The following are some of the multiple questions from the recent January 2019 New York State Common Core Algebra I Regents exam.
The answers to Part II can be found here
The answers to Parts III and IV can be found here
Omitted images will be added soon.
Each correct answer is worth up to 2 credits. No partial credit. Work need not be shown.
1. The scatter plot below shows the relationship between the number of
members in a family and the amount of the family's weekly grocery
bill.
Answer: (2) $300
2. The function g(x) is defined as g(x) = -2x2 + 3x. The value of
g(-3) is
Answer: (1) -27
3. Which expression results in a rational number?
Answer: (3) SQRT(36) / SQRT(225)
4. The math department needs to buy new textbooks and laptops for
the computer science classroom. The textbooks cost $116.00 each, and
the laptops cost $439.00 each. If the math department has $6500 to
spend and purchases 30 textbooks, how many laptops can they buy?
Answer: (1) 6
5. What is the solution to the equation (3/5)(x + 4/3) = 1.04?
Answer: (2) 0.4
January 2019 Algebra I, Part I
The most appropriate prediction of the grocery bill for a family that consists of six memebers is
It should be obvious that $100 is too low and $500 is too high. $400 is close to the top end of the range for 7 family members, while $300 is at the top of the range for 5 family members and in the middle for 7.
g(-3) = -2(-3)2 + 3(-3)
g(-3) = -2(9) + (-9) = -18 - 9 = -27
The square root of 36 is 6. The square root of 225 is 15. The quotient of these numbers is 6/15 or 2/5 or 0.4.
This is a rational number.
In (1), the difference of these two irrational numbers will be irrational. IT WILL NOT BE SQRT(100)!!!!
In (2), the product will be irrational (25 times the square root of 2)
In (4), the sum will be 5 times the square root of 5, which is irrational.
439x + 116(30) < 6500
439x + 3480 < 6500
439x < 3020
x < 6.87....
They can get 6. Do NOT round up to 7.
You could also have checked each of the choices, multiplying by 439 and adding to 3480, to see which was the largest correct answer.
(3/5)(x + 4/3) = 1.04
(3/5)x + (3/5)(4/3) = 1.04
(3/5)x + 4/5 = 1.04
3x + 4 = 5.20
3x = 1.2
x = 0.4
I don't like problems that mix decimals and fractions, but what are you going to do?
6. The area of a rectangle is represented by 3x2 - lOx - 8. Which expression can also be used to represent the area of the same rectangle?
Answer: (1) (3x + 2)(x - 4)
Factor the polynomial. (Or multiply the choices.)
The constant term -8 indicates that one binomial has a + and the other has a -.
The middle term is -10. (3)(-4) + (2)(1) = -10, which is Choice (1).
7. Which relation does not represent a function?
Answer: (4)
In choice (4), each input in the relation is mapped to two outputs. This is not allowed in a function.
In choice (1), the input (x) does not repeat. It is not a linear function, but that isn't what the question asks.
In choice (2), an absolute value function is graphed.
In choice (3), every x has one y value associated with it. (The radical sign means the
positive square root, unless preceded by a plus-or-minus symbol.)
8. Britney is solving a quadratic equation. Her first step is shown below.
I. addition property of equality
II. commutative property of addition
III. multiplication property of equality
IV. distributive property of multiplication over addition
Answer: (4) II and IV
The Commutative Property allows rearranging the order of the terms on the left side.
The Distributive Property changed the right side of the equation.
9. The graph of y = (1/2)x2 - x - 4 is shown below.
Which of these points can determine the zeros of the equation y = (1/2)x2 - x - 4?
Answer: (3) A and C, only
The zeroes are the points where the parabola intersects the x-axis. Point B is the y-intercept.
10. Given the parent function f(x) = x3, the function g(x) = (x - 1)3 - 2 is the result of a shift of f(x)
Answer: (3) 1 unit right and 2 units down
The number inside the parentheses shifts the graph left or right. If there is a minus, the graph moves to the right.
The number outside the parentheses shifts the graph up or down. If it is a minus, the graph moves down.
11. If C = 2a2 - 5 and D = 3 - a, then C - 2D equals
Answer: (3) 2a2 + 2a - 11
Substitution and Distributive property. Then Combine Like Terms.
= (2a2 - 5) - 2(3 - a)
= 2a2 - 5 - 6 + 2a
= 2a2 + 2a - 11
12. Marc bought a new laptop for $1250. He kept track of the value of
the laptop over the next three years, as shown in the table below.
Years After Purchase Value in Dollars
1 1000 2 800 3 640
Answer: (4) f(x) = 1250(0.8)x
The laptop is decreasing in value, of choices (1) and (3) are incorrect -- they both show an increase in value. The initial value is $1250, not $1000, so choice (2) is incorrect.
You didn't have to calculate the 0.8, but 800/1000 = 0.8 and 640/800 = 0.8, which is the Common Ratio.
13. The height of a ball Doreen tossed into the air can be modeled by the function h(x) = -4.9x2 + 6x + 5, where x is the time elapsed in seconds, and h(x) is the height in meters. The number 5 in the function represents
Answer: (1) the initial height of the ball
When x = 0, h(x) = 5, which is the initial height of the ball.
14. The function f(x) = 2x2 + 6x - 12 has a domain consisting of the integers from -2 to 1, inclusive. Which set represents the corresponding range values for f(x)?
Answer: (2) {-16, -12, -4}
If the domain consists of integers from -2 to 1, then you need to calculate f(-2), f(-1), f(0) and f(1).
You can take a short cut by graphing the function and checking the Table of Values. You'll see that f(-2) = -16, which eliminates choices (1) and (3), and f(0) = -12, which eliminates (4).
15. Which equation has the same solution as x2 + 8x - 33 = O?
Answer: (1) (x + 4)2 = 49
Complete the square.
x2 + 8x - 33 = O
x2 + 8x = 33
x2 + 8x + (8/2)2 = 33 + (8/2)2
x2 + 8x + 16 = 33 + 16
(x + 4)2 = 49
16. The table below shows the weights of Liam's pumpkin, l(w), and
Patricia's pumpkin, p(w), over a four-week period where w represents the number of weeks. Liam's pumpkin grows at a constant rate. Patricia's pumpkin grows at a weekly rate of approximately 52%.
Assume the pumpkins continue to grow at these rates through week 13. When comparing the weights of both Liam's and Patricia's pumpkins in week 10 and week 13, which statement is true?
Answer: (3) Liam's pumpkin will weigh more in week 10, and Patricia's pumpkin will weigh more in week 13.
Liam's pumpkin is growing at a rate of 3.1 pounds per week. Over the next four weeks, it will be at 14.8, 17.9, 21.0, and 24.1 in Week 13.
Patricia's pumpkin is growing at a rate of 52%, so each week is 1.52 times the previous week. The next four entries will be (rounded to one decimal place): 13.3, 20.3, 30.8, and 46.9.
17. The function f(x) is graphed below.
Answer: (4) x > -1
Choice (1) is eliminated because the graph has a starting point at x = -1. It does not go forever to negative infinity.
If you picked Choice (3), you may have confused domain with range (and x with y).
Choice (2) makes no sense because it says "integers" when rational numbers are included. It also says "positive", even though the graph included the interval [-1, 0].
18. Which pair of equations would have (-1,2) as a solution?
Answer: (3) y = x2 - 3x - 2 and y = 4x + 6
No shortcut. Substitute and check if it makes a true statement.
Choice (1): (2) = (-1) + 2 but (2) =/= 2(-1). 2(-1) = 1/2 or .5
Choice (2): (2) =/= (-1) - 1 even though (2) = 2(1).
Choice (3): (2) = (-1)2 - 3(-1) - 2 = 1 + 3 - 2 = 2. Check.
And 2 = 4(-1) + 6 = -4 + 6 = 2. Check. Correct choice.
Choice (4): 2(-1) + 3(2) = -2 + 6 = 4. Check. 2 = (-1/2)(-1) - 3/2 = 1/2 - 3/2 = -1. Not true.
19. W The formula for electrical power, P, is P = I2R, where I is current and R is resistance. The formula for I in terms of P and R is
Answer: (2) an = 2.5(an-1)
There is no common difference, so it is NOT an arithmetic sequence. Choice (1) and (3) out.
Choice (4) makes not sense -- it has a1 in place of the common ratio. If the common ratio was a1, which is 8, that a2 would have to be 8 * 8 = 64, which it is not.
Choice (2) is the only one that makes sense. The common ratio is 20/8 = 2.5. Correct.
20. The formula for electrical power, P, is P = I2R, where I is current and R is resistance. The formula for I in terms of P and R is
Answer: (2) I = SQRT(P/R)
Literal equations.
We need to isolate the I, which includes getting rid of the exponent.
Divide by R: I2 = P/R
Square root: I = SQRT(P/R)
21. The functions f(x), q(x), and p(x) are shown below.
Answer: (4) f(x), q(x), and p(x)
p(4) = 3, from the table.
f(4) = 3, from the graph.
q(4) = (4 - 1)2 - 6 = 32 - 6 = 9 - 6 = 3
All three functions will equal 3.
22. Using the substitution method, Vito is solving the following system of equations algebraically:
2x - 3y = -21
Answer: (3) 2x - 3(-3x - 4) = -21
If y + 3x = -4, then y = -3x - 4, which can be substituted into the second equation in place of y.
Choices (1) and (2) replaced the x and then changed the y to an x. Crazy talk.
Choice (4) has an arithmetic mistake made when solving for y.
23. W Materials A and B decay over time. The function for the amount of material A is A(t) = l000(0.5)2t and for the amount of material B is B(t) = l000(0.25)t, where t represents time in days. On which day will the amounts of material be equal?
Answer: (4) every day
(0.5)2t is the same as ((0.5)2)t, which is the same as (0.25)t.
So A(t) = B(t), and the amounts will always be the same.
24. TThe following conversion was done correctly:
Answer: (4) inches per minute
Cross out the common units -- ones found both in the numerator and denominator.
Miles cancels mile
Hour cancels hour
Feet cancels foot.
You are left with inches in the numerator and minutes in the denominator.
End of Part I
How did you do?
Questions, comments and corrections welcome.
2 comments:
we were doing this practice test at school. I gave in my answer sheet and I'm at home checking my answers... I got a 22/24 um that's good ig :)
Only you know what's "good". If you're just looking to pass, that score is excellent! (That's more than enough to just pass.)
If you're looking for a specific grade, it's very good but you have to keep up the good work on the open-ended problems. Only this exam, you could miss 10 credits and still get curved to 90. You missed four at this point.
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