This exam was adminstered in June 2022.
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June 2022
Part I
Each correct answer will receive 2 credits.
1. Which correlation shows a causal relationship?
(1) The more minutes an athlete is on the playing field, the more goals
he scores.
(2) The more gasoline that you purchase at the pump, the more you
pay.
(3) The longer a shopper stays at the mall, the more purchases she
makes.
(4) As the price of a gift increases, the size of the gift box increases.
Answer: (2) C(x) = 35x + 245
As always, the word is "causal" as in "cause and effect", not "casual" as opposed to formal.
The one which shows cause and effect is buying more gas means you pay more money, which is Choice (2).
Choice (1) looks reasonable that athletes can't score goals unless they play more. But more time doesn't mean more goals (or runs or baskets or whatever). This could be confusing to anyone who doesn't know much about sports, but Choice (2) should be obviously better.
Choice (3) is similar to (1). The longer someone is in the mall, the more likely they might be to make purchases, but it isn't a cause and effect relationship.
Choice (4) is not cause and effect. The price of gift isn't related to its size.
2. Given f(x) = 3x - 5, which statement is true?
(1) f(0) = 0
(2) f(3) = 4
(3) f(4) = 3
(4) f(5) = 0
Answer: (2) f(3) = 4
Subtitute and evaluate each choice, although f(0) is "obviously" -5.
Choice (1), f(0) = 3(0) - 5 = -5. Eliminate Choice (1).
Choice (2), f(3) = 3(3) - 5 = 4. Choice (2) is the correct answer.
Choice (3), f(4) = 3(4) - 5 = 7. Eliminate Choice (3).
Choice (4), f(5) = 3(5) - 5 = 10. Eliminate Choice (4).
3. At Benny’s Café, a mixed-greens salad costs $5.75. Additional toppings can be added for $0.75 each. Which function could be used to determine the cost, c(s), in dollars, of a salad with s additional toppings?
(1) c(s) = 5.75s + 0.75
(2) c(s) = 0.75s + 5.75
(3) c(s) = 5.00s + 0.75
(4) c(s) = 0.75s + 5.00
Answer: (2) c(s) = 0.75s + 5.75
The word "each" signals that this is the amount that gets the variable. It is a recurring charge, an extra $0.75 for every ounce. There $5.75 is a one-time charge, so it's the y-intercept in the function. That means that the correct answer is Choice (2).
4. Which expression is equivalent to x2 + 5x - 6?
(1) (x + 3)(x - 2)
(2) (x + 2)(x - 3)
(3) (x - 6)(x + 1)
(4) (x + 6)(x - 1)
Answer: (4) (x + 6)(x - 1)
The products of each pair of constants in all four choices are -6. The sum of the constants has to be +5.
Choice (1), 3 - 2 = 1. Eliminate Choice (1).
Choice (2), 2 - 3 = -1. Eliminate Choice (2).
Choice (3), -6 + 1 = -5. Eliminate Choice (3).
Choice (1), 6 - 1 = 5. Choice (4) is the correct answer.
In Choice (4), there are two arrows coming out of the number six, meaning that (6, 10) and (6, 12) are in the same relation. This would cause it to fail the vertical line test.
5. Peter has $100 to spend on drinks for his party. Bottles of lemonade
cost $2 each, and juice boxes cost $0.50 each.
If x is the number of bottles of lemonade and y is the number of juice
boxes, which inequality models this situation?
(1) 0.50x + 2y < 100
(2) 0.50x + 2y > 100
(3) 2x + 0.50y < 100
(4) 2x + 0.50y > 100
Answer: (3) 2x + 0.50y < 100
The limit is $100. He has to spend less than that. Eliminate Choices (2) and (4).
Lemonade is represented by x and it costs $2.00, so the total cost is 2x. Eliminate Choices (1) and (2).
That leaves Choice (3), which is the correct answer.
6. Which domain is most appropriate for a function that represents the number of items, f(x), placed into a laundry basket each day, x, for the month of January?
(1) integers
(2) whole numbers
(3) rational numbers
(4) irrational numbers
Answer: (2) whole numbers
Only whole numbers of items can be placed in a laundry basket. You can't place half a shirt or negative socks.
7. What is the solution to 3/2 b + 5 < 17?
(1) b < 8
(2) b > 8
(3) b < 18
(4) b > 18
Answer: (1) b < 8
If you let b = 0, then you get 5 < 17, which is a true statement. That means that b = 0 is in the solution to the inequality. You can eliminate Choices (2) and (4).
If you check b = 10, then you get 3/2 (10) + 5 < 17, which is 20 < 17. This is not true, so b = 10 is NOT in the solution set. So b < 18 is not a correct inequality. Eliminate Choice (3).
3/2 b + 5 < 17
3/2 b < 12
(2/3) 3/2 b < 12 (2/3)
b < 8
8. Which table of values represents an exponential relationship?
Answer: (3) [See Image]
Exponential relationships have a common ratio. Each output is the same multiple of the previous output.
Choice (1) has a common difference. Each output goes up by 3. It is a linear relationship.
Choice (2) has a common difference. Each output goes up by 5. It is a linear relationship.
Choice (1) has a common ratio. Each output if 4 times the previous output. It is an exponential relationship. This is the correct answer.
Choice (4) has a common difference. Each output goes down by 2.5. It is a linear relationship.
More to come. Comments and questions welcome.
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