Question 1 Topic 2.1 · Concept check
For i = √−1, what is the product (3 + 2i)(1 − i)?
A 3 − 2i B 1 + i C 5 − i D 5 + i
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Question 2 Topic 2.1 · Concept check
What is the value of 82/3 ?
A 16/3 B 4 C 2 D 12
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Question 3 Topic 2.1 · Concept check
Vectors u = ⟨2, −3⟩ and v = ⟨−1, 5⟩. What is u + v?
A ⟨1, 2⟩ B ⟨3, −8⟩ C ⟨1, −8⟩ D ⟨−2, −15⟩
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Question 4 Topic 2.1 · Concept check
What is the least common multiple of 12 and 18?
A 6 B 72 C 216 D 36
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Question 5 Topic 2.1 · Concept check
Which of the following numbers is irrational?
A 0.25 B √49 C √2 D 3/7
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Question 6 Topic 2.2 · Concept check
If 5(x − 2) = 3x + 6, what is the value of x?
A 2 B 8 C 4 D 16
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Question 7 Topic 2.2 · Concept check
Which expression is equivalent to (x + 3)2 ?
A x2 + 6x + 9 B x2 + 9 C x2 + 3x + 9 D 2x + 6
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Question 8 Topic 2.2 · Concept check
The lines y = 2x + 1 and y = −x + 7 intersect at which point?
A (5, 2) B (1, 3) C (6, 13) D (2, 5)
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Question 9 Topic 2.2 · Concept check
What is the sum of all solutions to the equation |x − 4| = 7?
A 11 B −3 C 8 D 14
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Question 10 Topic 2.2 · Concept check
Which inequality describes all values of x for which 3 − 4x ≤ 15?
A x ≤ −3 B x ≥ −3 C x ≥ 3 D x ≤ 3
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Question 11 Topic 2.2 · Apply it
A theater sold 50 tickets for a total of $480. Adult tickets cost $12 and student tickets cost $8. How many adult tickets were sold?
A 20 B 30 C 40 D 24
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Question 12 Topic 2.2 · Concept check
If x2 − 5x − 14 = 0 and x > 0, what is the value of x?
A 2 B 5 C 14 D 7
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Question 13 Topic 2.2 · Concept check
For nonzero x and y, which expression is equivalent to (6x3 y2 ) / (2xy)?
A 3x3 y B 4x2 y C 3x2 y D 3x4 y3
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Question 14 Topic 2.3 · Concept check
For f(x) = 3x2 − x, what is f(2)?
A 8 B 10 C 14 D 4
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Question 15 Topic 2.3 · Concept check
If f(x) = 2x + 1 and g(x) = x − 3, what is f(g(5))?
A 5 B 8 C 11 D 13
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Question 16 Topic 2.3 · Concept check
What is the domain of f(x) = √(x − 3) for real values of f(x)?
A x > 3 B All real numbers C x ≥ −3 D x ≥ 3
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Question 17 Topic 2.3 · Concept check
What is the value of log2 (32)?
A 16 B 4 C 5 D 6
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Question 18 Topic 2.3 · Apply it
A car worth $20,000 loses 15% of its value each year. Which function gives its value V, in dollars, after t years?
A V = 20,000(0.15)t B V = 20,000(0.85)t C V = 20,000 − 0.15t D V = 20,000(1.15)t
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Question 19 Topic 2.3 · Concept check
What is the 20th term of the arithmetic sequence 7, 11, 15, 19, …?
A 83 B 87 C 80 D 79
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Question 20 Topic 2.3 · Concept check
The graph of y = x2 is shifted 3 units to the right and 2 units up. Which equation describes the new graph?
A y = (x + 3)2 + 2 B y = (x − 2)2 + 3 C y = (x + 3)2 − 2 D y = (x − 3)2 + 2
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Question 21 Topic 2.3 · Concept check
What is the value of sin(π/6)?
A √3/2 B √2/2 C 1/2 D 1
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Question 22 Topic 2.4 · Concept check
What is the distance between the points (1, 2) and (4, 6) in the coordinate plane?
A 7 B 5 C √7 D 25
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Question 23 Topic 2.4 · Concept check
What is the midpoint of the segment joining (−2, 4) and (6, 0)?
A (2, 2) B (4, 4) C (8, −4) D (−4, 2)
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Question 24 Topic 2.4 · Concept check
What is the circumference of a circle with a diameter of 10?
A 25π B 100π C 5π D 10π
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Question 25 Topic 2.4 · Concept check
A triangle has a base of 12 inches and a height of 7 inches. What is its area, in square inches?
A 84 B 19 C 42 D 38
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Question 26 Topic 2.4 · Concept check
What is the sum of the interior angles of a hexagon?
A 540° B 720° C 1,080° D 360°
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Question 27 Topic 2.4 · Concept check
What is the volume of a cylinder with a radius of 3 and a height of 5?
A 45π B 15π C 30π D 75π
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Question 28 Topic 2.4 · Concept check
Which equation describes a circle with center (2, −1) and radius 4?
A (x + 2)2 + (y − 1)2 = 16 B (x − 2)2 + (y + 1)2 = 4 C (x + 2)2 + (y − 1)2 = 4 D (x − 2)2 + (y + 1)2 = 16
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Question 29 Topic 2.4 · Concept check
In a 30°-60°-90° triangle, the hypotenuse has length 10. What is the length of the side opposite the 30° angle?
A 10√3 B 5√3 C 5 D 20
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Question 30 Topic 2.5 · Concept check
A bag holds 4 red, 6 blue and 10 green marbles. One marble is chosen at random. What is the probability that it is blue?
A 6/14 B 3/10 C 1/6 D 3/5
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Question 31 Topic 2.5 · Concept check
The mean of five numbers is 12. Four of the numbers are 10, 14, 9 and 15. What is the fifth number?
A 12 B 10 C 14 D 48
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Question 32 Topic 2.5 · Concept check
What is the range of the data set 3, 8, 15, 4, 20?
A 15 B 8 C 20 D 17
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Question 33 Topic 2.5 · Concept check
In how many different orders can 4 different books be arranged on a shelf?
A 16 B 4 C 24 D 12
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Question 34 Topic 2.5 · Concept check
Two fair coins are tossed. What is the probability that both land heads up?
A 1/2 B 1/4 C 1/3 D 3/4
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Question 35 Topic 2.5 · Concept check
The probability of rain on Saturday is 0.3 and on Sunday is 0.4. If the two events are independent, what is the probability that it rains on both days?
A 0.12 B 0.7 C 0.35 D 0.58
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Question 36 Topic 2.6 · Apply it
After a 20% discount, a shirt costs $40. What was its original price?
A $48 B $32 C $60 D $50
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Question 37 Topic 2.6 · Apply it
A car uses 3 gallons of gas to travel 84 miles. At the same rate, how many gallons will it use to travel 140 miles?
A 4 B 6 C 5 D 7
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Question 38 Topic 2.6 · Apply it
A rectangular room is 12 feet by 15 feet. Carpet costs $3 per square foot. How much will it cost to carpet the whole floor?
A $81 B $540 C $180 D $162
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Question 39 Topic 2.6 · Apply it
A store raises the price of a jacket by 10% and later lowers the new price by 10%. Compared with the original price, the final price is:
A 1% lower. B the same. C 1% higher. D 10% lower.
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Question 40 Topic 2.6 · Apply it
A recipe that serves 4 people uses 2/3 cup of sugar. How many cups of sugar are needed to serve 10 people?
A 4/3 B 2 C 10/3 D 5/3
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Question 41 Topic 2.6 · Apply it
Maya drives 60 miles at 30 miles per hour and then another 60 miles at 60 miles per hour. What is her average speed for the whole trip, in miles per hour?
A 45 B 50 C 40 D 35
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Question 42 Topic 2.6 · Apply it
On a map, 1 inch represents 25 miles. How many miles do 3.5 inches represent?
A 75 B 87.5 C 100 D 28.5
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Question 43 Topic 2.6 · Apply it
A worker earns $15 per hour for the first 40 hours in a week and 1.5 times that rate for each hour over 40. How much does the worker earn for 46 hours?
A $735 B $690 C $1,035 D $825
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Question 44 Topic 2.6 · Concept check
A square has an area of 49 square units. What is its perimeter, in units?
A 14 B 49 C 7 D 28
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Question 45 Topic 2.6 · Apply it
A rectangular garden is twice as long as it is wide, and its perimeter is 60 feet. What is its area, in square feet?
A 100 B 300 C 200 D 180
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