CSET Mathematics Exam | Comprehensive Practice Questions, Constructed Responses & Detailed Explanations 2026/2027

CSET Mathematics Exam | Comprehensive Practice Questions,
Constructed Responses & Detailed Explanations 2026/2027


Question 1
What are the solutions to the quadratic equation 2𝑥 2 − 8𝑥 + 6 = 0?
• A. 𝑥 = 1and 𝑥 = 3
• B. 𝑥 = −1and 𝑥 = −3
• C. 𝑥 = 2and 𝑥 = 4
• D. 𝑥 = 0and 𝑥 = 3
Correct Answer: A. 𝑥 = 1and 𝑥 = 3
Detailed Rationale: Factoring out the greatest common factor gives
2(𝑥 2 − 4𝑥 + 3) = 0, which factors further into 2(𝑥 − 1)(𝑥 − 3) = 0.
Setting each factor to zero yields 𝑥 = 1and 𝑥 = 3.
Question 2
What is the sum of the first 20terms of an arithmetic sequence where
the first term is 3and the common difference is 4?
• A. 820
• B. 800
• C. 840
• D. 780
Correct Answer: A. 820

,Detailed Rationale: The sum of an arithmetic series is given by 𝑆𝑛 =
𝑛
[2𝑎1 + (𝑛 − 1)𝑑 ]. Substituting 𝑛 = 20, 𝑎1 = 3, and 𝑑 = 4yields
2
20
𝑆20 = [2(3) + (19)(4)] = 10[6 + 76] = 10(82) = 820.
2

Question 3
What is the derivative of the function 𝑓 (𝑥 ) = 3𝑥 4 − 5𝑥 2 + 7𝑥 − 2with
respect to 𝑥?
• A. 𝑓′(𝑥 ) = 12𝑥 3 − 10𝑥 + 7
• B. 𝑓′(𝑥 ) = 12𝑥 3 − 5𝑥 + 7
• C. 𝑓′(𝑥 ) = 3𝑥 3 − 5𝑥 + 7
• D. 𝑓′(𝑥 ) = 12𝑥 4 − 10𝑥 2 + 7
Correct Answer: A. 𝑓′(𝑥 ) = 12𝑥 3 − 10𝑥 + 7
𝑑
Detailed Rationale: Using the power rule (𝑥 𝑛 ) = 𝑛𝑥 𝑛−1 , we
𝑑𝑥
differentiate term by term: 3(4𝑥 3 ) − 5(2𝑥 ) + 7(1) − 0 = 12𝑥 3 −
10𝑥 + 7.
Question 4
If 𝑓 (𝑥 ) = 2𝑥 − 5and 𝑔(𝑥 ) = 𝑥 2 + 3, what is the composite function
(𝑓 ∘ 𝑔)(2)?
• A. 11
• B. 7
• C. 13
• D. 9
Correct Answer: A. 11

,Detailed Rationale: First evaluate 𝑔(2): 𝑔(2) = 22 + 3 = 4 + 3 = 7.
Next, substitute this result into 𝑓: 𝑓(7) = 2(7) − 5 = 14 − 5 = 11.
Question 5
𝜋
What is the exact value of sin ( )?
3

√3
• A.
2
1
• B.
2

√2
• C.
2

• D. 1
√3
Correct Answer: A.
2
𝜋
Detailed Rationale: On the unit circle, the angle radians (60∘ )
3
1 √3
corresponds to the coordinate point ( , ), where the sine value
2 2
represents the y-coordinate.
Question 6
In a triangle with sides measuring 𝑎 = 5, 𝑏 = 7, and 𝑐 = 10, what is the
measure of the angle opposite side 𝑐using the Law of Cosines (𝑐 2 =
𝑎2 + 𝑏 2 − 2𝑎𝑏 cos 𝐶)?
1
• A. cos 𝐶 = −
35
13
• B. cos 𝐶 =
35
13
• C. cos 𝐶 = −
35

, 1
• D. cos 𝐶 =
35
13
Correct Answer: C. cos 𝐶 = −
35

Detailed Rationale: Substituting the values into the formula gives
102 = 52 + 72 − 2(5)(7) cos 𝐶, which simplifies to 100 = 25 + 49 −
70 cos 𝐶, meaning 100 = 74 − 70 cos 𝐶, so −70 cos 𝐶 = 26, leading to
26 13
cos 𝐶 = − =− .
70 35

Question 7
3𝑥 2 −5𝑥+1
What is the limit of the rational function lim ?
𝑥→∞ 2𝑥 2 +4𝑥−7
3
• A.
2

• B. 0
3
• C.
4

• D. Undefined
3
Correct Answer: A.
2

Detailed Rationale: For a rational function where the degree of the
numerator matches the degree of the denominator (both are 2), the
3
limit as 𝑥approaches infinity is the ratio of the leading coefficients: .
2

Question 8
4 5
What is the determinant of the 2 × 2matrix 𝐴 = ( )?
2 3
• A. 2
• B. 12