Math - Mix Up Across Topics (Sample)
Comprehensive Mathematics Question Set
Introduction
Welcome to this comprehensive set of mathematics questions covering a wide range of topics and difficulty levels. This collection is designed to challenge students, from those just beginning their journey in advanced mathematics to those preparing for high-level examinations or academic competitions.
The questions are organized into 19 distinct mathematical categories, each representing a crucial area of study in mathematics. Within most categories, you'll find questions of varying difficulty, labeled as Easy, Medium, or Hard. This tiered approach allows for progressive learning and provides opportunities for students at different levels to engage with each topic.
Key features of this question set include:
- Diverse Topics: From basic arithmetic and algebra to complex geometrical problems and statistical analysis, this set covers a broad spectrum of mathematical disciplines.
- Varying Difficulty Levels: The inclusion of Easy, Medium, and Hard questions in most categories allows for differentiated learning and practice.
- Real-World Applications: Many questions are framed in real-life contexts, helping students understand the practical applications of mathematical concepts.
- Analytical Thinking: The questions are designed not just to test mathematical knowledge, but also to encourage critical thinking and problem-solving skills.
- Comprehensive Coverage: With 19 different categories, this set provides a thorough review of key mathematical concepts typically covered in advanced high school and early college curricula.
Whether you're a student looking to challenge yourself, an educator seeking quality problems for your class, or someone who simply enjoys mathematical puzzles, this set of questions offers something for everyone. Engage with these problems to sharpen your mathematical skills, deepen your understanding of key concepts, and prepare for future academic and professional challenges in fields that require strong quantitative abilities.
Mathematics Topics and Questions
1. Circles
Easy
- Perpendicular diameters divide the circumference of a circle into four equal arcs. If one of the minor arcs is 1/5 of the circumference, what is the length of the entire circumference?
Medium
- An angle has a measure of 2 radians. What is the measure of the angle in degrees?
2. Area and Volume
Easy
- The figure shows a right rectangular prism. The volume V of a right rectangular prism is V = lwh, where l is the length of the prism, w is the width of the prism, and h is the height of the prism. What is the volume, in cubic centimeters, of the prism?
Medium
- What is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 centimeters, a width of 9 centimeters, and a height of 10 centimeters?
Hard
- A cube has an edge length of 6 inches. A solid sphere with a radius of 3 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?
3. Equivalent Expressions
Easy
- Which of the following is equivalent to 3(x + 3) - 6?
Medium
- If p = 2x + 3 and v = x + 5, which of the following is equivalent to p^v?
Hard
- Which of the following expressions is equivalent to (x^2 + 2x + 1) / (x + 1), for x ≠ -1?
4. Evaluating Statistical Claims: Observational Studies and Experiments
Hard
- A psychologist designed and conducted a study to determine whether playing a certain educational game increases middle school students' accuracy in adding fractions. For the study, the psychologist chose a random sample of 35 students from all of the students at one of the middle schools in a large city. The psychologist found that students who played the game showed significant improvement in accuracy when adding fractions. What is the largest group to which the results of the study can be generalized?
5. Inference From Sample Statistics and Margin of Error
Easy
- At a large high school, 300 students were selected at random and were asked in a survey about a menu change in the school cafeteria. All 300 students completed the survey. It was estimated that 38% of the students were in support of a menu change, with a margin of error of 5.5%. Which of the following is the best interpretation of the survey results?
Hard
- A researcher interviewed 411 randomly selected US residents and asked about their views on the use of nuclear energy. The table summarizes the responses of the interviewees. If the population of the United States was 300 million when the survey was given, based on the sample data for the 411 US residents, what is the best estimate, in millions, of the difference between the number of US residents who somewhat favor or strongly favor the use of nuclear energy and the number of those who somewhat oppose or strongly oppose it? (Round your answer to the nearest whole number.)
6. Linear Equations in One Variable
Easy
- If 7x = 42, what is the value of 6x?
Medium
- A grain silo contains 24,000 bushels of corn. An auger can move 930 bushels of corn out of the silo each hour. If the auger runs continuously, which of the following functions models the number of bushels of corn remaining in the silo t hours after the auger begins running?
Hard
- A science teacher is preparing the 5 stations of a science laboratory. Each station will have either Experiment A materials or Experiment B materials, but not both. Experiment A requires 6 teaspoons of salt, and Experiment B requires 4 teaspoons of salt. If x is the number of stations that will be set up for Experiment A and the remaining stations will be set up for Experiment B, which of the following expressions represents the total number of teaspoons of salt required?
7. Linear Equations in Two Variables
Easy
- A machine makes large boxes or small boxes, one at a time, for a total of 480 minutes each day. It takes the machine 8 minutes to make a large box or 5 minutes to make a small box. Which equation represents the possible number of large boxes, l, and small boxes, s, the machine can make each day?
Medium
- A certain apprentice has enrolled in 110 hours of training courses. The equation 15o + 10s = 110 represents this situation, where o is the number of on-site training courses and s is the number of online training courses this apprentice has enrolled in. How many more hours does each online training course take than each on-site training course?
Hard
- How many liters of a 25% saline solution must be added to 3 liters of a 10% saline solution to obtain a 15% saline solution?
8. Linear Functions
Medium
- c(x) = mx + 500. A company's total cost c, in dollars, to produce x shirts is given by the function above, where m is a constant and x > 0. The total cost to produce 100 shirts is $800. What is the total cost, in dollars, to produce 1,000 shirts?
Hard
- One gallon of paint will cover 400 square feet of a surface. A room has a total wall area of w square feet. Which equation represents the total amount of paint p, in gallons, needed to paint the walls of the room twice?
9. Linear Inequalities in One or Two Variables
Easy
- A school is ordering shirts and hats for its students. The shirts cost $8 each and the hats cost $12 each. The school must spend no more than $80. Let x represent the number of shirts ordered and let y represent the number of hats ordered. Which of the following inequalities represents this situation?
Medium
- Each parking space in a parking lot is either 8 feet wide or 10 feet wide. A total of 30 parking spaces are to be placed along a 135-foot-long curb. If n is the number of 8-foot-wide parking spaces that will be placed along the curb, which of the following inequalities gives all possible values of n?
Hard
- A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are non-negative integers. Which of the following systems of inequalities best represents this situation?
10. Lines, Angles and Triangles
Hard
- In the figure shown, points B, C, D, and E lie on line segment AE, and line segment BF intersects line segment CE at point D. The measure of ∠BDC is 90°, the measure of ∠ADB is 40°, the measure of ∠CED is 60°, and the measure of ∠CDE is x°. What is the measure, in degrees, of ∠AED?
11. Nonlinear Equations in One Variable and Systems of Equations in Two Variables
Easy
- Which of the following is a solution to the equation x^2 = 2x + 15?
Medium
- If (x + 1)^2 = (x^2 + x), what is one possible solution to the equation?
Hard
- During a 5-second time interval, the average acceleration a, in meters per second squared, of an object with an initial velocity of 12 meters per second is given by the equation a = (v - 12)/5, where v is the final velocity of the object in meters per second. If the average acceleration of the object is 3.5 meters per second squared during this time interval, what is the final velocity, v, of the object?
12. Nonlinear Functions
Easy
- If f(x) = -3x^2 - x + 4, what is f(-2)?
Medium
- f(θ) = -0.28(θ - 27)^2 + 880. An engineer wanted to identify the best angle for a cooling fan in an engine in order to get the greatest airflow. The engineer discovered that the function above models the airflow f, in cubic feet per minute, as a function of the angle of the fan θ, in degrees. According to the model, what angle, in degrees, will result in the greatest airflow?
Hard
- N(d) = 115(0.90)^d. The function N defined above can be used to model the number of species of brachiopods at various ocean depths d, where d is in hundreds of meters. Which of the following does the model predict?
13. One-Variable Data: Distributions and Measures of Center and Spread
Easy
- The dot plot represents the 8 values in data set A. Data set B is created by adding 5 to each of the values in data set A. Which of the following correctly compares the medians and the ranges of data sets A and B?
Medium
- The bar graph shows the distribution of 150 books collected by 5 different groups for a book drive. How many books were collected by Group C?
Hard
- Data set A consists of 11 positive integers less than 50. The list shown gives 10 of the integers from data set A. 5, 7, 10, 14, 17, 19, 22, 26, 33, 48. If the mean of data set A is 23, what is the median of data set A?
14. Percentages
Easy
- Of the 120 marbles in a bag, 40 are blue. What percentage of the marbles are blue?
Medium
- A gift shop buys souvenirs at a wholesale price of w dollars each and resells them each at a retail price that is 80% greater than the wholesale price. At the end of the season, any remaining souvenirs are marked at a discounted price that is 40% off the retail price. What is the discounted price of each remaining souvenir, in dollars?
Hard
- 40% of the items in a box are green. Of those, 25% are also rectangular. Of the green rectangular items, 60% are also metal. Which of the following is closest to the percentage of the items in the box that are not rectangular green metal items?
15. Probability and Conditional Probability
Easy
- A bag contains a total of 60 marbles. A marble is to be chosen at random from the bag. If the probability that a blue marble will be chosen is 0.35, how many marbles in the bag are blue?
Medium
- The table above shows the number of students from two different high schools who completed summer internships in each of five years. No student attended both schools. Of the students who completed a summer internship in 2010, which of the following represents the fraction of students who were from Valley High School?
Hard
- The same 20 contestants, on each of 3 days, answered 5 questions to win a prize. Each contestant received 1 point for each correct answer. The number of contestants receiving a given score on each day is shown in the table above. No contestant received the same score on two different days. If a contestant is selected at random, what is the probability that the selected contestant received a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on one of the three days?
16. Ratios, Rates, Proportional Relationships and Units
Easy
- A wind turbine completes 12 revolutions in 3 minutes. At this rate, how many revolutions per minute does this turbine complete?
Medium
- A printer produces posters at a constant rate of 42 posters per minute. At what rate, in posters per hour, does the printer produce the posters?
Hard
- The density of a certain type of wood is 352 kilograms per cubic meter. A sample of this type of wood is in the shape of a cube and has a mass of 10 kilograms. To the nearest hundredth of a meter, what is the length of one edge of this sample?
17. Right Triangles and Trigonometry
Hard
- In triangle ABC, angle B is a right angle, point D lies on AC, point E lies on BC, and DE is parallel to AB. If the length of DE is 14 units, the length of AD is 8 units, and the area of triangle CDE is 84 square units, what is the length of CE?
18. Systems of Two Linear Equations in Two Variables
Easy
- A dance teacher ordered outfits for students for a dance recital. Outfits for boys cost $26, and outfits for girls cost $35. The dance teacher ordered a total of 28 outfits and spent $881. If b represents the number of outfits the dance teacher ordered for boys and g represents the number of outfits the dance teacher ordered for girls, which of the following systems of equations can be solved to find b and g?
Medium
- The score on a trivia game is obtained by subtracting the number of incorrect answers from twice the number of correct answers. If a player answered 40 questions and obtained a score of 50, how many questions did the player answer correctly?
Hard
- At a certain movie theater, the price of each adult ticket is $10, and the price of each child ticket is $6. On Tuesday, the theater sold a total of 120 tickets for a total of $840. The system of equations below represents this situation. How many adult tickets did the theater sell on Tuesday?
19. Two-Variable Data: Models and Scatterplots
Easy
- The line graph shows the number of graduates from the classes of 2001 through 2007 at a certain school who enrolled in college within 24 months of graduation. Of the following, which class had the fewest graduates who enrolled in college within 24 months of graduation?