Practice Test 1 | SATurn Bound

Question Section

Question 1

The graph shows the height above ground, in meters, of a ball x seconds after the ball was launched upward from a platform. Which statement is the best interpretation of the marked point (2.5, 6.3) in this context? A) 2.5 seconds after being launched, the ball's height above ground is 6.3 meters. B) 6.3 seconds after being launched, the ball's height above ground is 2.5 meters. C) The ball was launched from an initial height of 2.5 meters with an initial velocity of 6.3 meters per second. D) The ball was launched from an initial height of 6.3 meters with an initial velocity of 2.5 meters per second.

Question 2

The x-intercept of the graph shown is (x,0). What is the value of x?

X-intercept (seconds):

Question 3

The function f is defined by f(x) = 5 + √x. What is the value of f(169)? A) 0 B) 18 C) 42 D) 81

Question 4

What is the x-intercept of the graph shown

A) (-5,0) B) (3,0) C) (-3,0) D) (5,0)

Question 5

The graph shown models the number of residents of a certain city as years after 2010. How many residents does this model estimate the city had in 2010?

A) 0 B) 50 C) 100 D) 1,000

Question 6

y = (8w)(w). A rectangle has a length that is 8 times its width. The given function calculates the area of the rectangle in square meters, where y > 0. Which of the following is the best interpretation of 8w in this context? A) The length of the rectangle, in meters B) The area of the rectangle, in square meters C) The difference between the length and the width of the rectangle, in meters D) The perimeter of the rectangle, in meters

Question 7

The table shows the exponential relationship between the number of years, x, since Hans started training in pole vault, and the estimated height h(x), in meters, of her best pole vault for that year. Which of the following functions best represents this relationship, where x ≤ 5?

x	h(x)
0	1.25
2	2.18
4	3.80

A) h(x) = 1.25(0.32)^x
B) h(x) = 1.25(1.32)^x
C) h(x) = 1.32(0.25)^x
D) h(x) = 1.32(1.25)^x

Question 8

A rectangular volleyball court has an area of 200 square meters. If the length of the court is twice the width, what is the width of the court, in meters? A) 10 B) 20 C) 30 D) 40

Question 9

g(x) = x² + 60. What is the minimum value of the given function? A) 0 B) 60 C) 120 D) 3,600

Question 10

f(x) = 4,000(0.80)^x. A conservation scientist implemented a program to reduce the population of a certain species in an area. The given function estimates this species' population x years after 2010, where x ≤ 10. Which of the following is the best interpretation of 4,000 in this context? A) The estimated percent decrease in the population for this species and area every 10 years after 2010 B) The estimated percent decrease in the population for this species and area each year after 2010 C) The estimated population for this species and area 10 years after 2010 D) The estimated initial population for this species and area in 2010

Question 11

The first term of a sequence is 12. Each term after the first is 5 times the preceding term. If w represents the nth term of the sequence, which equation gives w in terms of n? A) w = 5(12^n) B) w = 5(12^{n-1}) C) w = 12(5^n) D) w = 12(5^{n-1})

Question 12

f(x) = (x - 50)(x - 52). The function f is defined by the given equation. For what value of x does f(x) reach its minimum? A) 52 B) 51 C) 50 D) -2

Question 13

The function g is defined by g(x) = (x + 20)(t - x), where t is a constant. In the xy-plane, the graph of y = g(x) passes through the point (30, 0). What is the value of g(0)? A) 600 B) -600 C) 20t D) -20t

Question 14

The population P of a certain city y years after the last census is modeled by the equation below, where r is a constant and p₀ is the population when y = 0: P = P₀(1 + r)^y. If during this time the population of the city decreases by a fixed percent each year, which of the following must be true? A) r < -1 B) -1 < r < 0 C) 0 < r < 1 D) r > 1

Question 15

f(x) = |65 - 3x|. The function f is defined by the given equation. For which of the following values of k does f(k) = 4k? A) 65/7 B) 65/3 C) 195/7 D) 65

Question 16

The function f is defined by f(x) = a^x + b, where a and b are constants and a > 0. In the xy-plane, the graph of y = f(x) has a y-intercept at (0, -30) and passes through the point (3, 34). What is the value of a + b? A) -26.98 B) -27 C) 4.02 D) -31

Question 17

The function f(x) = (1/12)(x - 10)² + 5 gives a metal ball's height above the ground f(x), in inches, x seconds after it started moving on a track, where 0 ≤ x ≤ 15. Which of the following is the best interpretation of the vertex of the graph of y = f(x) in the xy-plane? A) The metal ball's minimum height was 5 inches above the ground. B) The metal ball's minimum height was 10 inches above the ground. C) The metal ball's height was 5 inches above the ground when it started moving. D) The metal ball's height was 10 inches above the ground when it started moving.

Question 18

In the xy-plane, a parabola has vertex (12, -18) and intersects the x-axis at two points. If the equation of the parabola is written in the form y = ax² + bx + c, where a, b, and c are constants, which of the following could be the value of a + b + c? A) -26 B) -22 C) -18 D) -14

Question 19

The function f is defined by f(x) = (x + 5)(x + 2). The graph of f in the xy-plane is a parabola. Which of the following intervals contains the x-coordinate of the vertex of the graph of f? A) -6 < x < -5 B) -5 < x < 2 C) 2 < x < 5 D) 5 < x < 6

Question 20

A right rectangular prism has a height of 12 inches. The length of the prism's base is x inches, which is 8 inches more than the width of the prism's base. Which function V gives the volume of the prism, in cubic inches, in terms of the length of the prism's base? A) V(x) = x(x + 12)(x + 8) B) V(x) = x(x + 12)(x - 8) C) V(x) = 12x(x + 8) D) V(x) = 12x(x - 8)