Number Sense
What is the result of 7 x 8?
56
What is the name of a triangle with three equal sides?
An equilateral triangle
Solve for x: x + 5 = 12
x = 7
Solution: Subtract 5 from both sides of the equation.
What is the mean of the numbers 2, 4, 6, 8, 10?
6
Solution: Sum all numbers and divide by count.
Mean = (2 + 4 + 6 + 8 + 10) ÷ 5 = 30 ÷ 5 = 6
How many inches are in 2 feet?
24 inches
Solution: 1 foot = 12 inches, so 2 feet = 24 inches.
What is the square root of 144?
12
Solution: 12 x 12 = 144, so the square root of 144 is 12.
What is the formula for the area of a rectangle?
Area of rectangle = length × width
What is the slope of the line y = 2x + 3?
Slope = 2
Solution: In y = mx + b form, m represents the slope.
If you flip a fair coin, what is the probability of getting heads?
1/2 or 0.5 or 50%
Solution: Equal chance for heads or tails.
Convert 1.5 kilometers to meters
1500 meters
Solution: 1 km = 1000 m, so 1.5 km = 1500 m.
Simplify the fraction: 48/64
3/4
Solution: Simplify by dividing both numerator and denominator by their greatest common divisor (16).
Find the area of a circle with radius 5 cm. (Use π = 3.14)
78.5 cm²
Solution: Use the formula for circle area with given radius. πr² = 3.14 × 5² = 3.14 × 25 = 78.5 cm²
Factor the expression: x² - 9
(x+3)(x-3)
Solution: Recognize this as a difference of squares.
Calculate the median of the dataset: 3, 7, 8, 9, 11, 15
9
Solution: Order numbers, select middle value.
How many milliliters are in 2.5 liters?
2500 milliliters
Solution: 1 L = 1000 mL, so 2.5 L = 2500 mL.
What is the value of 2³ + 4² - 3¹?
21
Solution: Calculate each exponent, then perform addition and subtraction.
What is the volume of a rectangular prism with length 4 cm, width 3 cm, and height 5 cm?
60 cm³
Solution: Apply the formula for rectangular prism volume. Volume = length × width × height = 4 × 3 × 5 = 60 cm³
Solve the system of equations: y = 2x + 1 and y = -x + 7
x = 2, y = 5
Solution: Solve by substitution or elimination method.
A bag contains 3 red marbles, 4 blue marbles, and 5 green marbles. What is the probability of drawing a blue marble?
4/12 = 1/3
Solution: Number of favorable outcomes divided by total outcomes.
Convert 98.6°F to °C
Use formula (F - 32) × 5/9 = C
37°C
Solve for x: 2^x = 32
x = 5
Solution: 2⁵ = 32, or use logarithms: log₂(32) = 5
In a right triangle, if one angle is 30°, what are the other two angles?
The other angles are 60° and 90°
Solution: In a right triangle, one angle is always 90°. The sum of angles in a triangle is 180°, so 180° - 90° - 30° = 60°.
Find the equation of a line passing through points (2, 3) and (4, 7)
y - 3 = 2(x - 2) or y = 2x - 1
Solution: Use point-slope form or slope-intercept form.
Calculate the standard deviation of the dataset: 2, 4, 4, 4, 5, 5, 7
Standard deviation ≈ 1.5
Solution: Calculate mean, squared differences, average them, then square root.
If a car travels at 65 miles per hour, how many kilometers does it travel in 2.5 hours? (1 mile ≈ 1.60934 km)
Approximately 261.5 km
Solution: 65 mph × 2.5 h = 162.5 miles, then convert to km