SAT 07/28/23 Math Test – No Calculator
You will have 25 minutes to complete 20 questions in this portion exam from the moment you click the start button.
- The use of calculators is NOT permitted
- All variables and expressions used represent real numbers unless otherwise indicated.
- Figures provided in this test are drawn to scale unless otherwise indicated.
- All figures lie in a plane unless otherwise indicated.
- 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.
The timer will continue to count even if you leave the page, so do your best not to leave the page.
You may only take this exam once.
Please have scrap paper and writing utensils handy.
You must answer all questions to submit the exam. If you don’t know an answer, try your best to select the right one!
Once you complete the exam, you may leave the page.
Good Luck!
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- Question 1 of 20
1. Question
Math Test – No Calculator
25 MINUTES, 20 QUESTIONSFor 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 ?
CorrectIncorrect - Question 2 of 20
2. Question
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) ?
CorrectIncorrect - Question 3 of 20
3. Question
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 ?CorrectIncorrect - Question 4 of 20
4. Question
4. If f(x) = −2x + 5, what is f(−3x) equal to?
CorrectIncorrect - Question 5 of 20
5. Question
5. 3(2x + 1)(4x + 1)
Which of the following is equivalent to the expression above?
CorrectIncorrect - Question 6 of 20
6. Question
6. If (a – b)/b = (3/7), which of the following must also be true?
CorrectIncorrect - Question 7 of 20
7. Question
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?
CorrectIncorrect - Question 8 of 20
8. Question
8. Which of the following equations represents a line that is parallel to the line with equation
y = −3x + 4 ?
CorrectIncorrect - Question 9 of 20
9. Question
9. √(x – a) = x – 4
If a = 2, what is the solution set of the equation above?
CorrectIncorrect - Question 10 of 20
10. Question
10. If (t + 5) / (t – 5) = 10, what is the value of t ?
CorrectIncorrect - Question 11 of 20
11. Question
11. x = 2y + 5
y = (2x – 3)(x + 9)How many ordered pairs (x , y) satisfy the system of equations shown above?
CorrectIncorrect - Question 12 of 20
12. Question
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.)
CorrectIncorrect - Question 13 of 20
13. Question
13.
CorrectIncorrect - Question 14 of 20
14. Question
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) )
CorrectIncorrect - Question 15 of 20
15. Question
15.
CorrectIncorrect - Question 16 of 20
16. Question
16.
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
CorrectIncorrect - Question 17 of 20
17. Question
17.
In the triangle above, the sine of x° is 0.6. What is the cosine of y° ?
The cosine of y° is
CorrectIncorrect - Question 18 of 20
18. Question
18. x³ − 5x² + 2x − 10 = 0
For what real value of x is the equation above true?
x =
CorrectIncorrect - Question 19 of 20
19. Question
19. -3x + 4y = 20
6x + 3y = 15If (x, y) is the solution to the system of equations above, what is the value of x ?
x =
CorrectIncorrect - Question 20 of 20
20. Question
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 ?
k =
CorrectIncorrect
