CAST Math Test 1 — Questions and Answers
Question 1: What is the area of a circle with a diameter of 12 cm?
- 48cm²
- 113cm² (Correct answer)
- 300cm²
- 218cm²
Correct answer: 113cm²
The area of a circle is calculated using the formula A = πr², where 'r' is the radius. Given a diameter of 12 cm, the radius is half of that, which is 6 cm. Plugging this into the formula gives A = π * (6 cm)² = 36π cm², which approximates to 113.097 cm² when using π ≈ 3.14159, rounded to 113 cm².
Question 2: What is the area of a rectangle with a length of 5cm and a width of 7cm?
- 35cm² (Correct answer)
- 45cm²
- 55cm²
- 15cm²
Correct answer: 35cm²
The area of a rectangle is found by multiplying its length by its width. For a rectangle with a length of 5 cm and a width of 7 cm, the area is simply 5 cm * 7 cm, which equals 35 cm². This calculation gives the total two-dimensional space enclosed by the rectangle.
Question 3: Calculate the value of the following expression if w=7:
- 337 (Correct answer)
- 447
- 129
- 264
Correct answer: 337
To calculate the value of the expression (which is implicitly w³ - 6 based on the answer) when w=7, substitute 7 for w. First, calculate 7 cubed (7 * 7 * 7), which equals 343. Then, subtract 6 from 343, resulting in 337.
Question 4: What is the value of x?
- 84 (Correct answer)
- 106
- 287
- 69
Correct answer: 84
Without the specific diagram or equation, 'x' often represents an unknown angle in geometry or a variable in an algebraic equation. For example, if x were an angle on a straight line with an adjacent angle of 96 degrees, then x would be 180 - 96 = 84 degrees. Similarly, in a triangle, if the other two angles sum to 96 degrees, the third angle x would be 180 - 96 = 84 degrees.
Question 5: What is the length of a cube if its volume is 8cm³?
- 2 cm (Correct answer)
- 4 cm
- 9 cm
- 12 cm
Correct answer: 2 cm
The volume of a cube is calculated by cubing the length of one of its sides (side * side * side). To find the side length when the volume is 8 cm³, you need to find the cube root of 8. The cube root of 8 is 2, meaning each side of the cube is 2 cm long.
Question 6: What is the value of x if 25% of x is 250?
- 1000 (Correct answer)
- 500
- 250
- 750
Correct answer: 1000
To find the value of x when 25% of x is 250, you can set up the equation 0.25 * x = 250. To solve for x, divide 250 by 0.25. Since 0.25 is equivalent to 1/4, dividing by 0.25 is the same as multiplying by 4, which gives x = 1000.
Question 7: Simplify the following expression:
- 10x²-80x-200 (Correct answer)
- 70x-200-80
- 10x²-70x-200
- 10x²-120x+200
Correct answer: 10x²-80x-200
To simplify the expression (which is implicitly 10(x-10)(x+2) based on the answer), first multiply the two binomials using the FOIL method: (x-10)(x+2) = x² + 2x - 10x - 20 = x² - 8x - 20. Then, distribute the 10 to each term inside the parentheses: 10 * (x² - 8x - 20) = 10x² - 80x - 200. This results in the simplified quadratic expression.
CAST Math Test 1
What is the area of a circle with a diameter of 12 cm?