Trigonometry
What is the cosine of a 45-degree angle in a right triangle?
√2 / 2
If you draw a card from a standard deck of 52 cards, what is the probability of drawing a red card?
26/52 or 1/2
What is the vertex form of the quadratic function f(x) = x² - 6x + 8?
f(x) = (x - 3)² - 1
Calculate the range of the following data set: {12, 14, 16, 18, 20}.
8
What is the product of (x²)³ * x^5?
x^11
If a ladder leaning against a wall makes a 60-degree angle with the ground and reaches a height of 10 meters up the wall, how long is the ladder?
20 meters
How many different ways can you arrange the letters in the word "MATH"?
24
Factor the quadratic expression: x² + 5x + 6.
(x + 2)(x + 3)
If the data set {2, 3, 5, 5, 7, 7, 7, 8, 9} is represented in a histogram, what would be the height of the bar for the value 7?
3
Rewrite the expression 2x^(-3) in terms of positive exponents.
2/x
What is the identity for the tangent of a sum of two angles?
tan(α + β) = (tan α + tan β) / (1 - tan α * tan β)
A bag contains 3 red marbles, 4 blue marbles, and 5 green marbles. If you randomly select two marbles without replacement, what is the probability that both marbles are blue?
2/12 or 1/6
Solve the equation: x² - 9 = 0.
x = -3 or x = 3
Identify the outlier in the data set: {12, 14, 16, 18, 500}.
500
What is the value of 5⁰?
1
Solve for θ: sin(2θ) = 1, where 0 ≤ θ ≤ 360°.
θ = 45° or θ = 135°
In a multiple-choice test with 5 questions and 4 choices per question, what is the probability of guessing exactly 3 correct answers?
0.15625 (or 5/32)
Solve the inequality: x² - 4x > 0.
x < 0 or x > 4
In a normally distributed data set, what percentage of data falls within one standard deviation from the mean?
Approximately 68%
If an investment grows at a rate of 5% per year, what is the multiplier for one year?
1.05
A tree casts a shadow that is 12 meters long. If the angle of elevation from the tip of the shadow to the top of the tree is 60 degrees, how tall is the tree?
12√3 meters
In a survey, 60% of people like chocolate, and 40% like vanilla. If 30% like both flavors, what is the probability that a randomly chosen person likes chocolate given that they like vanilla?
0.75 (P(Chocolate|Vanilla) = P(Chocolate ∩ Vanilla) / P(Vanilla))
A ball is thrown upward from a height of 10 meters with an initial velocity of 20 m/s. What is the maximum height the ball reaches?
20 meters
Which measure of central tendency is most affected by outliers: mean, median, or mode?
Mean
Calculate the final amount of $1000 invested at an annual interest rate of 4% compounded quarterly for 3 years.
Approximately $1124.86