CAST Math Test

Question 1

What is the area of a circle with a diameter of 12 cm?

Accepted Answer

113cm²

Answer

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?

Accepted Answer

35cm²

Answer

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:

Accepted Answer

337

Answer

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?

Accepted Answer

84

Answer

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?

Accepted Answer

2 cm

Answer

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.

CAST Test Practice Test

CAST Test Practice Test

CAST Math Test