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SAT® Total Prep 2023 - Math Test

1. A biologist develops the equation y = 20.942x + 127 to predict the regrowth of a certain species of plant x months after a natural disaster occurred. Which of the following describes what the number 20.942 represents in this equation?
A) The estimated number of the plants after x months
B) The estimated monthly increase in the number of the plants
C) The estimated monthly decrease in the number of the plants
D) The estimated number of the plants that survived the natural disaster 

 

A) -4/3
B) −1
C) 4/3
D) 5/2

 

6. Which of the following equations could represent a parabola that has a minimum value of −5 and whose axis of symmetry is the line x = 1 ?
A) y = (x − 5)2 + 1
B) y = (x + 5)2 + 1
C) y = (x − 1)2 − 5
D) y = (x + 1)2 − 5

 

8. If A = x2 + 4x + 9 and B = x3 + 6x − 2, what is 3A + B ?
A) 4x2 + 18x + 25
B) x3 + x2 + 10x + 7
C) x3 + 3x2 + 18x + 25
D) 3x3 + 3x2 + 30x + 29

9. How many real values of x satisfy the quadratic equation 9x2 −12x + 4 = 0 ?
A) 0
B) 1
C) 2
D) 4

12. Which of the following equations when graphed on a coordinate plane will not cross the y-axis?
A) 0.5(4x + y) = y − 9
B) 2(x + 7) − x = 4(y + 3)
C) 0.25(8y + 4x) − 7 = −2(−y + 1)
D) 6x − 2(3y + x) = 10 − 3y

18. If the area of the shaded sector in circle C shown above is 6π square units, what is the diameter of the circle?
19. What is the diameter of the circle given by the equation x2 + y2 + 10x − 4y = 20 ?
20. In economics, the law of demand states that as the price of a commodity rises, the demand for that commodity goes down. A company determines that the monthly demand for a certain item that it sells can be modeled by the function q(p) = −2p + 34, where q represents the quantity sold in hundreds and p represents the selling price in dollars. It costs $7 to produce this item. How much more per month in profits can the company expect to earn by selling the item at $12 instead of $10? (Profit = sales − costs)

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