Math 161!
Algebra: Advanced Questions! Prerequisite: Math score of 600+ on most recent prac7ce exam
Course Description
In this micro-course, we’ll work through more challenging versions of practice problems involving basic concepts such as average, rate, ratios/proportions, and percent change. We’ll also work through more advanced concepts such as simultaneous equations, FOIL identities, exponents, absolute value inequalities, and multiple functions. !
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Formula Review
Don’t forget:! ! The SAT will provide you with formulas for area, volume, circumference and the properties of special right triangles. What the SAT won’t provide are these basic formulas, which you need to memorize:!
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Average = ! !If the average (arithmetic mean) of 2n, 7n, and 3n is 16, what is the value of n ? (A) (B) (C) (D) (E)
1 2 4 6 16
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Formula Review Distance =! Airplane 1 flew 510 miles in 3 hours. If Airplane 2 flew at two times the speed of Airplane 1, how many miles did it travel in 4 hours? (A) (B) (C) (D) (E)
340 680 1020 1360 2040
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Formula Review Percent Change =! An automobile factory made 4,500 cars in January. The factory then hired more workers, which caused its production to increase by 14% in February. How many cars did the factory make in February? (A) (B) (C) (D) (E)
9630 5130 3870 2050 630
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Formula Review Probability =! A high school principal forgot his coat in one of his school’s 180 classrooms. It is equally likely that his coat is in any of these 180 rooms. If exactly 30 of these 180 classrooms are used for math classes, what is the probability that his coat is in a math classroom? (A) (B) (C) (D) (E)
1 3 1 6 1 9 1 12 1 18
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Review Questions If ax2 = –ax for all values of x, what are all the possible values of a ? (A) 0 only (B) 1 only (C) –1 only (D) 0 and –1 only (E) 1, 0, and –1
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Review Questions A used car dealer assigns an initial price to every used car on the lot, and for every month that a certain car isn’t sold, the current price on that car is lowered by 10%. If the current price of a car is $3,645, and its price has been lowered three times by the dealer, what was the initial price, in dollars that the dealer originally assigned to the car? (A) $4,500 (B) $4,739 (C) $4,851 (D) $5,000 (E) $5,207
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Review Questions A museum charges different rates for adult and child tickets. If 2 adult tickets and 1 child ticket cost $18.50, while 1 adult ticket and 2 child tickets cost $16.00, what is the total cost of 3 adult tickets? (A) (B) (C) (D) (E)
$4.50 $7.00 $13.50 $21.00 $34.50
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Review Questions If (4ab)3 = [(a + b)2]3, which of the following must be true? (A) (B) (C) (D) (E)
a2 + b2 = 0 a2 + b2 = 2ab a2 = b2 a2 + b2 = 4ab a2 + 4ab + b2 = 0
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Review Questions If –1 ≤ x ≤ 1, then which of the following must be true? (A) 0 ≤ | x – 1| ≤ 1 (B) 0 ≤ | x | ≤ 1 (C) 0 ≤ | x + 1 | ≤ 1 (D) –x ≥ 0 (E)
1 ≥1 x
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Review Questions Let the function f be defined by f ( x) =
1 2 x +4. 3
If f (3p) = 8p, what is one possible value of p?
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Review Questions At a high school, the average age for the freshman class is 14, while the average age for the senior class is 18. If the average age of the two combined classes is 15, what is the ratio of the number of freshmen to seniors? (A) (B) (C) (D) (E)
2 5 1 3 7 12 3 1 3 2
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Review Questions If p is a positive integer, and 2 p-1 + 2 p+1 = n, what is the value of 2 p in terms of n? n−2 2 2n (B) 5 (C) 2n (D) 2n − 2 (A)
(E) n 2 − 1
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Review Questions Erica’s average rate going uphill was 80% of her average rate going downhill over the same route, and it took Erica 10 minutes longer to go up the hill than to go down the hill. What was the total number of minutes Erica spent going uphill and downhill? (A) 30 (B) 50 (C) 70 (D) 90 (E) 110
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Review Questions For all numbers a and b, let the operation ¤ be defined by a ¤ b = 2ab – 4a. If a and b are positive integers, which of the following can be equal to zero? I. a ¤ b II. (a – b) ¤ b III. b ¤ (a – b) (A) (B) (C) (D) (E)
I only II only III only I and II only I, II, and III
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Review Questions Edward and Jacob work on an assembly line that produces widgets. Edward can make 24 widgets in one hour, and Jacob can make 16 widgets, every half-hour. If they work together for 7.5 hours, how many widgets can they make? (A) (B) (C) (D) (E)
120 180 210 240 420
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Review Questions Let the function f (x) = 2x2 – 4x + 3. If q is a positive number such that f (2q – 1) = f (q), what is the value of q?
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Review Questions One week before New Years, the price of a television was increased by 20%. This new price was then reduced by 30% after New Years. What was the final price of the television as a percentage of the initial price? (A) (B) (C) (D) (E)
80% 82% 84% 88% 90%
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Review Questions If
−4
( ) x
= 16 , what does x equal?
1 4 1 (B) 2 (C) 1 (A)
(D) 2 (E) 4
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Review Questions If 44y = 163y – 2, what is the value of y ? (A) (B) (C) (D) (E)
1 2 3 4 5
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Review Questions If x2 + y2 = 40 and xy = 12, what is the value of (x + y)2 ? (A) (B) (C) (D) (E)
36 40 64 72 108
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Review Questions If (x + y)2 = 100 and xy = 24, what is the value of (x – y)2? (A) (B) (C) (D) (E)
2 4 5 16 25
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Review Questions Sam bought a shirt. Two years later, he sold the shirt to a second-hand store for 40 percent less than he paid for it. The store then added 20 percent onto the price it paid and resold it. What percent of the original price paid by Sam is represented by the price this last customer paid for the shirt? (A) 40% (B) 60% (C) 72% (D) 80% (E) 88%
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Review Questions If x2 – y2 = 12 and x + y = 3, what is the value of x? (A) 2 (B) 3 (C) 3.5 (D) 4 (E) 5
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Review Questions Let the function g be defined by g(x) = x + 2. If 4g(t) = 16, what is the value of g(2t)? (A) 2 (B) 6 (C) 18 (D) 32 (E) 34
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Review Questions The average of four integers is greater than 7 and less than 11. What is one possible value for the sum of these four integers?
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Review Questions There are three bags containing different quantities of marbles. If the ratio of marbles in the three bags is 3:2:1 and there are 30 marbles total in the bags, what is the greatest number of marbles that one bag could contain? (A) (B) (C) (D) (E)
3 5 15 20 30
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