Practice Test 4 - PSAT Math

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

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1. A taxi ride costs a base fare of $4.50 plus $2.00 per mile. Let $m$ be the number of miles and $C$ be the total cost in dollars. What does the $y$-intercept represent in this context? Choose the interpretation that matches the model $C=2.00m+4.50$.
2. A function satisfies $f(0)=7$ and for each increase of 1 in $x$, the output is multiplied by 4. Which equation defines $f(x)$? Choose the exponential function with initial value 7.
3. The graph of a line is shown on a coordinate plane. It crosses the y-axis at $-2$ and the x-axis at $4$. Which equation represents the line? (A common error is using the reciprocal slope from swapping rise and run.)
4. A circle is inscribed in a square of side length $10$ inches (the circle is tangent to all four sides). What is the area of the region inside the square but outside the circle, in square inches? (Use $\pi$.)
5. A roller-coaster car travels the entire $1.2$-kilometer track in $90$ seconds at a constant average speed. What is this speed, to the nearest mile per hour?
6. The quadratic expression $x^{2}+4x+4$ is equivalent to which of the following?
7. The pressure on the ocean floor being studied is 3.2 atmospheres. What is this pressure in pascals? (1 atm = 101.3 kPa and 1 kPa = 1,000 Pa)
8. A point on a number line is $5$ units from $-2$. Which equation represents this situation, and what are the solutions?
9. Refer to the double-line graph shown, which displays monthly revenue (in thousands of dollars) for Store A and Store B from January through June. During which month was the percent difference between the stores' revenues the greatest (relative to the smaller value)?
10. In the figure, $\triangle ABC$ and $\triangle ADE$ share vertex $A$, with $D$ on $\overline{AB}$ and $E$ on $\overline{AC}$. Given $AD=4$, $AE=5$, $AB=10$, and $AC=8$, which statement correctly describes the relationship between these triangles?
11. The graph of the rational function $f(x) = \dfrac{ax + b}{x + c}$ is shown. What is the value of $a + b + c$?
12. A bakery tracked the number of cupcakes sold each day for 6 days: 34, 40, 41, 41, 43, 58. What is the range of the data set? (Some students mistakenly compute $Q_3-Q_1$ instead of max minus min.)
13. A line passes through $( -4, -9)$ and $(0, -1)$. What is the equation of the line?
14. A swimmer completes $1{,}200$ meters in $15$ minutes. What is the swimmer's speed in kilometers per hour? Use $1000$ m $= 1$ km and $60$ min $= 1$ hr.
15. Which expression is equivalent to $(2m-1)^2$ after expanding?
16. A class collected donations in $5 and $10 bills only. They collected 38 bills total worth $275. Let $f$ be the number of $5 bills and $t$ be the number of $10 bills. What is $(f,t)$?
17. A line is given by $6y-3x=12$. Which equation is equivalent and solved for $y$?
18. A coordinate plane shows the graph of $y=|x-1|-2$. Which statement correctly identifies a key feature of this function?
19. A student simplifies $(x^2-9) - (2x^2-5x+4) + (x-1)$. What is the resulting polynomial in standard form, and what is its degree?
20. Two lines, $\ell_1$ and $\ell_2$, are graphed on the coordinate plane. Line $\ell_1$ is $y=x+1$ and line $\ell_2$ is $y=-2x+7$. What is the solution $(x,y)$ to the system (the intersection point of the two lines)?​

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