PCAT |VERIFIED QUESTIONS AND CORRECT DETAILED ANSWERS|RATED AND GRADED A+ NEW UPDATE| 2026/2027

PCAT :QUANTITATIVE REASONING|VERIFIED QUESTIONS AND
CORRECT DETAILED ANSWERS|RATED AND GRADED A+ NEW
UPDATE| 2026/2027

What is the range of the function below?

f(x) = 3x2- 5



A. (-∞, ∞)

B. (0, ∞)

C. (-5, ∞)

D. (5, ∞) - ANSWER✔ Answer: C

Explanation: The range of a function is the list of possible outputs of the function. It is impossible for this
function to generate any number less than -5, and there is no upper limit to the output of this function.
The range is (-5, ∞).



Which is equivalent to 3i2 + 2i4?



A. -1

B. 1

C. 5

D. 3 + 2i - ANSWER✔ Answer: A

Explanation: This question asks you to manipulate complex numbers. The key to solving this problem is
that i2 = -1. Substitute this into the expression:

3i2+2i4=3i2+2(i2)(i2)=3(−1)+2(−1)(−1)=−3+2=−1



If f(x)=x+25 , then what is f-1(x)?



A. x−2/5

B. 5x- 2

, C. 5/x+2

D. 2−x/5 - ANSWER✔ Answer: B

Explanation: If the function is y=f(x)=x+2/5. To find the inverse function, switch x and y and then solve
for y:



x = y+2/5

5x = y+2

y = 5x-2



What is the sum of the two vectors (3 + 2i) and (-2 + i)?



A. 2 + 2i

B. -8

C. -6 + 2i

D. 1 + 3i - ANSWER✔ Answer: D

Explanation: To add vectors, group the real parts together and the imaginary parts together, and then
add:

(3 + 2i) + (-2 + i) = (3 + -2) + (2i + i) = 1 + 3i



Which of the following is equivalent to (-2 + i)(3 + 2i)?



A. -8 -i

B. 1 + 3i

C. -6 + 2i

D. 5 + 3i - ANSWER✔ Answer: A

Explanation: To multiply two complex numbers, first distribute the parenthesis:

(-2 + i)(3 + 2i) = -6 + 3i- 4i + 2i2 = -6 - i + 2i2.

Then use the fact that i2 = -1:

-6 - i + 2 i2 =-6 - i + 2(-1) = -8 - i.