MATH101/MATH 101 Module Exam 4 | College Algebra | Portage Learning | Q & A | 2026 Edition (PDF)

,MATH101/MATH 101 Module Exam 4 | College Algebra
| Portage Learning | Q & A | 2026 Edition (PDF)
1. Solve the system of equations: \(x + y = 10\) and \(x - y = 2\).

A) \(x = 6, y = 4\)

B) \(x = 4, y = 6\)

C) \(x = 5, y = 5\)

D) \(x = 7, y = 3\)



Correct Answer: \(x = 6, y = 4\)



Rationale: Add the equations to eliminate \(y\): \(2x = 12\), so \(x = 6\). Substitute \(x = 6\) into the first
equation: \(6 + y = 10\), so \(y = 4\).



2. Solve the system using substitution: \(2x + 3y = 12\) and \(x - y = 1\).

A) \(x = 2, y = 1\)

B) \(x = 3, y = 2\)

C) \(x = 4, y = 0\)

D) \(x = 5, y = 4\)



Correct Answer: \(x = 3, y = 2\)



Rationale: From the second equation, \(x = y + 1\). Substitute into the first: \(2(y + 1) + 3y = 12\).
Simplify: \(5y + 2 = 12\), so \(y = 2\). Then \(x = 2 + 1 = 3\).



3. Multiply the matrices: \(A = \begin{bmatrix}1 & 2\\3 & 4\end{bmatrix}\) and \(B = \begin{bmatrix}2 &
0\\1 & 3\end{bmatrix}\). Find \(AB\).

A) \(\begin{bmatrix}4 & 6\\10 & 12\end{bmatrix}\)

B) \(\begin{bmatrix}4 & 6\\7 & 12\end{bmatrix}\)

C) \(\begin{bmatrix}3 & 6\\9 & 12\end{bmatrix}\)

,D) \(\begin{bmatrix}4 & 3\\10 & 12\end{bmatrix}\)



Correct Answer: \(\begin{bmatrix}4 & 6\\10 & 12\end{bmatrix}\)



Rationale: Multiply rows of A by columns of B: Row 1: \((1\cdot2+2\cdot1, 1\cdot0+2\cdot3) = (4, 6)\).
Row 2: \((3\cdot2+4\cdot1, 3\cdot0+4\cdot3) = (10, 12)\).



4. Find the determinant of the matrix \(\begin{bmatrix}3 & 5\\2 & 7\end{bmatrix}\).

A) 11

B) 21

C) 26

D) 31



Correct Answer: 11



Rationale: The determinant of a 2x2 matrix \(\begin{bmatrix}a & b\\c & d\end{bmatrix}\) is \(ad - bc\).
Here, \(3 \cdot 7 - 5 \cdot 2 = 21 - 10 = 11\).



5. Solve the system using elimination: \(3x + 2y = 12\) and \(5x - 2y = 4\).

A) \(x = 2, y = 3\)

B) \(x = 3, y = 2\)

C) \(x = 1, y = 4.5\)

D) \(x = 4, y = 0\)



Correct Answer: \(x = 2, y = 3\)



Rationale: Add the equations to eliminate \(y\): \(8x = 16\), so \(x = 2\). Substitute into \(3(2) + 2y = 12\):
\(6 + 2y = 12\), so \(y = 3\).



6. What is the sum of the first 10 terms of the arithmetic sequence where \(a_1 = 2\) and \(d = 3\)?

, A) 155

B) 110

C) 145

D) 170



Correct Answer: 155



Rationale: Use the sum formula: \(S_n = \frac{n}{2}(2a_1 + (n-1)d)\). \(S_{10} = \frac{10}{2}(2(2) + 9(3)) =
5(4 + 27) = 155\).



7. What is the common ratio of the geometric sequence \(2, 6, 18, 54\)?

A) 2

B) 3

C) 4

D) 6



Correct Answer: 3



Rationale: Divide any term by the previous term: \(6/2 = 3\), \(18/6 = 3\), etc. The common ratio is 3.



8. What is the next term in the geometric sequence \(5, -10, 20, -40\)?

A) 60

B) -60

C) 80

D) -80



Correct Answer: 80



Rationale: The common ratio is -2. Multiply the last term by -2: \((-40) \times (-2) = 80\).