More STAAR problems.
Administered May 2019
Read each question carefully. For a multiple-choice question, determine the
best answer to the question from the four answer choices provided. For a
griddable question, determine the best answer to the question.
16. Which expression is equivalent to (10 + 7r - r2) + (−6r2 − 18 + 5r)
F -7r2 + 2r + 8
G 7r2 + 12r + 8
H -7r2 + 12r - 8
J 7r2 + 2r - 8
Answer: H -7r2 + 12r - 8
Combine the like terms: r2 goes with r2, r goes with r, and constant goes with constant. Then, arrange them in standard order, which is from highest exponent to lowest.
10 + 7r - r2 + −6r2 − 18 + 5r
-r2 − 6r2 + 7r + 5r + 10 − 18
-7r2 + 12r − 8
17.Which graph best represents the solution set of y > 3x − 4?
[SEE IMAGE]
Answer: D
The inequality have a > sign, not a > sign. Therefore, it will have a broken (dotted or dashed) line to represent the boundary that is NOT part of the solution. And since it is "greater" and not "less than", the points above the line are the ones that have to be shaded.
That's Choice D.
18. A bank account earning annual compound interest was opened, and no additional deposits or
withdrawals were made after the initial deposit. The balance in the account after x years can
be modeled by b(x) = 850(1.025)x.
Which statement is the best interpretation of one of the values in this function?
F The initial balance of the account decreases at a rate of 97.5% each year.
G The balance in the account increases at a rate of 2.5% each year.
H The initial balance of the account was $1,025.
J The balance in the account at the end of one year is $850.
Answer: G The balance in the account increases at a rate of 2.5% each year.
Looking at the numbers in the equation:
850 represents the opening balance before any time has passed.
1.025 is the growth rate, which as a percentage is 102.5%. That means an additional 2.5% is being added to the balance
x is the number of years that pass, the more years, the bigger the balance.
The initial balance is increasing, not decreasing, so F is eliminated
2.5% is the rate of increase, so this is the answer.
The initial balance is $850. 102.5% represents the growth. Eliminate H.
The initial balance of $850 is at Year 0 before any time has passed. It is not the balance after one year. Eliminate choice J.
19. A company collected data for the number of text messages sent and received using a
text-message application since October 2011. The table shows the number of text messages
sent and received in billions over time. The data can be modeled by a quadratic function.
Which function bests models the data?
Which function best models the data?
A n(t) = −0.002t2 + 0.55t + 5.02
B n(t) = 0.072t2 − 0.15t + 2.73
C n(t) = −0.002t2 + 5.02
D n(t) = 0.072t2 + 2.73
Answer: B n(t) = 0.072t2 − 0.15t + 2.73
You have a few options here.
You can plot each of the four graphs in your calculator and do a visual check. You can enter the data into a table and do a quadratic regression. Or you can reason out which choices to eliminate.
For example, in Choices C and D, the middle coefficent, b is 0, so the vertex is 0. The positive x values are rising, so the t2 term can't have a negative coefficient. So C is eliminated.
Calculating -b/2a for A, we get -.55/(2(-0.002)) = 137.5. The values would be rising for x < 137.5, but the rate of change would be decresasing. Choice A can be eliminated.
Calculating -b/2a for B, we get -0.15/(2(0.072)) = 1.041666..., so this is also a possibility.
Now there are only two formulas to check.
0.072(40)2 - 0.15(40) + 2.73 = 111.93
0.072(40)2 + 2.73 = 117.93
Choice B is a better fit.
0.072(10)2 - 0.15(40) + 2.73 = 8.43
0.072(20)2 - 0.15(20) + 2.73 = 28.53
0.072(30)2 - 0.15(30) + 2.73 = 63.03
This look pretty close with the -0.15t middle term.
All of that said, I put all of the numbers into a Desmos quadratic regression calcuator and got the following results:
a = 0.0721429, b = -0.14881, c = 2.73214. Which is Choice B.
20. The graph of a linear function is shown on the grid.
What is the rate of change of y with respect to x for this function?
Record your answer and fill in the bubbles on your answer document.
Answer:
What is the rate of change? That is, what is the slope of this line?
= - 1.6 / 8 = -16 / 80 = -1 / 5 or -0.2.
More to come. Comments and questions welcome.
More STAAR problems.
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