Practice Test 2 - PSAT Math

20 questions. Answer them in any order, then submit to see your score and every explanation.

The perimeter of a rectangle is equal to the perimeter of a regular pentagon. The length of the rectangle is 4 cm more than its width, $w$ . The side length of the regular pentagon is equal to the width of the rectangle. What is the length of the rectangle?
A line is graphed on the coordinate plane. It crosses the $y$ -axis at $-1$ and rises 2 units for every 1 unit it moves to the right. Which equation represents the line?
The graph shown represents the function $f(x) = a(x-h)^2 + k$ , where $a$ , $h$ , and $k$ are constants. Based on the graph, what is the value of $f(1) + f(5)$ ?
A recipe uses 2.5 cups of flour to make 20 muffins. At this same rate, how many cups of flour are needed to make 32 muffins?
A polynomial is shown on the coordinate plane. It crosses the x-axis at $x=-2$ and $x=3$ and touches the x-axis at $x=1$ . Which polynomial could match the graph if the leading coefficient is positive?
A scientist studied 24 mice and randomly assigned 12 to receive a new medicine and 12 to receive a placebo. After treatment, the medicine group had a lower average symptom score. Which statement is most justified?
Refer to the figure. In $\triangle LMN$ , side $LM$ is extended through $M$ to point $P$ . If $\angle LMP = 7z + 9$ degrees, $\angle L = 47$ degrees, and $\angle N = 3z + 2$ degrees, what is the measure of $\angle N$ ?
On a coordinate plane, $A(1,1)$ , $B(4,5)$ , and $C(7,1)$ form triangle $ABC$ . Which statement is true?
A store's online sales follow $S(t)=150\cdot 1.2^t$ , where $t$ is weeks. Which best describes the growth rate? Interpret $1.2$ as a weekly multiplier.
In the coordinate plane, a circle has equation $(x-3)^2+(y+2)^2=49$ . Which of the following gives the center and radius of the circle?
The expression $x^{2}+10x+25-(x^{2}-6x+9)$ is equivalent to which of the following?
Two triangles are similar. In triangle $ABC$ , $AB=6$ and $BC=9$ . In similar triangle $DEF$ , the side corresponding to $AB$ is $DE=10$ . What is the length of the side corresponding to $BC$ , $EF$ ?
A car's fuel economy is rated at 30 miles per gallon. What is the equivalent rating in kilometers per liter? (1 mile = 1.609 km and 1 gallon = 3.785 L)
A class collects $180 total from a fixed fee of $30 plus $x$ dollars per student. If there are 10 students, then $30+10x=180$ . What is $x$ ?
A full fuel tank holds 50 liters. If the volume decreases by 7\% each minute, which function gives the number of liters $V(t)$ remaining $t$ minutes after the leak begins?
Solve the equation $\sqrt{2x-1}+1=5$ . Be careful not to divide the radical incorrectly; isolate the radical first, then square both sides, and confirm the solution satisfies the original equation.
A researcher measured the number of hours 40 college students studied for a midterm and their exam scores. The scatterplot shows a positive trend: students who studied more tended to score higher, though points are spread out. The researcher claims, "Studying more guarantees a higher score for any student." Which statement best evaluates this claim?
A company's cost to produce $x$ items is $C=150+7x$ . What is the value of $x$ when $C=381$ ?
On the coordinate plane, the line $y=x+2$ and the parabola $y=x^2$ are graphed. How many solutions does the system have (that is, how many intersection points are there)?
Which expression is equivalent to $\sqrt{12x^2y^3}$ for $x\ge 0$ and $y\ge 0$ ? Make sure your answer has no perfect-square factors left under the radical; a common error is forgetting that $\sqrt{x^2}=x$ only because $x\ge 0$ is given.

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