Practice Test 5 - 7th Grade Math

18 of the 20 questions below are in this test; the other 2 can't be scored yet. Answer them in any order, then submit to see your score and every explanation.

A standard die has 6 equally likely outcomes. What is the probability of rolling a 1? Then classify it as impossible, unlikely, equally likely, likely, or certain.
Emma wants to show that $4(x^2 + 3) - 2(x^2 + 3) = 2(x^2 + 3)$ . Which property allows her to factor out the common expression $(x^2 + 3)$ ?
A teacher wants to estimate the mean number of minutes students spend reading each night. Four random samples of 30 students each were taken, and the sample means were 22 minutes, 25 minutes, 24 minutes, and 23 minutes. Which statement best describes the sampling variability and a reasonable estimate of the population mean?
A student flips a fair coin 100 times and records 56 heads. Based on this data, what is the best estimate for $P(\text{heads})$ ?
Two numbers $M$ and $N$ have prime factorizations $M = 2^3 \cdot 5^2$ and $N = 2^2 \cdot 3 \cdot 5$ . The least common multiple (LCM) of $M$ and $N$ has the form $2^p \cdot 3^q \cdot 5^r$ . What is $p + q + r$ ?
A car travels at a constant speed of $55$ miles per hour. Let $d$ be the distance (in miles) and let $h$ be the time (in hours). Which equation represents this proportional relationship?
A science club says a homemade rocket launches successfully about 60% of the time. You want to simulate the compound event: in 3 launches, the rocket succeeds exactly 2 times. Which plan is a complete and correct simulation?
A science class records the elevation of a drone relative to the launch point (launch point is $0$ m). The drone rises $12\frac{1}{2}$ m, then drops $18.75$ m, then rises again by $\frac{2}{3}$ of $9$ m. What is the drone's final elevation relative to the launch point?
Two classes took the same quiz. The table shows each class's scores. Use the means and the ranges to decide whether the distributions have high overlap or noticeable separation. Which statement is correct?
The figure shows a trapezoid inscribed in a rectangle. What fraction of the rectangle's area is occupied by the trapezoid?
Two students are debating whether $(-3)^2$ and $-3^2$ represent the same value. Student A claims they're equal, while Student B claims they're different. Based on mathematical precision and order of operations, which student is correct?
A machine fills bottles at a rate of $\frac{7}{12}$ bottle per minute. At this rate, how long will it take to fill $35$ bottles?
Sarah claims that $x + 2x + 3x = (1 + 2 + 3)x$ demonstrates the distributive property. Is she correct?
The temperature difference between two cities is $23.8°F$ . If City $A$ has a temperature of $-12.3°F$ , and City $B$ is warmer, what is the temperature in City $B$ ?
A bag contains 5 red marbles, 3 blue marbles, and 4 green marbles. Two marbles are drawn without replacement. What is the probability that the first marble is red and the second marble is not red, expressed as a decimal?
A student has $45.00 in a wallet. They spend $18.50, then deposit $30.00. Next, they spend $\tfrac{1}{4}$ of the money they have at that point. How much money is left? (Round to the nearest cent.)
A student simplifies an expression for points earned in a game: $12x+18$ . Factor the expression completely by finding the greatest common factor (GCF).
In the expression $(2x + 4) + (3x + 1)$ , a student removes parentheses to get $2x + 4 + 3x + 1$ . Which property justifies this step?
Based on the dimensions shown in the diagram, what is the volume of the rectangular prism if its length is three times its width?
A student is explaining why $\sqrt{50} = 5\sqrt{2}$ . Which approach demonstrates the MOST thorough mathematical communication of radical simplification?

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