PCAT PCAT Certifications PCAT-SECTION3 Questions & Answers

• Question 61:

  Find the roots of the quadratic equation x2 2x 1 = 0.

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  Correct Answer: A

  The equation is in the form of a quadratic equationax2 +bx+c= 0, where a = 1, b=2, and c=1. To solve this

  

  problem, you use the quadratic formula or

• Question 62:

  Given the equation,

  

  What is the value of x?

  A. 64

  B. 110

  C. 164

  D. 215

  Correct Answer: B

  

  , the goal is to isolate the unknown variablexon one side of the equation with all other terms on the

  

  other side. You begin by multiplying both sides of the equation by 4x+ 8:

  You then divide both sides by 1/8 which, in essence, means you multiply both sides of theequation

  

  by 8/1 its reciprocal:

  You then subtract 8 from both sides with the final step of dividing both sides by 4, giving you the desired

  result.

  

• Question 63:

  What is the solution of the inequality 3x9>12x?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  Correct Answer: C

  To solve the inequality 3x 9 > 1 2x, you need to collect like terms ofxon one side of the inequality and all other values to the other side. You first add 9 to both sides of the inequality:

  

  You then add 2xto both sides of the inequality:

  

  Dividing both sides by 5 yieldsx> 2.

• Question 64:

  (

  5.4 × 107) ÷ (2.7 × 103) =

  A.

  Option A

  B.

  Option B

  C.

  Option C

  D.

  Option D

  

  Correct Answer: B

  To divide the two numbers in scientific notation, you have:

  

• Question 65:

  Express 239 in scientific notation.

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  Correct Answer: C

  The number 239 is expressed in scientific notation by first expressing the value in terms of a real number such that 1 a < 10. In this case, the number becomes 2.39. In order to retain the original number, the number must be multiplied by 100 which, in terms of exponents, is 102. Thus, in scientific notation, 239 =

  2.39 × 100 = 2.39 × 102.

• Question 66:

  What is the average of the numbers 24, 53, 70, 89, 34, and 30?

  A. 84

  B. 39

  C. 71

  D. 50

  Correct Answer: D

  The average of a set of numbers is calculated by:

  

• Question 67:

  1/3 ÷ 5/9 =

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  Correct Answer: A

  The quotient of the two fractions can be found by writing the fractions as: