Free FAST Diagnostic Assessments Basic Questions and Answers — Questions and Answers
Question 1: The temperature in Bismarck, North Dakota on the coldest day in December was -3 degrees Fahrenheit. If the coldest day in Bismak in January was colder than this, which of the following could be its possible temperature in degrees Fahrenheit?
- 5
- 0
- -5 (Correct answer)
- -2
Correct answer: -5
If January was colder than December's low of -3°F, the January temperature must be less than -3 on the number line. -5 is the only option below -3; the values 5, 0, and -2 are all warmer than -3°F, so they cannot represent a colder temperature.
Question 2: Dustin is reorganizing hid room and creates a Cartesian coordinate plane to help him place all of his furniture with enough space in Quadrant I. He places his (2, 3) and his desk at (6, 3). If each unit is equal to a foot, how much space in feet does Dustin have between his bed and his desk?
- 12
- 3
- 4 (Correct answer)
- 6
Correct answer: 4
Both the bed (2, 3) and the desk (6, 3) share the same y-coordinate, so the distance between them is simply the difference in their x-values: 6 − 2 = 4 feet. The other options confuse multiplication of coordinates or use the y-value instead of the x-difference.
Question 3: Oliver is grabbing a pencil from his backpack. He has 6 pencils in his backpack, 4 of which are mechanical and 2 of which are standard non-mechanical pencils. What is the probability that he will get a non-mechanical pencil if he selects randomly?
- 1/3 (Correct answer)
- 1/6
- 1/4
- 2/3
Correct answer: 1/3
There are 2 non-mechanical pencils out of 6 total, giving a probability of 2/6, which simplifies to 1/3. 1/6 would be the probability of picking one specific pencil, 1/4 doesn't reflect the actual ratio, and 2/3 is the probability of picking a mechanical pencil — the complement.
Question 4: Savannah has taken five spelling quizzes and wants to determine her overall grade on the spelling quizzes. She earned a 74 on quiz 1, 83 on quizzes 2 and 4, 96 on quiz 3 and 84 on quiz 5.<br> What is her mean grade on spelling quizzes in the class?
- 84 (Correct answer)
- 83
- 105
- 96
Correct answer: 84
Adding all five quiz scores: 74 + 83 + 83 + 96 + 84 = 420. Dividing by the number of quizzes (5) gives 420 ÷ 5 = 84. Note that quizzes 2 and 4 both scored 83, so that value must be counted twice in the sum.
Question 5: Kevin is creating a small birdhouse with a cube base using the following net with dimensions in inches. If each square of wood is equal and each triangle for the top is equal, how many square inches of wood does Kevin need?
- 130
- 185
- 155 (Correct answer)
- 160
Correct answer: 155
The surface area of the birdhouse net is calculated by summing the area of each panel: the five square faces of the cube base plus the two triangular roof panels. Using the given dimensions, the total comes to 155 square inches. The other values result from miscounting panels or using incorrect dimensions.
Question 6: Winston as 45 magnets of various colors that are all squares with 2 inch sides. Cutting some of the magnets into triangles to fit inside, he uses all of the squares with no gaps between them to fill a triangle on a magnetic board. What is the surface area of the triangle in square feet?
- 90
- 15 (Correct answer)
- 45
- 180
Correct answer: 15
Each square magnet has 2-inch sides, giving an area of 4 square inches per magnet. With 45 magnets, the total area is 45 × 4 = 180 square inches. Converting to square feet by dividing by 12 yields 15 square feet, which is the area of the triangle filled on the board.
Question 7: In a given circle, the diameter is 8 inches across the middle of the circle. How can we determine the radius of the circle?
- Multiply the diameter by 2
- Divide the diameter by ?
- Divide the diameter by 2 (Correct answer)
- Multiply the diameter by ?
Correct answer: Divide the diameter by 2
By definition, the radius of a circle is exactly half its diameter. Dividing 8 inches by 2 gives a radius of 4 inches. Multiplying by 2 would give the diameter again (16 inches), and dividing or multiplying by π (≈3.14) is used to calculate circumference or area, not the radius.
Question 8: What is the value of the following expression to the nearest whole number? 1,580 ÷ 25
- 63 (Correct answer)
- 36
- 73
- 25
Correct answer: 63
Performing the long division, 1,580 ÷ 25 = 63.2, which rounds to 63. 25 × 63 = 1,575 and 25 × 64 = 1,600, confirming the answer is between 63 and 64 and rounds down to 63. The other options are not close to the correct quotient.
Question 9: May is donating towels to the animal shelter for dogs and cats in need. She finds towels in bulk for $45 for 25 towels. How much is she paying per towel?
- $1.80 (Correct answer)
- $0.44
- $5.00
- $20.00
Correct answer: $1.80
Dividing $45 by 25 towels gives $45 ÷ 25 = $1.80 per towel. $0.44 would be far too low, $5.00 would be 25 × $5 = $125 total (not $45), and $20.00 would make 25 towels cost $500 — all inconsistent with the bulk price given.
Question 10: What is the value of the following expression? 123.64 = 71.58
- 195.22 (Correct answer)
- 152.14
- 52.06
- 194.12
Correct answer: 195.22
Adding the two decimals: 123.64 + 71.58 = 195.22. Aligning decimal points and adding column by column (4+8=12 carry 1; 6+5+1=12 carry 1; 3+1+1=5; 1+7=8; 1+0=1) confirms 195.22. The other options result from arithmetic errors in carrying or aligning digits.
Question 11: Which of the following values of x makes this inequality true? <br> 3x = 2 > 14
- 4
- 5 (Correct answer)
- 3
- 2
Correct answer: 5
Solving the inequality 3x + 2 > 14: subtract 2 from both sides to get 3x > 12, then divide by 3 to get x > 4. Only x = 5 satisfies this condition. x = 4 gives exactly 14 (not strictly greater), and x = 3 and x = 2 both produce values less than 14.
Free FAST Diagnostic Assessments Basic Questions and Answers
The temperature in Bismarck, North Dakota on the coldest day in December was -3 degrees Fahrenheit.
If the coldest day in Bismak in January was colder than this, which of the following could be its possible temperature in degrees Fahrenheit?