Free FSA 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?
Correct answer: -5
On a number line, 'colder' means a lower numerical value, so a temperature colder than −3°F must be less than −3. Of the choices, only −5 is less than −3. The values 5, 0, and −2 are all greater than −3, meaning they would represent warmer temperatures, not colder ones.
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?
Correct answer: 4
Both the bed at (2, 3) and the desk at (6, 3) share the same y-coordinate of 3, so they lie on the same horizontal line. The distance between them is simply the difference in their x-coordinates: 6 − 2 = 4 feet. No distance formula is needed when both points are on the same horizontal line.
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
Probability equals favorable outcomes divided by total outcomes. There are 2 non-mechanical pencils out of 6 total pencils, giving a probability of 2/6, which simplifies to 1/3. The answer 2/3 would be the probability of selecting a mechanical pencil, and 1/6 or 1/4 do not correspond to any valid grouping from the given counts.
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
To find the mean, add all five scores: 74 + 83 + 96 + 83 + 84 = 420, then divide by 5, giving 84. The score of 83 is just one of the individual quiz scores, not the average. The value 105 is impossible as a quiz grade, and 96 was only one quiz score, not the overall mean.
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
To find the total surface area from a net, calculate the area of each face individually and sum them. The net consists of square faces and triangular faces for the roof; multiplying each face's dimensions, calculating triangle areas as ½ × base × height, and totaling all faces yields 155 square inches. The other options result from omitting faces or miscalculating the triangle areas.
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 of the 45 square magnets has sides of 2 inches, so each has an area of 4 square inches. The total area is 45 × 4 = 180 square inches. Dividing by 12 converts to 15 square feet, which matches the correct answer. The other options (90, 45, 180) reflect the area in square inches without the unit conversion, or errors in multiplying the magnet count.
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
The radius of a circle is exactly half the diameter, because the diameter spans the full width through the center while the radius only reaches from the center to the edge. Dividing the diameter of 8 inches by 2 gives a radius of 4 inches. Multiplying by 2 would give the diameter again, and dividing or multiplying by π is used for circumference and area calculations, not to find the radius from the diameter.
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
Dividing 1,580 by 25: 25 × 60 = 1,500, leaving a remainder of 80; 80 ÷ 25 = 3.2, so the total is 63.2, which rounds to 63. The answer 36 is the result reversed, 73 overshoots the correct quotient, and 25 is just the divisor itself.
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 the total cost by the number of towels: $45 ÷ 25 = $1.80 per towel. The value $0.44 would come from dividing incorrectly (25 ÷ 45 ≈ 0.44, reversing numerator and denominator). $5.00 and $20.00 are far too high for a unit price from that bulk purchase.
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
The expression adds the two decimal values: 123.64 + 71.58. Adding the cents: 64 + 58 = 122, carry the 1; adding the whole numbers: 123 + 71 + 1 = 195; giving 195.22. The value 52.06 would result from subtracting rather than adding, and 152.14 and 194.12 reflect misaligned decimal addition errors.
Question 11: Which of the following values of x makes this inequality true? <br>
3x = 2 > 14
Correct answer: 5
Solving 3x + 2 > 14: subtract 2 from both sides to get 3x > 12, then divide by 3 to get x > 4. Only x = 5 satisfies x > 4. The values 4, 3, and 2 all fail because 4 is not greater than 4 (it equals 4), and 3 and 2 are less than 4.
