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.
11. A student worked out at a gym continuously for 50 minutes. The graph shows the remaining percentage of the workout as a linear function of x, the time in minutes.
Which answer choice best describes the domain and range of the function for this situation?
A Domain: All real numbers greater than or equal to 0 and less than or equal to 100
Range: All real numbers greater than or equal to 0 and less than or equal to 50
B Domain: {-2}
Range: {100}
C Domain: All real numbers greater than or equal to 0 and less than or equal to 50
Range: All real numbers greater than or equal to 0 and less than or equal to 100
D Domain: {100}
Range: {-2}
Answer: C Domain: All real numbers greater than or equal to 0 and less than or equal to 50
Range: All real numbers greater than or equal to 0 and less than or equal to 100
The domain is all of the possible x values. The range is all of the possible y values.
The domain goes from 0 to 50. The range goes from 0 to 100.
12.The graph of quadratic parent function f was transformed to create the graph of g(x) = f(x + 2) −5. Which graph best represents g?
[SEE IMAGE]
Answer: G
The parent function would have a vertex at the origin, (0, 0).
The transformation y = a(x - h)2 + k moves the graph h units to the left and k units up. However, in this equation, h is +2 and k is -5. We have to flip the signs. So the graph will move two spaces to the right and five units down.
13. Which expression is equivalent to (45 m-6p2v12) / (15 m-2p8v-4)
A (3 v8) / (m8p6)
B (3 v16) / (m4p6)
C (30 m3) / (p4p3)
D (30 v3) / (m3p4)
Answer: B (3 v16) / (m4p6)
Put whatever confusions or misconceptions you may have about exponents aside for one moment. The first thing you need to do is divide 45 by 15 and get 3. Eliminate Choices C and D immediately. If you subtracted 45 - 15 and got 30, you need to review the basics. (Harsh, maybe, and sorry, but very true.)
There are two rules that have to be used here. First, when you have the same variables with exponents in both the numerator and denominator, you subtract the exponents. Second, a negative exponent on top becomes a postive exponent by moving the variable to the bottom, and vice versa.
Let's subtract the exponents: m, -6 - (-2) = -4; p, 2 - 8 = -6; v, 12 - (-4) = 16
So we have m-4, p-6 and v16
Only the v is staying on top. The m and p go to the bottom.
The correct choice is B.
14.What is the positive solution to this equation?
Record your answer and fill in the bubbles on your answer sheet.
Answer:
First step in solving a quadratic equation is setting the equation equal to 0. Then we can either factor or use the quadratic formula.
4x2 + 12x - 135 = 0
Find ac: (4)(135) = -540
Are there factors of -540 that sum to +12?
(-2, 270), (-3, 180), (-4, 135), (-5, 108), (-6, 90),
(-9, 60), (-10, 54), (-12, 45), (-15, 36), (-18, 30) < -- This one.
4x2 - 18x + 30x - 135 = 0
At this point, I would usually draw a table, and do the box method in reverse. Instead, we'll work by grouping.
(4x2 - 18x) + (30x - 135) = 0
Find the Greatest Common Factor of each pair of terms, and factor it out.
2x(2x - 9) + 15(2x - 9) = 0
Factor (2x - 9) from each expression.
(2x - 9)(2x + 15) = 0
2x - 9 = 0 or 2x + 15 = 0
2x = 9 or 2x = -15
x = 4.5 or x = -7.5
The positive solution is 4.5.
NOTE: After you factor, if you aren't sure if you factored correctly, "FOIL" your answer and see if you got your original expression back.
(2x - 9)(2x + 15) = 4x2 - 18x + 30x - 135.
15. A grill at a barbecue restaurant will be used to cook sausage links that are 2 lb each and briskets that are 6 lb each. No more than 120 lb of sausage links and briskets will be cooked on the grill.
Which inequality represents all possible combinations of x, the number of sausage links that will be cooked on the grill, and y, the number of briskets that will also be cooked?
A 6x + 2y < 120
B 2x + 6y < 120
C 6x + 2y > 120
D 2x + 6y > 120
Answer: B 2x + 6y < 120
If x is the number of sausage links and each link weighs 2 lbs, then the weight of all the sausage links is 2x. Choices A and C are eliminated.
The weight needs to be "no more than" 120, which means "less than or equal to" 120. Only one choice has a "less than or equal to" symbol, and that's Choice B.
More to come. Comments and questions welcome.
More STAAR problems.
No comments:
Post a Comment