Precal Spring 2026 Final Exam document
Precal Spring 2026 Final Exam
Name:
Date:
Period:
Instructions
Choose the best answer for each question. You may use a scientific or graphing calculator. Ensure your calculator is in the correct mode (Degree or Radian) where applicable. Show your work on a separate sheet of paper.
Part 1: Logarithms
1. Evaluate \(\log_{4} 64\).
A) 2
B) 3
C) 4
D) 16
2. Which of the following is equivalent to \(\log_{5} \left(\frac{1}{25}\right)\)?
A) 2
B) 5
C) -2
D) -5
3. Expand the expression \(\log(x^3 y^2)\) completely using properties of logarithms.
A) \(3\log x + 2\log y\)
B) \(6\log(xy)\)
C) \(\log(3x) + \log(2y)\)
D) \(x^3 + y^2\)
4. Condense the expression \(2\ln a - 3\ln b + \ln c\).
A) \(\ln(a^2 - b^3 + c)\)
B) \(\ln\left(\frac{a^2c}{b^3}\right)\)
C) \(\ln\left(\frac{2ac}{3b}\right)\)
D) \(\ln(a^2 b^3 c)\)
5. Solve for \(x\): \(3^{x-1} = 27\).
A) \(x = 2\)
B) \(x = 3\)
C) \(x = 4\)
D) \(x = 5\)
6. Use the Change of Base Formula to approximate \(\log_{7} 15\) to three decimal places.
A) 1.392
B) 0.718
C) 2.143
D) 1.176
7. Solve for \(x\): \(\log_{2}(x + 4) = 5\).
A) \(x = 6\)
B) \(x = 21\)
C) \(x = 28\)
D) \(x = 32\)
8. What is the value of \(\ln(e^5)\)?
A) 1
B) \(e\)
C) 5
D) 0
Part 2: Solving Triangles
9. In a right triangle, if the opposite side is 8 and the hypotenuse is 10, what is the value of \(\sin \theta\)?
A) 0.6
B) 0.8
C) 1.25
D) 0.75
10. A ladder leans against a wall making a \(70^\circ\) angle with the ground. If the ladder is 12 feet long, how far up the wall does it reach?
A) 4.1 ft
B) 11.3 ft
C) 33.0 ft
D) 12.8 ft
11. In triangle \(ABC\), angle \(A = 40^\circ\), angle \(B = 60^\circ\), and side \(c = 10\). Find side \(a\) using the Law of Sines.
A) 6.53
B) 8.79
C) 7.42
D) 9.12
12. In triangle \(XYZ\), side \(x = 5\), side \(y = 7\), and angle \(Z = 45^\circ\). Find the length of side \(z\).
A) 4.95
B) 5.12
C) 8.60
D) 24.50
Part 3: Sequences & Series
13. What is the 10th term of the arithmetic sequence \(5, 12, 19, 26, \dots\)?
A) 63
B) 68
C) 75
D) 70
14. Find the sum of the first 20 terms of the arithmetic series \(2 + 5 + 8 + \dots\)
A) 590
B) 610
C) 1220
D) 620
15. Evaluate the sum: \(\sum_{k=1}^{5} (2k + 1)\).
A) 35
B) 15
C) 25
D) 30
16. Which recursive formula describes the sequence \(4, 12, 36, 108, \dots\)?
A) \(a_n = a_{n-1} + 8\)
B) \(a_n = 3 \cdot a_{n-1}\)
C) \(a_n = (a_{n-1})^2\)
D) \(a_n = a_{n-1} + 3\)
17. Evaluate \(\sum_{n=0}^{4} 2^n\).
A) 15
B) 30
C) 31
D) 63
18. A sequence is defined by \(a_n = n^2 - n\). What is the 5th term?
A) 20
B) 25
C) 30
D) 15
End of Precal Spring 2026 Final Exam • Precalculus
