MAT1581/101/0/2025
Tutorial letter 101/0/2025
MATHEMATICS I (ENGINEERING)
MAT1581
Year module
Department of Mathematical Sciences
IMPORTANT INFORMATION:
Please activate your my Unisa and myLife e-mail account and
make sure that you have regular access to the myUnisa module
website MAT1581-25-Y, as well as your group website.
Note: This is a fully online module. It is therefore, only available on my Unisa.
university
Define tomorrow. of south africa
, MAT1581/101/0/2025
ASSIGNMENT 02
Due date: Friday, 27 June 2025
Total Marks: 30
YEAR MODULE
This assignment covers Modules 4 & 5 of the study guide 1, it is specifically based on
Complex numbers and analytic geometry
Question 1: 6 Marks
π
(1.1) Write the polar co-ordinates 3; in cartesian form. (3)
2
(1.2) Determine the modulus and argument of j(1 − j2). (3)
Question 2: 14 Marks
π 3π Z1
(2.1) If Z1 = e1−j 2 and Z2 = 4ej 4 . Find and give the answer in polar form. (3)
Z2
(2.2) Solve for x and y if −x + j2y = (3 + j2)(−1 − j2). (5)
(2.3) Determine the two square roots of the complex number (−3 − j5) in polar form. (6)
Question 3: 10 Marks
(3.1) Write down the radius and co-ordinates of the center of the circle (3)
(y − 3)2 + (y + 4)2 = 16.
(3.2) Write down the equation of the ellipse with center (0; 0), one focal point at (0; 3) (4)
and one vertex at (0; 4).
(3.3) Name and sketch the curve y 2 = 36 − x 2 . (3)
Unisa ©2025
29
, MAT1581/101/0/2025
Tutorial letter 101/0/2025
MATHEMATICS I (ENGINEERING)
MAT1581
Year module
Department of Mathematical Sciences
IMPORTANT INFORMATION:
Please activate your my Unisa and myLife e-mail account and
make sure that you have regular access to the myUnisa module
website MAT1581-25-Y, as well as your group website.
Note: This is a fully online module. It is therefore, only available on my Unisa.
university
Define tomorrow. of south africa
, ASSIGNMENT 03
Due date: Tuesday, 5 August 2025
Total Marks: 41
YEAR MODULE
This assignment covers Module 6 of the study guide. Its topic is Differentiation.
Note that this assignment will close on 05 August 2025 at 23:59
Question 1: 6 Marks
Determine the following limits:
x3 − 2
(1.1) lim (3)
x→−1 x 4 + 4x − 3
x3 − 8
(1.2) lim (3)
x→3 x 2 − 4
Question 2: 22 Marks
Differentiate the following to the appropriate independent variable and simplify where possible:
1 √
(2.1) y= − cos x (4)
x
(2.2) y = (x 3 + 2)(x 2 − 2x + 1) (6)
√
1 + tan2 x
(2.3) y= (6)
sec2 x
43
x x −2
(2.4) y = ln e (6)
x +3
Question 3: 4 Marks
The loading distribution y on a beam is given by y = −25x 2 + 45x.
Question 4: 9 Marks
Given the curve y = 2x 3 + 3x 2 − 12x. Find the turning points and the intercepts with the axes. Sketch the
curve.
30
Tutorial letter 101/0/2025
MATHEMATICS I (ENGINEERING)
MAT1581
Year module
Department of Mathematical Sciences
IMPORTANT INFORMATION:
Please activate your my Unisa and myLife e-mail account and
make sure that you have regular access to the myUnisa module
website MAT1581-25-Y, as well as your group website.
Note: This is a fully online module. It is therefore, only available on my Unisa.
university
Define tomorrow. of south africa
, MAT1581/101/0/2025
ASSIGNMENT 02
Due date: Friday, 27 June 2025
Total Marks: 30
YEAR MODULE
This assignment covers Modules 4 & 5 of the study guide 1, it is specifically based on
Complex numbers and analytic geometry
Question 1: 6 Marks
π
(1.1) Write the polar co-ordinates 3; in cartesian form. (3)
2
(1.2) Determine the modulus and argument of j(1 − j2). (3)
Question 2: 14 Marks
π 3π Z1
(2.1) If Z1 = e1−j 2 and Z2 = 4ej 4 . Find and give the answer in polar form. (3)
Z2
(2.2) Solve for x and y if −x + j2y = (3 + j2)(−1 − j2). (5)
(2.3) Determine the two square roots of the complex number (−3 − j5) in polar form. (6)
Question 3: 10 Marks
(3.1) Write down the radius and co-ordinates of the center of the circle (3)
(y − 3)2 + (y + 4)2 = 16.
(3.2) Write down the equation of the ellipse with center (0; 0), one focal point at (0; 3) (4)
and one vertex at (0; 4).
(3.3) Name and sketch the curve y 2 = 36 − x 2 . (3)
Unisa ©2025
29
, MAT1581/101/0/2025
Tutorial letter 101/0/2025
MATHEMATICS I (ENGINEERING)
MAT1581
Year module
Department of Mathematical Sciences
IMPORTANT INFORMATION:
Please activate your my Unisa and myLife e-mail account and
make sure that you have regular access to the myUnisa module
website MAT1581-25-Y, as well as your group website.
Note: This is a fully online module. It is therefore, only available on my Unisa.
university
Define tomorrow. of south africa
, ASSIGNMENT 03
Due date: Tuesday, 5 August 2025
Total Marks: 41
YEAR MODULE
This assignment covers Module 6 of the study guide. Its topic is Differentiation.
Note that this assignment will close on 05 August 2025 at 23:59
Question 1: 6 Marks
Determine the following limits:
x3 − 2
(1.1) lim (3)
x→−1 x 4 + 4x − 3
x3 − 8
(1.2) lim (3)
x→3 x 2 − 4
Question 2: 22 Marks
Differentiate the following to the appropriate independent variable and simplify where possible:
1 √
(2.1) y= − cos x (4)
x
(2.2) y = (x 3 + 2)(x 2 − 2x + 1) (6)
√
1 + tan2 x
(2.3) y= (6)
sec2 x
43
x x −2
(2.4) y = ln e (6)
x +3
Question 3: 4 Marks
The loading distribution y on a beam is given by y = −25x 2 + 45x.
Question 4: 9 Marks
Given the curve y = 2x 3 + 3x 2 − 12x. Find the turning points and the intercepts with the axes. Sketch the
curve.
30
