Math 105, Midterm exam (1)
majmaa’h Engineering College
King Saud University
Differential Calculus (Math 105)
25/1/1431
Name:
Level 2
Academic Number:
Time allowed: 90 minutes
Midterm Exam (1)
1. Find the set of solutions (represented as intervals) for each of the
following inequalities. Then explain your answer graphically.
a) |3𝑥 − 2| ≥ |2𝑥 + 1|
b) −𝟓 ≤ 𝟒−𝟑𝒙
<1
𝟐
(1 mark)
(1 mark)
2. Which of the following represents a function and why?
X
a
b
c
X
Y
1
a
X
Y
1
2
3
(2 marks)
2
b
Y
a
b
c
1
2
3
3. Find the equation of the straight line that passes with the point (3,-3) and
a. Parallel to the line y = 2x + 5
b. Perpendicular to the line x= 8
c. Parallel to the line that passes with the two points (-1,2) , (3, -1)
(4 marks)
1
Math 105, Midterm exam (1)
4. Which of the following three vertices is forming a right angle triangle?
(3 marks)
a. A (2,9) , B (-1, 3) , C (6,7)
b. A (-1, 4) , B (3, 6) , C (1,1)
5. Find Domain and Range of each of the following functions and draw the
last function (c).
(3 marks)
a. 𝑔(𝑥 ) = 𝑥 3 − 2𝑥
b. 𝑓(𝑥 ) = 𝑥
3
1
−√𝑥
c. 𝑦 = 𝑐𝑜𝑠 𝑥
6. Find the value of 𝜹 (as 𝜺) so that the following mathematical sentence is
|𝑥 − 2| < 𝛿 → |4𝑥 − 8| < 𝜀
right:
(2 marks)
7. Examine the function 𝒉(𝒙) =
𝐱
𝒙𝟑 −𝒙
if it is even or odd?
and
𝐠(𝐱) = √𝐱 𝟑 − 𝟐 Find:
i. (f+g)(3)
ii. (g/f)(2)
8. If 𝐟(𝐱) =
(𝐱+𝟏)
Best wishes…
Dr. SaMeH Ahmed
2
𝒙𝟐 +𝟒
(2 marks)
(2 marks)