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Math Test – No Calculator
25 MINUTES, 20 QUESTIONS
For questions 1-15, solve each problem, choose the best answer from the choices
provided, and fill in the corresponding circle on your answer sheet. For questions 16-20,
solve the problem and enter your answer in the grid on the answer sheet. Please refer to
the directions before question 16 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 not 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. 3x + x + x + x – 3 – 2 = 7 + x + x
In the equation above, what is the value of x ?
The graph above shows the distance traveled d, in feet, by a product on a conveyor belt m minutes after the product is placed on the belt. Which of the following equations correctly relates d and m ?
3. The formula below is often used by project managers to compute E, the estimated time to complete a job, where O is the shortest completion time, P is the longest completion time, and M is the most likely completion time.
Which of the following correctly gives P in terms of E, O, and M ?
In the figure above, RT = TU. What is the value of x ?
5. The width of a rectangular dance floor is w feet. The length of the floor is 6 feet longer than its width. Which of the following expresses the perimeter, in feet, of the dance floor in terms of w ?
y > 2x + 1
2x > 5
Which of the following consists of the y-coordinates of all the points that satisfy the system of inequalities above?
What is the solution set of the equation above?
f(x) = x³ – 9x
g(x) = x² – 2x – 3
Which of the following expressions is equivalent to
f(x) / g(x), for x > 3
9. (x – 6)² + (y + 5)² = 16
In the xy-plane, the graph of the equation above is a circle. Point P is on the circle and has coordinates (10, −5). If PQ is a diameter of the circle, what are the coordinates of point Q ?
10. A group of 202 people went on an overnight camping trip, taking 60 tents with them. Some of the tents held 2 people each, and the rest held 4 people each. Assuming all the tents were filled to capacity and every person got to sleep in a tent, exactly how many of the tents were 2-person tents?
Which of the following could be the equation of the graph above?
12. If ((2a)/b) = (1/2), what is that value of b/a?
13. Oil and gas production in a certain area dropped from 4 million barrels in 2000 to 1.9 million barrels in 2013. Assuming that the oil and gas production decreased at a constant rate, which of the following linear functions f best models the production, in millions of barrels, t years after the year 2000?
y = x² + 3x – 7
y – 5x + 8 = 0
How many solutions are there to the system of equations above?
g(x) = 2x – 1
h(x) = 1 – g(x)
The functions g and h are defined above. What is the value of h(0) ?
Directions: For questions 16-20, solve the problem and enter your answer in the blank space below.
16. x² + x − 12 = 0
If a is a solution of the equation above and a > 0, what is the value of a ?
17. The sum of −2x² + x + 31 and 3x² + 7x − 8 can be written in the form ax² + bx + c, where a, b, and c are constants. What is the value of a + b + c ?
a + b + c =
-x + y = -3.5
x + 3y = 9.5
If (x, y) satisfies the system of equations above, what is the value of y ?
19. A start-up company opened with 8 employees. The company’s growth plan assumes that 2 new employees will be hired each quarter (every 3 months) for the first 5 years. If an equation is written in the form y = ax + b to represent the number of employees, y, employed by the company x quarters after the company opened, what is the value of b ?
In the circle above, point A is the center and the length of arc BC is 2/5 of the circumference of the circle. What is the value of x ?