1) Perform the indicated operation.
(2 + 3i) + (13 - 2i) =
A) 15 + 5i
B) 15 + i
C) 11 - 5i
D) -11 - i
2) Which has the same value as (4 + 3i)2?
A) 7
B) 7 + 24i
C) 25
D) 25 + 24i
3) Simplify: (3 - i)(3 + 2i)(1 - 5i)
A) 7 - 4i
B) 9 - 5i
C) 26 - 52i
D) 29 - 34i
4)Multiply and simplify.
A) 24 - 8i
B) 36 - 8i
C) 36 + 8i
D) 24 + 8i
5) Simplify: i4 + i3 + i2 + i
A) 0
B) 1
C) -1
D) i
6) The solution set for the equation x5 = x is
A) {0, 1}
B) {-1, 0, 1}
C) {-i, i, -1, 1}
D) {0, -i, i, -1, 1}
7) The graph represents Jason's speed on a trip. What is the rate of change for the period of time between 10 and 20 minutes?
A) 0B) 1/3 C) ½ D) 1
8)What is the vertex of this function?
A) (1, 5)
B) (1, 6)
C) (1, 7)
D) (1, 8)
9)The graph shows the number of customers eating at a local diner from 11:00-3:00. At what time does the diner have the fewest customers?
A) 11:00B) 1:00C) 2:00D) 3:00
10)What is the x-intercept of this piecewise function?
A) (0, 2)B) (2, 0)C) (0, 4)D) (4, 0)
11)Which absolute value function is equivalent to the piecewise function shown ?
A) f(x) = |x| + 3
B) f(x) = |x + 3|
C) f(x) = |x| - 3
D) f(x) = |x - 3|
12) Which shows f(x) = |3x + 3| in piecewise form?
13) Solve the equation. 3|2x - 5| = 12
A) {-5,10}
B) {0,5}
C) {0.5,4.5}
D) {2,7}
14)Which shows the graph of the piecewise function given?
15) The equation y = |x + 2| - 3 is shown.
Use it to solve the equation |x + 2| - 3 = 0.
A) {-1}
B) {-1, 1}
C) {-1, -5}
D) {1, -5}
16) Simplify.
A) B) C) D)
17) Describe the end behavior of f(x) = -2x + 3 - 1.
A) x→ -∞ f(x)→ -1 x→ ∞ f(x)→ ∞
B) x→ -∞ f(x)→ 0 x→ ∞ f(x)→ -∞
C) x→ -∞ f(x)→ 0 x→ ∞ f(x)→ ∞
D) x→ -∞ f(x)→ -1 x→ ∞ f(x) → -∞
18)In the graph shown, suppose that f(x) = ax, g(x) = bx, and h(x) = cx. Choose the true statement.
A) c < a < b
B) a < c < b
C) b < c < a
D) c < b < a
19) You bought a new car for $15,000 and know that it loses 1/5 of it's value every year. The equation that models the value of your car is y = 15000(1/5)x. What is a reasonable range for this function?
A) (0, 15,000]
B) [0, 15,000)
C) (0, ∞)
D) (-∞, ∞)
20) When Katie was born her mother invested $5000 in an account for her college savings. We can use the formula V = 5000(1 + r)t where r represents the interest rate and t represents the time in years. If Katie has approximately $11,042 in her account after 18 years, what was the interest rate for the account?
A) 3.5%
B) 4.5%
C) 5.5%
D) 6.5%
21) Which is equivalent to 243?
A) (2 x 102) + (4 x 101) + (3 x 100)
B) (2 x 103) + (4 x 102) + (3 x 101)
C) (200 x 100) + (40 x 10) + (3 x 1)
D) (2 x 10) + (4 x 10) + (3 x 10)
22)Which graph matches the equation y = -x2 - 2 ?
23) Charlie uses the function f(x) = 2x2 + 5x + 3 to track the temperature of a substance, where x represents the time. When you evaluate f(5) you find that the temperature of the substance is 78°C. What is the domain of the situation of Charlie's quadratic function?
A) all real numbers
B) all real numbers less than zero
C) all real numbers greater than zero
D) all real integers less than or equal to zero
24)The function whose graph is shown is
A) f(x) = x2 - 5
B) f(x) = x2 - 9
C) f(x) = x2 - 4x - 5
D) f(x) = x2 - 4x - 9
25) At a canning company the daily production cost, y, is given by the quadratic equation y = 650 – 15x + 0.45x2, where x is the number of canned items. What is the MINIMUM daily production cost?
A) $1,025.00
B) $1,186.25
C) $525.00
D) $536.25
26)Jerry has been asked to solve the quadratic equation -x2 + 4x - 5 = 0, and he has decided to do it by graphing. The graph of y = -x2 + 4x - 5 is shown here. The solution set for Jerry's equation contains
A) no solutions.
B) two real numbers.
C) two imaginary numbers.
D) one real and one imaginary number.
27)The graphs represent equations of the form y = x2 + c. For which graph is the value of c the smallest?
28)Which graph matches the equation y = -x2 + 2 ?
29)Kara creates the table shown to represent the function ƒ(x) = x2 + 2x - 3.
Determine the zero(s) of the function.
A) x = -3
B) x = -2 and x = 0
C) x = -3 and x = 1
D) x = -4 and x = 2
30) Identify the real zero(s) for f(x) = 3x2 + 2x + 4.
A) 1 and -1
B) 0 and -1
C) no solution
D) infinite solutions
31) Solve. x2 + 4 = 0
A) x = 2
B) x = 2i
C) x = ±2
D) x = ±2i
32)A system of linear equations has been graphed in the diagram. Determine a reasonable solution for the system of equations.
A) (-1, 4)
B) (1, 4)
C) (-1, -4)
D) (1, -4)
33) Solve the equation.
x2 - 6x + 9 = 0
A) x = 3
B) x = 6
C) x = 3 or x = -3
D) x = 9 or x = -9
34) Solve the inequality.x2 + 7x > -12
A) (-4, -3)
B) all real numbers
C) (-∞, -4) and (-3, ∞)
D) (-∞, -12) and (7, ∞)
35) If the domain is {0, 2, -6}, what is the range of y = -2x + 3?
A) {0, 7, 29}
B) {0, 7, 15}
C) {3, -1, -9}
D) {3, -1, 15}
36)The graph shows the number of students who earned a score in math. Find the domain.
A) 10 < x < 100
B) 0 ≤ x ≤ 24
C) 10 ≤ x ≤ 100
D) {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
37) What is the inverse of g? g(x) = 4 –x
A) g -1 (x) = 4x
B) g -1 (x) = 4 + x
C) g -1 (x) = 4 - x
D) g -1 (x) = 4 / x
38) The length of a rectangle is 3 cm more than 10 times its width. The area of the rectangle is 75 cm2. A quadratic function can be used to represent the dimensions of the rectangle. What quantity of the rectangle represents the domain of that function?
A) the area
B) the width
C) the length
D) the perimeter
39)Determine the domain and range of the graphed function.
A) domain: (-∞, ∞) range: (-∞, 10)
B) domain: (-∞, ∞) range: (-∞, 10]
C) domain: (-∞, 10) range: (-∞, ∞)
D) domain: (-∞, 10] range: (-∞, ∞)
40)Which function does pass the horizontal line test?
41) Find the altitude of an equilateral triangle, if each side of the triangle has a length of 20 meters.
A) metersB)metersC) 10 metersD) 20 meters
42)In the diagram, assume that y = 7. Find x and z.
A) x =; z = 14B) x = 14; z = C) x =; z = 14D) x = 14; z =
43)Determine the length of side CB.
A) 3
B)
C)
D) 6
44)A tree casts a shadow that is 150 feet long. If the angle of elevation from the tip of the shadow to the top of the tree is 30°, how tall is the tree to the nearest foot?
A) 87 feet
B) 106 feet
C) 212 feet
D) 259 feet
45)The angle of depression from the top of a flag pole to a point on the ground is 30°. If the point on the ground is 75 feet from the base of the flag pole, how tall is the pole to the nearest foot?
A) 43 feet
B) 53 feet
C) 106 feet
D) 130 feet
46)Given: ΔBCD ~ ΔEFG Find x.
A) 4
B) 8
C) 10
D) 12
47)A man on the tenth floor of a building shouts down to a person on the street. If the man is 25 feet up and the distance between the person on the street and the man in the building is 50 feet, what is the angle of elevation (in degrees) between the person on the street and the person in the building?
A) 30°B) 45°C) 60° D) 75°
48) Which trigonometric value is equal to cos 62°?
A) cos 28°
B) sec 28°
C) sin 28°
D) tan 28°
49)The Eastern Point Lighthouse in Gloucester, Massachusetts was established in 1832 to help fishermen into the harbor. It is still used today by the Coast Guard. A fisherman along the shore wanted to know how tall it was. He is 6 ft. tall and he measures his shadow to be 1.7 ft. The lighthouse casts a shadow of 10.2 ft., approximately how tall is the Eastern Point Lighthouse?
A) 17.9 feet
B) 36 feet
C) 61.2 feet
D) 104 feet
50)On a sunny day an office building casts a shadow that is 80 feet long. At the same time, a 5 foot person casts a 6 foot shadow. Determine the height of the office building to the nearest foot.
A) 30 feetB) 67 feetC) 79 feetD) 82 feet
51)Find the height of the tree in the diagram shown.
A) h = 45sin31° ft
B) h = 45sin59° ft
C) h = 45tan31° ft
D) h = 45tan59° ft
52)A round cookie cake, divided into 8 equal pieces, has a diameter of 16 inches. Chase eats one piece of cake. What is the area of the piece of cake that Chase eats? Leave your answer in terms of pi.
A) 4π in2
B) 8π in2
C) 16π in2
D) 64π in2
53)If segment AC is a diameter of the circle what can you conclude about triangle ABC?
A) It is rightB) It is obtuseC) It is scaleneD) It is isosceles
54)Equilateral triangle PBJ is inscribed in a circle as shown. Determine the measure of arc PB.
A) 60°B) 90°C) 120°D) 200°
55) The circumference of a circle is 8π cm. What is the RADIUS of the circle?
A) 2 cm
B) 4 cm
C) 8 cm
D) 16 cm
56)Find x.
A) 4
B) 6.7
C) 7.2
D) 9
57)In the diagram, if EC = 8, ED = 6 and AE = 12 solve for EB.
A) 2
B) 4
C) 6
D) 8
58)Find m∠DOB.
A) 73°
B) 107°
C) 136°
D) 170°
59)A state park is designed in a circular pattern as shown. A park ranger drives along the circular path from the ranger station to the nature center and then from the nature center to the petting zoo. How far does he drive to the nearest tenth of a mile?
A) 1.7 milesB) 2.3 milesC) 3.7 milesD) 6.3 miles
60)In the neighborhood park there is a circular grassy picnic area, but half of the grass has died. The city wants to replant the grass, but needs to know the square footage of the damaged area. If the circular picnic area is 150 feet across, what is the square footage of the damaged area?
A) 8831.25 sq. feet
B) 17662.5 sq. feet
C) 35325 sq. feet
D) 70650 sq. feet
61) During play, a ball with a diameter of 3.00 inches splits exactly in half. What is the volume of each portion of the ball?
A) 1.75 in.3.
B) 3.52 in.3.
C) 7.05 in.3.
D) 14.1 in.3.
62) If the radius of a sphere is doubled, how does this affect the volume?
A) It will be one-half larger.
B) It will be two times larger.
C) It will be four times larger.
D) It will be eight times larger.
63) Mrs. Bergstedt found the mean of her 15 Algebra II students' latest test scores. It was 85. She thought this was exceptional and slightly skewed by Jill's grade, so she removed her test grade and found that the new mean was 84.
What was Jill's test grade?
A) 84
B) 85
C) 98
D) 99
64)Coach King is holding a free-throw shooting contest for some students in his PE class. The students participating in the contest shoot 50 free throws each. The results are shown in the table. What is the mean of the data?
A) 27
B) 33.2
C) 34.5
D) 45
65) Suppose two sets of data, A and B, have the same MIN and MAX values, but that the IQR for A is larger than the IQR for B. What can you CORRECTLY conclude about the two sets?
A) Set A has a lower median than set B.
B) Set A has a higher median than set B.
C) Set A is more clustered around the median.
D) Set A is more widely spread around the median.
66)Sam's grades are shown in the table. If quizzes, tests, and homework equally make up half the overall grade, while the final exam makes up the other half, what is Sam's overall average?
A) 84%
B) 85%
C) 86%
D) 87%
67)Jeffrey surveys the 13 girls and 13 boys in his class to find out how many pairs of shoes they have in their closets. Which statement is true?
A) The value of Q1 for the girls is greater than the value of Q1 for the boys.
B) The value of Q3 for the boys is greater than the value of Q3 for the girls.
C) The mean number of shoes for the boys is greater than the mean number of shoes for the girls.
D) The median number of shoes for the boys is greater than the median number of shoes for the girls.
68)The graph shows a scatterplot, along with the best fit line. The points A, B, C, and D are not part of the set. Adding which point will most DECREASE the value of the correlation coefficient?
69)Which equation is the BEST fit for the data in the graph?
A) y = x + 3B) C) D) y = x + 4
70)Which graph shows the line of best fit for the scatterplot?
71) When Danielle goes grocery shopping, she usually buys a gallon of milk and some dinner rolls. She has noticed that there seems to be a correlation between the price of milk and dinner rolls. In other words, when the price of milk goes up, the price of dinner rolls goes up, and when the price of milk goes down, the price of dinner rolls goes down. Which fact would lead you to believe that the relationship between the prices is not only a correlation, but also one of causation?
A) Whenever milk is on sale, dinner rolls are also on sale.
B) Milk and dinner rolls are often served during the same meal.
C) Milk is one of the major ingredients used to make dinner rolls.
D) The prices of milk and dinner rolls both move with the rate of inflation.
72)The graph shows the relationship between the distance a car travels and the time the car travels. Determine the rate of the car.
A) 25 mph
B) 50 mph
C) 75 mph
D) 150 mph