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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. Which of the following expressions is equal to 0 for some value of x ?
2. f(x) = (3/2)x + b
In the function above, b is a constant. If f(6) = 7, what is the value of f(−2) ?
3. (x/y) = 6
4(y + 1) = x
If (x, y) is the solution to the system of equations
above, what is the value of y ?
4. If f(x) = −2x + 5, what is f(−3x) equal to?
5. 3(2x + 1)(4x + 1)
Which of the following is equivalent to the expression above?
6. If (a – b)/b = (3/7), which of the following must also be true?
7. While preparing to run a marathon, Amelia created a training schedule in which the distance of her longest run every week increased by a constant amount. If Amelia’s training schedule requires that her longest run in week 4 is a distance of 8 miles and her longest run in week 16 is a distance of 26 miles, which of the following best describes how the distance Amelia runs changes between week 4 and week 16 of her training schedule?
8. Which of the following equations represents a line that is parallel to the line with equation
y = −3x + 4 ?
9. √(x – a) = x – 4
If a = 2, what is the solution set of the equation above?
10. If (t + 5) / (t – 5) = 10, what is the value of t ?
11. x = 2y + 5
y = (2x – 3)(x + 9)
How many ordered pairs (x , y) satisfy the system of equations shown above?
12. Ken and Paul each ordered a sandwich at a restaurant. The price of Ken’s sandwich was x dollars, and the price of Paul’s sandwich was $1 more than the price of Ken’s sandwich. If Ken and Paul split the cost of the sandwiches evenly and each paid a 20% tip, which of the following expressions represents the amount, in dollars, each of them paid? (Assume there is no sales tax.)
14. (8 – i) / (3 – 2i)
If the expression above is rewritten in the form a + bi, where a and b are real numbers, what is the value of a ? (Note: i = √(−1) )
Jim has a triangular shelf system that attaches to his showerhead. The total height of the system is 18 inches, and there are three parallel shelves as shown above. What is the maximum height, in inches, of a shampoo bottle that can stand upright on the middle shelf?
The maximum height, in inches, is
In the triangle above, the sine of x° is 0.6. What is the cosine of y° ?
The cosine of y° is
18. x³ − 5x² + 2x − 10 = 0
For what real value of x is the equation above true?
19. -3x + 4y = 20
6x + 3y = 15
If (x, y) is the solution to the system of equations above, what is the value of x ?
20. The mesosphere is the layer of Earth’s atmosphere between 50 kilometers and 85 kilometers above Earth’s surface. At a distance of 50 kilometers from Earth’s surface, the temperature in the mesosphere is −5° Celsius, and at a distance of 80 kilometers from Earth’s surface, the temperature in the mesosphere is −80° Celsius. For every additional 10 kilometers from Earth’s surface, the temperature in the mesosphere decreases by k° Celsius, where k is a constant. What is the value of k ?