PCAT PCAT Certifications PCAT Questions & Answers

• Question 41:

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  Correct Answer: A

  Evaluate the integral using a u-substitution: u = sinx, du = cosx dx

  

  The integral becomes: Evaluate:

  

• Question 42:

  Two rats are chosen for an experiment out of a group of 17 black rats and 11 white rats. The two rats must be of a different color for each experiment. What is the probability that the second rat is white?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  Correct Answer: D

  In order to satisfy the condition of choosing a white rat second, the first rat chosen must be black. The probability of selecting a black rat is:

  

• Question 43:

  A lab requires 0.76 L of a solution. How many 100 mL vials must be used in the lab?

  A. 7

  B. 8

  C. 6

  D. 10

  Correct Answer: B

  Recall that 100 mL = 0.1 L. Because the smaller vials only come in amounts of 100 mL, 8 vials will be needed to provide 0.76 L.

• Question 44:

  p = -3x + 5y q = x + 2y

  What is the value of p - 2q?

  A. 5x + y

  B. -5x + y

  C. -y + 5x

  D. 5 + y

  Correct Answer: B

  Substitute the values of p and q into the expression:

  (-3x + 5y) - 2(x + 2y)

  Distribute and combine like terms to simplify:

  = -3x + 5y - 2x - 4y

  = -5x + y

• Question 45:

  What is the probability of rolling a prime number in each roll in 4 consecutive rolls of a 6 sided die?

  A. 1/4

  B. 1/8

  C. 1/16

  D. 1/32

  Correct Answer: C

  The prime numbers in the range are: 2, 3, 5. On any roll, the probability of rolling a prime number is:

  

  The probability of rolling this 4 times in a row is:

  

• Question 46:

  If (x) = 2x2 - x3, what is '(3)?

  A. 15

  B. -9

  C. -15

  D. 18

  Correct Answer: C

  Recall the power rule: If (x) = xn, '(x) = nxn - 1 Here, '(x) = 2 ?2x1 - 3x2 Evaluating the derivative at '(3) = (4 ?3) ?(3 ?32) = 12 - 27 = -15

• Question 47:

  

  A.

  B. 0

  C. 1/2

  D. ∞

  Correct Answer: A

  Begin by factoring out the largest power of x in the denominator from both the numerator and denominator:

  

  Cancel out the x and evaluate the limits:

  

  Recall that

  

• Question 48:

  If a vector is multiplied by 4, which statement is false?

  A. The second coordinate is 3 times the first.

  B. The second coordinate is 8x greater than the first.

  C. The second coordinate is 8x times the first.

  D. After the multiplication, the second coordinate undergoes a greater overall change.

  Correct Answer: C

  Apply the scalar multiplication to the vector and evaluate the answer choices:

  4 ?;x, 3>; =<;4x, 12>;

  4x ?3 = 12x, so answer choice [The second coordinate is 3 times the first.] is true. 4x + 8x = 12x, so answer choice [The second coordinate is 8x greater than the first.] is true. 4x ?8x = 32x2 12x, so answer choice [The second coordinate is 8x times the first.] is false.

• Question 49:

  What is the third derivative of -3sin(x)?

  A. -3cosx

  B. 3cosx

  C. -3sinx

  D. 3sinx

  Correct Answer: B

  Recall that the derivative of sin(x) = cos(x) and the derivative of cos(x) = -sin(x). First derivative: -3 ?cos(x). Second derivative: -3 ?(-sin(x)) = 3sin(x). Third derivative: 3 ?cos(x).

• Question 50:

  John is running towards a finish line at 10 m/s and is 50 m away. Bolt is running at 14 m/s but is 75 m away. Assuming they keep their constant speed, who will reach the finish line first?

  A. John

  B. Bolt

  C. It is a tie

  D. Neither will finish

  Correct Answer: A

  Calculate how long it will take each runner to finish, the shorter time length indicates the first to finish. Recall that:

  distance = rate ?time:

  

  John (5 seconds) finishes before Bolt (5.4 seconds).