Practice Test 4 - 7th Grade Math

19 of the 20 questions below are in this test; the other one can't be scored yet. Answer them in any order, then submit to see your score and every explanation.

Jake draws one card from a standard deck of 4 cards {Ace, King, Queen, Jack} and then draws a second card without replacing the first. The tree diagram shows all possible outcomes. Which branch represents the probability path for drawing a King first AND a Queen second?
A bus travels 180 miles in 3 hours at a constant speed. Let $d$ be the distance (in miles) and let $t$ be the time (in hours). Which equation models this proportional relationship?
The trapezoid shown in the figure represents a cross-section of a swimming pool. If each unit represents 2 meters, what is the actual area of the cross-section in square meters?
Factor the expression $\frac{3}{5}x+\frac{6}{5}$ by taking out the greatest common factor.
A submarine starts at sea level and descends $150$ meters. It then ascends $\frac{2}{5}$ of the distance it descended. What is the submarine's final depth below sea level?
A student writes two expressions for points scored in a game: $\left(\frac{3}{4}x+5\right)$ and $\left(\frac{1}{2}x-3\right)$ . Simplify the sum $\left(\frac{3}{4}x+5\right)+\left(\frac{1}{2}x-3\right)$ .
After Sarah analyzes the given information, what should be her next step in formulating a plan to solve this problem?
A proportional relationship can be written as $y = \frac{3}{4}x$ . Which table correctly represents three coordinate pairs from this relationship, and what does the unit rate represent in this context?
A student is explaining why $\frac{2}{3} \div \frac{1}{4} = \frac{8}{3}$ . Which representation BEST communicates the reasoning behind division of fractions?
A student is given $\angle A=40^\circ$ , $\angle B=60^\circ$ , and the included side $AB=6\text{ cm}$ . The student constructs $\triangle ABC$ with a protractor and ruler. How many different triangles are possible with these conditions (up to congruence)?
On a calculator, $\frac{17}{12}$ displays as $1.41666667$ while $\frac{17}{11}$ displays as $1.54545455$ . A student notices both displays end differently than expected and concludes the calculator is malfunctioning. What should the student understand about these displays?
A basketball player makes a free throw with probability about 0.7. You want to simulate the compound event: the player takes 3 free throws and makes at least 2. Which simulation plan is best?
A company's profit in dollars is represented by $50x - 200$ , where $x$ is the number of items sold. How many items must be sold for the company to break even (profit = 0)?
A middle school student wants to find out which type of music is most popular among students at her school. She surveys 30 students who are standing in line at the school's music room during lunch. Which statement best describes a potential problem with this survey method?
At a movie theater, adult tickets cost $12 and student tickets cost $8. The theater sold 150 tickets and collected $1,520 in revenue. If $a$ represents adult tickets and $s$ represents student tickets, which equation represents the revenue constraint?
A cylinder is sliced by a vertical plane that passes through the center axis of the cylinder (straight down the middle). What 2D shape is the cross-section?
A circular sprinkler covers a region with radius $8$ feet. If the sprinkler head moves in a complete circle, approximately how far does it travel? Use $\pi \approx 3.14$ .
A spinner has four sections labeled A, B, C, and D. After 200 spins, the results were: A 70, B 50, C 60, D 20. Which probability model best matches the results?
A painter finishes $\tfrac{3}{5}$ of a wall in $\tfrac{1}{4}$ hour. At this rate, how many walls can the painter finish in 1 hour?
On a number line, Maria moves from position $\frac{3}{4}$ to position $-\frac{5}{8}$ . Using subtraction as adding the additive inverse, what is her displacement?

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