PANPACIFIC UNIVERSITY
ENGINEERING-L
TECHirven
Midterm Examination in BEM 111 - BASIC ENG' m-
Full Term | 1H Trimester | AY-2024-2025
I. Analyze and solve the following problems. Show your solution in a separate sheet of paper and shade your answer on your scantron sheet.
1-2. The sum of the first 10 terms of a geometric progression \( 2,4,8, \ldots \) is
A. 1023
B. 2046
C. 225
D. 1596
2-4. Determine the sum of the progression if there are 7 arithmetic means between 3 and 35
A. 171
B. 182
C. 232
D. 216
5-6. What is the sum of the progression \( 4,9,14,19, \ldots \) up to the 20 th term?
A. 1030
B. 1035
C. 1040
D. 1045
\( 7-8 \). Find the 9 term of the harmonic progression \( 3,2,3 / 2, \ldots \)
A. \( 3 / 5 \)
B. \( 3 / 8 \)
C. \( 4 / 5 \)
D. \( 4 / 9 \)
9-10. If the first term of a Geometric Progression is 9 and the common ratio is \( -2 / 3 \), find the fifth term.
A. \( 8 / 5 \)
B. \( 16 / 9 \)
C. \( 15 / 7 \)
D. \( 13 / 4 \)
SITUATION I: Given the following matrices
11-15. Determine \( 2 A+2 B \)
\[
\begin{aligned}
A & =\left[\begin{array}{cccc}
-7 & 12 & -3 & 5 \\
4 & -8 & 1 & -6 \\
9 & -2 & 0 & 14 \\
-1 & 11 & -10 & 3
\end{array}\right] \\
B & =\left[\begin{array}{cccc}
6 & -3 & 8 & -12 \\
-2 & 4 & -9 & 1 \\
5 & -7 & 13 & -10 \\
-14 & 2 & 0 & 11
\end{array}\right]
\end{aligned}
\]
16-20. Determine \( A-3 B \)
21-25. Determine \( A B \)
26-30. Determine the determinant of the square matrix formed by the first 3 columns and first three rows of matrix A
SITUATION 2: A man finds the angle of elevation of the top of a tower to be 30 degrees. He walks \( 85 m \) nearer the tower and finds its angle of elevation to be 60 degrees.
31-35. What is the height of the tower?
A. 76.31 m
B. 73.31 m
C. 73.16 m
D. 73.61 m
SITUATION 3: Points A and B are 100 m apart and are of the same elevation as the foot of a building. The angles of elevation of the top of the building from points \( A \) and \( B \) are \( 21^{\circ} \) and \( 32^{\circ} \) respectively.
36-40. How far is \( A \) from the building in meters?
A. 259.28
B. 265.42
C. 271.64
D. 277,29
Panpaciflel-A0-Form-02-RevistonStanus/Date:01/031une2024