axis
c) Origin
14. The measure of straight angle is β¦.
a) 90Β°
b) 180Β°
c) 360Β°
15. π
3 πππ = _________Β° (πππππππ )
a) 30Β°
b) 270Β°
c) 60Β°
MTCG1016 Basic Mathematics Page 5 of 15
16. If π πππ₯ =3
2, then πππ π₯ =β¦..
a) 2
3
b) 5
2
c) 5
3
17. The amplitude of the curve π¦ = β2π ππ3ππ₯ isβ¦
a) π
b) 2
c) β2
18. The x-intercept of the line π¦ = 2π₯ + 8 isβ¦
a) 10
b) 8
c) β4
19. The center of the circle (π₯ β 2)2 + (π¦ + 2)2 = 25 isβ¦
a) (2, β2)
b) 5
c) (β2, 2)
20. The curve which is symmetric about the y-axis is β¦
a) π¦ = π₯2 β 1
b) π₯ = π¦2 β 1
c) π¦ = 2π₯ + 3
MTCG1016 Basic Mathematics Page 6 of 15
Section B
Answer the following 6 questions. Show your solution step by step.
Each question carries 2 marks [Total Marks 12]
1. Find the LCM of 4, 6 and 8 [2 Marks]
2. Simplify 236122 [2 Marks]
3. Simplify nn
n
66
662
[2 Marks]
4. If π΄ = { 0, 1, 2, 9, 10} πππ π© = {5, 6, 7, 8} then find
[2 Marks]
(a) π¨ βͺ π©
(b) π¨ β© π©
MTCG1016 Basic Mathematics Page 7 of 15
5. Perform the indicated operation and simplify [2 Marks]
)23)(15( 22 xx
6. Rationalize the denominator and simplify the fraction.
35
2
[2 Marks]
MTCG1016 Basic Mathematics Page 8 of 15
Section C
Answer the following 6 questions. Show your solution step by step.
Each question carries 3 marks [Total Marks 18]
1. Solve the following simultaneous equations: [π π΄ππππ]
123
32
yx
yx
2(a). Find angle c from the following figure if angle π = 75Β° [π π΄πππ]
MTCG1016 Basic Mathematics Page 9 of 15
2(b). Find the angle πΒ° from the following figure. [π π΄ππππ] (Write final answer up to two decimal places)
3(a). Find the distance of a boat B from the foot of the lighthouse if the lighthouse is
125 metres tall, and the angle of depression is 6Β°. [π π΄ππππ]
πΏππβπ‘ βππ’π π
125π
6Β°
F
T
B
Q R 6cm
MTCG1016 Basic Mathematics Page 10 of 15
3(b). Solve 2π₯ β 10 = 0 [π π΄πππ]
4(a). A firefighter places the ladder against the side of a 7m house. If the base of the ladder
is 6m away from the house, how long is the ladder? [π π΄ππππ]
4(b). 0 πΎ = _____Β°πΆ [π π΄πππ]
Base = 6 m
Wal
l= 7
m
MTCG1016 Basic Mathematics Page 11 of 15
5. A line passes through (2, 10) and is parallel to the line π¦ = 3π₯ + 2. Find the equation of the line. [π π΄ππππ]
6. Perform the indicated operations and reduce the answer to its lowest terms.
4
1
2
122
xx
[π π΄ππππ]
End of Examination
MTCG1016 Basic Mathematics Page 12 of 15
Formula Sheet- GFP-Basic Maths
1. Conversions
1 inch = 2.54 cm
1 metre = 39.37 inches
1 mile = 1.609 km
1 ton = 1000 kg
1 kg = 2.2 pounds
1 ounce = 0.0625 pounds
1 litre = 1000 ππ3
1 imperial gallon = 4.55 litres
K = Β°C + 273.15
Β°F = 1.8 Β°C + 32
2. Sector
Angle in radians( ) =
)(CircleofRadius
)(ArcofLength
r
S
π πππ = ππππ
3. Pythagoras theorem
(ππππ1)2 + (ππππ2)2=(π»π¦πππ‘πππ’π π)2
or 222 cba
4. Trigonometry
H
OC
AC
ABsinsin
H
AC
AC
BCcoscos
A
OC
BC
ABtantan
sin
1csc
cos
1sec
tan
1cot
MTCG1016 Basic Mathematics Page 13 of 15
5. Quadrant System
For π = ππ¬π’π§ ππ and π = ππππ ππ
β’ π΄πππππ‘π’ππ = |π|
β’ No of Cycles from 0Β° to 360Β° = |π|
β’ ππππππ =2Γ180Β°
π=
360Β°
π
6. Straight line
General equation of the straight
line is
Ax + By = C , where A, B and C are
constants (with A and B not both zero) &
x and y are variables.
Slope-intercept form of the straight
line can also be written as y = mx + c
where,
m =12
12
xx
yy
= slope or gradient of the
line
and c = y-intercept
Equation of straight line passing
through (x1, y1) and slope m is
π¦ β π¦1 = π(π₯ β π₯1)
7. Quadratic Equation
Solution of ax2 + bx + c = 0 is given by
a
acbbx
2
42
8. Circle
Equation of circle with center C(h, k ) and
radius r, where r > 0 is
222 )()( rkyhx
9. Distance formula
The distance between two points
),( 11 yxA and ),( 22 yxB is
2
12
2
12 yyxxd
II Quadrant
Sin Positive
900 + π,
1800 β π
I Quadrant
All Positive
900 β π
3600 + π
III Quadrant
Tan Positive
2700 β π
1800 + π
IV Quadrant
Cos Positive
2700 + π
3600 β π
MTCG1016 Basic Mathematics Page 14 of 15
Rough/Draft work
MTCG1016 Basic Mathematics Page 15 of 15
Rough/Draft work