# SAT Math Multiple Choice Practice Test 57

### Test Information

16 questions

24 minutes

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1. If a and b are solutions to the equation, and a < b, what is the value of a?

• A. -4
• B. -1
• C. 1
• D. 4

2. If g(x) = -2(x2 – 6x – 12) + 3(kx) and g(x) is evenly divisible by x, then what is the value of k?

• A. -8
• B. -3
• C. 2
• D. 3

3. Professors Lambert and Stassen team-teach an advanced psychology class. Their studentsrecently took their final exams, and the professors are preparing to grade them. ProfessorStassen predicts that, if she graded all the exams, she would take 50% more time thanProfessor Lambert would if he graded all the exams. They estimate that it will takethem 40 hours to grade all the exams if they grade together. Which of the followingequations best represents the situation described?

• A.
• B.
• C.
• D.

4. Using a riding lawnmower, Joe can cut his lawn in 45 minutes. Using a push mower,Joe's son can cut the lawn in 3 hours. If they work together, how long will it takethem to cut the lawn?

• A. 24 minutes
• B. 30 minutes
• C. 36 minutes
• D. 40 minutes

5.

Which of the following polynomial equations could be used to represent the area ofthe trapezoid shown in the figure?

• A.
• B.
• C.
• D.

6.

Which of the following is a factor of the polynomial given above?

• A.
• B.
• C.
• D.

7. If the expressionis rewritten in the form, which of the following gives A in terms of x?

• A.
• B.
• C.
• D.

8.

Two polynomial functions p(x) and q(x) are defined above. Which of the following polynomial functions is divisible by?

• A.
• B.
• C.
• D.

9. If f(x) = x3 + 6, what is the value of f (3)?

• A. 15
• B. 33
• C. 39
• D. 729

10.

If the above graph shows f (x) = 7x2, which of the following is the graph of f (x) = 7x2 + 1?

• A.
• B.
• C.
• D.

11. If g(x) represents a quadratic function, which of the following best describes the relationshipbetween the graphs of g(x) and g(x – 3)?

• A. The graph of g(x – 3) is 3 units to the left of the graph of g(x).
• B. The graph of g(x – 3) is 3 units to the right of the graph of g(x).
• C. The graph of g(x – 3) is 3 units lower than the graph of g(x).
• D. The graph of g(x – 3) is 3 units higher than the graph of g(x).

12.

If p(x) is the polynomial function shown in the graph above, which of the following couldbe the factored form of p(x)?

• A.
• B.
• C.
• D.

13.

The graph of y = f(x) is given above. For what value of x is y = f(x – 4) undefined?

• A. -3
• B. 1
• C. 2
• D. 5

14. A college campus has vending machines, which must be periodically restocked. The restockingfrequency depends primarily on how many students have classes near the machine eachsemester. The vending machine company uses the function shown above, where s is the number of students estimated to have classes within the immediate vicinityon a daily basis, to determine how many times per semester the machine must be restocked.How many more times must a vending machine that has 400 students in the immediatevicinity be restocked compared to one that has 300 students in the immediate vicinity?

• A. 2
• B. 4
• C. 7
• D. 13

15.

What is the maximum value of the function graphed on the coordinate plane above, overthe interval –8≤ x ≥ 8?

• A. 4
• B. 6
• C. 8
• D. ∞ (infinity)

16.

The complete graph of the function h is shown in the xy plane above. For what value of x is the value of h(x) at its maximum?

• A. 5
• B. 6
• C. 8
• D. 10