AC-66_2-1A-AMEL-Examination-Subject-1AAeronautical-Science Assessment Task – 1
/85
STUDENT ID NUMBER
STUDENT NAME
CLASS
YEAR
SEMESTER
INSTRUCTION: Assessment Tasks weigh 30% of the overall assessment for this semester. The
assessment tasks will help prepare you for your casa exam. You are to write your answers neat and tidy
on a separate paper or type and submit the hard copy for marking.
Make sure to reference the source you got your answers from to get the full marks. Include any
diagrams/pictures, formula and working out to get the full mark.
This Assessment Task is out of 85 marks and is due on Thursday 16 March 2023, 4:06pm before tutorial
class begins.
1.1
Arithmetic
1.1.1
Identify and write arithmetical terms and signs. (23 marks)
1.
Addition (
…)
I.
Addition - ………………………………………………………………………………………………….
II.
Sum - …………………………………………………………………………………………………………
2. Subtraction (….)
I.
Subtrahend - ……………………………………………………………………………………………..
II.
Minuend - …………………………………………………………………………………………………
III.
Difference - ……………………………………………………………………………………………….
3. Multiplication (….)
I.
Multiplicand -……………………………………………………………………………………………
II.
Multiplier -………………………………………………………………………………………………..
III.
Product -…………………………………………………………………………………………………..
4. Division (÷)
I.
dividend -………………………………………………………………………………………………….
II.
Divisor - ……………………………………………………………………………………………………
III.
Quotient - ……………………………………………………………………………………………….
IV.
Remainder -…………………………………………………………………………………………….
5. Fractions………………………………………………………………………………………………………………………
Denominator………………………………………………………………………………………………………
Numerator………………………………………………………………………………………………………….
Mixed Fraction……………………………………………………………………………………………………
Improper Fraction………………………………………………………………………………………………
5. The laws of signs numbers
a)
First law - ……………………………………………………………………………………………….
b)
Second law - …………………………………………………………………………………………..
c)
Third law - ……………………………………………………………………………………………..
d)
Fourth law –…………………………………………………………………………………………..
6. The commutative, associative and distributive laws of numbers are valid for both positive and
negative numbers.
1.1.2
a)
Commutative law - …………………………………………………………………………………
b)
Associative law - …………………………………………………………………………………….
c)
Distributive law - ……………………………………………………………………………………
Round decimal numbers (3 marks)
Round-off the following numbers correct to three significant figures:
(a)
1.1.3
2.713 =
(b) 0.0001267 =
(c) 5.435×104 =
Convert between fractions and decimals (1 marks)
The width of a hex head bolt is 0.3123 inches. Convert the decimal 0.3123 to a common fraction
to decide which socket would be the best fit for the bolt head.
1.1.4
Perform calculations involving:
A. Addition, subtraction, multiplication and division of whole numbers, fractions and decimals.
(13 marks)
Whole numbers
3+4=
5+(−3) =
12×8=
12÷3=
Fractions
a) 1/8 + 1/3 + 2/5 =
b) 3/8 – 1/5 =
c) × =
d)
÷
=
e) What is the length of the grip of a bolt?
The overall length of the bolt is 3 and 1⁄2 inches, the shank length is 3 and 1⁄8 inches, and the
threaded portion is 1 and 5⁄16 inches long. To find the grip, subtract the length of the threaded
portion from the length of the shank.
3 1⁄8 inches – 1 5⁄16 inches = grip length
Decimals
a) 2.34 + 37.5 + .09 =
b) 37.272 – 14.88 =
c) 0.2 × 6.03 =
d) 0.144 ÷ 0.12 =
B. Percentages, ratios, proportions, powers, averages, squares, cubes, and square/cube roots.
(10 marks)
Percentages
 Finding a Percentage of a Given Number
a) In a shipment of 80 wingtip lights, 15% of the lights were defective. How many of
the lights were defective?(show working out)
 Finding What Percentage One Number Is of Another(show working out)
b) A small engine rated at 12 horsepower is found to be delivering only 10.75
horsepower. What is the motor efficiency expressed as a percent?
 Finding a Number When a Percentage of It Is Known(show working out)
c) Eighty ohms represents 52% of a microphone’s total resistance. Find the total
resistance of this microphone.
Average
The barometric pressure, measured in mm of mercury (mmHg), was taken every day for a week.
The readings obtained are shown below. What is the average pressure for the week in mmHg?
(show working out)
Day
1
2
3
4
5
6
7
mmHg 75.2 76.1 76.3 75.7 77.1 75.3 76.3
Ratio
A pinion gear with 10 teeth is driving a spur gear with 40 teeth. The spur gear is rotating at 160
rpm. Determine the speed of the pinion gear. (show working out)
Proportions
An airplane flying a distance of 300 miles used 24 gallons of gasoline. How many gallons will it
need to travel 750 miles? (show working out)
Powers, squares, cubes, square/cube roots (show working out)
3
0
2 =
√
7 =
=
√
=
C. Factors and multiples(2 marks)
a) Factors of 12=
b) Multiples of 12=
1.4.5 Calculate
Volumes of common engineering object(4 marks)
a) A rectangular baggage compartment measures 5 feet 6 inches in length, 3 feet 4 inches in width,
and 2 feet 3 inches in height. How many cubic feet of baggage will it hold? (show working out)
b) A large, cube-shaped carton contains a shipment of smaller boxes inside of it. Each of the
smaller boxes is 1 ft × 1 ft × 1 ft. The measurement of the large carton is 3 ft × 3 ft × 3 ft. How
many of the smaller boxes are in the large carton? (show working out)
c) Find the piston displacement of one cylinder in a multi-cylinder aircraft engine. The engine has a
cylinder bore of 5.5 inches and a stroke of 5.4 inches. (show working out)
d) A pressure tank inside the fuselage of a cargo aircraft is in the shape of a sphere with a diameter
of 34 inches. What is the volume of the pressure tank? (show working out)
Areas of Plain figures(6 marks)
a) An aircraft floor panel is in the form of a rectangle having a length of 24 inches and a width of 12
inches. What is the area of the panel expressed in square inches? (show working out)
b) What is the area of a square access plate whose side measures 25 inches? (show working out)
c) Find the area of a triangle with height of 2feet and 6 inches and a base of 3 feet and 2 inches?
(show working out)
d) What is the area of a trapezoid whose bases are 14 inches and 10 inches, and whose height (or
altitude) is 6 inches? (show working out)
e) The bore, or “inside diameter,” of a certain aircraft engine cylinder is 5 inches. Find the area of
the cross section of the cylinder. (show working out)
f)
Find the area of a tapered wing whose span is 50 feet and whose mean chord is 6'8".(show
working out)
Surface area of regular solids(1 marks)
a) What is the surface area of a cube with a side measure of 8 inches? (show working out)
1.1.6 Perform calculations involving (2 marks)
i) Binary system of numbers (Show working out)
The denary number 37 =………. binary number?
ii)Hexadecimal system of numbers(Show working out)
a) The hexadecimal number 6E16 =………denary
b) The denary number 5138 =………. hexadecimal
1.2 Algebra(8 marks)
1.2.1 Perform algebraic calculation involving (Show working out)
a) The addition, subtraction, multiplication and division of like and unlike terms
(i) 3ab+2ac−3c+5ab−2ac−4ab+2c−b =
b) Factors and brackets
1) xy + xz
2) (3x+2y)(2x−3y+6z)
=
=
c) Indices including negative fraction
=
d) Transposition of formula
Velocity = Distance x Time, make time the subject.
1.1.2 Solve
a) Linear equation (Show working out)
3x−4=6−2x
Then: Find x
b) Simultaneous equation with one unknown (Show working out)
3x + 2y = 12 (1)
x − 3y = −1 (2)
c) Quadratic equation with one variable(Show working out)
5x(x+1) −2x (2x−1) =20.
1.3 Graphs(4 marks)
1.3.1 Describe the nature and uses of graphs (in your own words)
………………………………………………………………………………………………………….
1.3.2 Construct graphs containing (Draw graph)
a) Linear function y=2x−4
Now every linear equation may be written in standard form, i.e.: y = mx + c
b) Exponential function Draw the graph of y=x
2
−3x+2, taking values of the independent variable x, between 0 and 4.
c) Sine and cosine equation – (Draw graph)
1.3.3 Extract performance data from graphs found in trade-related manuals – Class activity
1.4 Geometry and Trigonometry (7 marks)
Describe simple geometry constructions (in your own words)
1.4.2 Calculate
Circumference, radius and diameter of a circle
a) If a circle has a diameter of 10 inches, calculate the circumference and area
Circumference =
Area =
b) The length of any sides of a triangle using Pythagoras theorem.
What is the length of the longest side of a right triangle, given the other sides are 7
inches and 9 inches? The longest side of a right triangle is always side c, the
hypotenuse. Use the Pythagorean Theorem to solve for the length of side c.
c) Any angle of a right angle triangle using sine, cosine, tangent and cotangent
Find the angle of the above right angle triangle using tangent?
d) Any angle and the length of sides of various types of triangle
For the above triangle, find the length of the hypotenuse using Pythagorean formula
and sine function?
1.4.3 Differentiate between polar and rectangular coordinates (Using the formula given)
A useful skill is to be able to convert rectangular to polar co-ordinates and vice versa. This is
particularly helpful, when dealing with sinusoidal functions and other oscillatory functions.
Then to convert rectangular to polar co-ordinates, we use Pythagoras theorem and the tangent
ratio to give:
To convert polar to rectangular co-ordinates, we use the sine and cosine ratios to give:
(a) Convert the rectangular co-ordinates (−5, −12) into polar co-ordinates.
(b) Convert the polar co-ordinates (150∠300) into rectangular co-ordinates.
1.5 Vectors (9 marks)
1.5.1 Differentiate between scalar and vector quantities with examples
Vector quantity …………………………………….. Scalar quantity ………………………………..
Velocity ……………………………………………………………………………………………………
Speed …………………………………………………………………………………………………….
1.5.2 Perform vector calculation including
a) Addition and displacement of vector
. ̅̅̅̅ + ̅̅̅̅ =
b) Triangle of vector
Draw the triangle vector for the above vector sum in question (a)
c) forces in equilibrium
If p = a force of 40 N, acting in the direction due east,
q = a force of 30 N, acting in the direction due north,
What will be the vector sum r of these two forces?
d) Polygon of vector
A plane travels East from Nadzab to Hoskins, then travels north-east to Tokua airport to refuel
and headed North West to Kavieng aiport. From there it travels west to Madang Airport, refuels
again and travels south to Lae. (Draw the polygon of vector).
e) Resultant of vector
What is the sum of the vectors a,b,c,d,e in the above polygon?
End of Unit 1 Mathematics