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Math Test – Calculator
55 MINUTES, 38 QUESTIONS
Directions: For questions 1-30, solve each problem, choose the best answer from the choices
provided, and fill in the corresponding circle on your answer sheet. For questions 31-38,
solve the problem and enter your answer in the grid on the answer sheet. Please refer to
the directions before question 31 on how to enter your answers in the grid. You may use
any available space in your test booklet for scratch work.
1. The use of a calculator is permitted.
2. All variables and expressions used represent real numbers unless otherwise indicated.
3. Figures provided in this test are drawn to scale unless otherwise indicated.
4. All figures lie in a plane unless otherwise indicated.
5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for
which f(x) is a real number.
1. Which expression is equivalent to (2x² – 4) – (-3x² + 2x – 7) ?
3. Snow fell and then stopped for a time. When the snow began to fall again, it fell at a faster rate than it had initially. Assuming that none of the snow melted during the time indicated, which of the following graphs could model the total accumulation of snow versus time?
4. A website-hosting service charges businesses a onetime setup fee of $350 plus d dollars for each month. If a business owner paid $1,010 for the first 12 months, including the setup fee, what is the value of d ?
5. 6x − 9y > 12
Which of the following inequalities is equivalent to the inequality above?
7. The members of a city council wanted to assess the opinions of all city residents about converting an open field into a dog park. The council surveyed a sample of 500 city residents who own dogs. The survey showed that the majority of those sampled were in favor of the dog park. Which of the following is true about the city council’s survey?
9. The total area of a coastal city is 92.1 square miles, of which 11.3 square miles is water. If the city had a population of 621,000 people in the year 2010, which of the following is closest to the population density, in people per square mile of land area, of the city at that time?
10. Between 1497 and 1500, Amerigo Vespucci embarked on two voyages to the New World. According to Vespucci’s letters, the first voyage lasted 43 days longer than the second voyage, and the two voyages combined lasted a total of 1,003 days. How many days did the second voyage last?
11. 7x + 3y = 8
6x – 3y = 5
For the solution (x, y ) to the system of equations above, what is the value of x – y ?
12. Over which of the following time periods is the average growth rate of the sunflower least?
13. The function h, defined by h(t) = at + b , where a and b are constants, models the height, in centimeters, of the sunflower after t days of growth during a time period in which the growth is approximately linear. What does a represent?
14. The growth rate of the sunflower from day 14 to day 35 is nearly constant. On this interval, which of the following equations best models the height h, in centimeters, of the sunflower t days after it begins to grow?
17. Which of the following expresses the riser height in terms of the tread depth?
18. Some building codes require that, for indoor stairways, the tread depth must be at least 9 inches and the riser height must be at least 5 inches. According to the riser-tread formula, which of the following inequalities represents the set of all possible values for the riser height that meets this code requirement?
19. An architect wants to use the riser-tread formula to design a stairway with a total rise of 9 feet, a riser height between 7 and 8 inches, and an odd number of steps. With the architect’s constraints, which of the following must be the tread depth, in inches, of the stairway? (1 foot = 12 inches)
20. What is the sum of the solutions to (x – 6)(x + 0.7) = 0 ?
21. A study was done on the weights of different types of fish in a pond. A random sample of fish were caught and marked in order to ensure that none were weighed more than once. The sample contained 150 largemouth bass, of which 30% weighed more than 2 pounds. Which of the following conclusions is best supported by the sample data?
24. A customer’s monthly water bill was $75.74. Due to a rate increase, her monthly bill is now $79.86. To the nearest tenth of a percent, by what percent did the amount of the customer’s water bill increase?
27. In the xy-plane, the graph of 2x² – 6x + 2y² + 2y = 45 is a circle. What is the radius of the circle?
28. Two different points on a number line are both 3 units from the point with coordinate −4. The solution to which of the following equations gives the coordinates of both points?
29. A motor powers a model car so that after starting from rest, the car travels s inches in t seconds, where s = 16t√t . Which of the following gives the average speed of the car, in inches per second, over the first t seconds after it starts?
31. A group of friends decided to divide the $800 cost of a trip equally among themselves. When two of the friends decided not to go on the trip, those remaining still divided the $800 cost equally, but each friend’s share of the cost increased by $20. How many friends were in the group originally?
friends were in the group originally
32. 2(5x – 20) – (15 + 8x) = 7
What value of x satisfies the equation above?
33. A laboratory supply company produces graduated cylinders, each with an internal radius of 2 inches and an internal height between 7.75 inches and 8 inches. What is one possible volume, rounded to the nearest cubic inch, of a graduated cylinder produced by this company?
is one possible volume
34. In the xy-plane, the graph of y = 3x² – 14x intersects the graph of y = x at the points ( 0, 0 ) and ( a, a ). What is the value of a ?
35. The line with the equation ⅘x + ⅓y = 1 is graphed in the xy-plane. What is the x-coordinate of the x‑intercept of the line?
is the x-coordinate of the x-intercept.
37. Jeremy deposited x dollars in his investment account on January 1, 2001. The amount of money in the account doubled each year until Jeremy had 480 dollars in his investment account on January 1, 2005. What is the value of x ?
38. A school district is forming a committee to discuss plans for the construction of a new high school. Of those invited to join the committee, 15% are parents of students, 45% are teachers from the current high school, 25% are school and district administrators, and the remaining 6 individuals are students. How many more teachers were invited to join the committee than school and district administrators?
more teachers were invited to join the committee than school and district administrators.