Practice Test 3 - PSAT Math

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

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1. A student solves the system $y=x^2+2x$ and $y=4x$ to find when a quadratic growth model matches a linear estimate. What is the product $x_1x_2$ of the $x$-values of all solutions?
2. A parabola is graphed on the coordinate plane and opens downward. Its vertex is at $(-1,4)$, and it crosses the $y$-axis at $(0,3)$. What are the $x$-intercepts of the parabola?
3. If $r$ and $s$ are the roots of $4x^{2}-12x+9=0,$ what is $r+s$ ?
4. A student needs an average of at least 85 on 4 tests. The first three scores are 82, 90, and 84. Let $x$ be the fourth test score. Which inequality shows the requirement?
5. The scatterplot above shows the relationship between a car's age, in years, and its resale value, in thousands of dollars, for 14 used cars. The curve of best fit is given by $V(a) = 28(0.85)^a$. Based on the model, what is the best approximation of the percent decrease in predicted resale value per year?
6. The relationship between the number of adult tickets $a$ and student tickets $s$ sold for a show is given by $12a+8s=480$, where 12 and 8 are the ticket prices in dollars and 480 is the total revenue. Rewrite the equation to solve for $s$ in terms of $a$.
7. On a coordinate plane, a polynomial $h(x)$ has $x$-intercepts at $x=-3$ and $x=2$. The graph crosses the axis at both intercepts. Which factor must be a divisor of $h(x)$? Do not confuse an $x$-intercept with a $y$-intercept.
8. A ball's height (in meters) after $t$ seconds is modeled by $h(t)=-5t^2+20t+1$. At what time does the ball reach its maximum height?
9. A ride-share company charges a $3.50 booking fee plus $1.25 per mile. Let $y$ be the total cost (in dollars) for a trip of $x$ miles. Which equation represents this relationship in slope-intercept form?
10. A circle has circumference $18\pi$ inches. What is the area of the circle, in square inches?
11. If $2(x-3)+5x=7x+k$ for all values of $x$, what is the value of the constant $k$? Distribute first, then compare the constant terms on both sides.
12. A runner's distance is modeled by $d=1.2t$, where $d$ is miles and $t$ is minutes. Which statement is true about the relationship?
13. Let $f(x) = -4x + 9$. What is the value of $f(-2)$?
14. A triangle has side lengths $7$ cm, $12$ cm, and $(x+2)$ cm. If these lengths form a valid triangle, what is the greatest integer value of $x$?
15. Which expression is equal to $(2\sqrt3+\sqrt5)^2\;?$
16. A line passes through $(1, -4)$ and $(6, 11)$. What is the equation of the line in slope-intercept form?
17. A right triangle has a 30^ angle, and the side opposite the 30^ angle is $5$ meters. What is the length of the hypotenuse?
18. On a coordinate plane, a triangle has vertices $A(1,1)$, $B(7,1)$, and $C(1,6)$. What is the area of triangle $ABC$ in square units?
19. A cylinder has radius $4\text{ cm}$ and height $15\text{ cm}$. What is the volume of the cylinder? Use $\pi$ in your answer.
20. Use the distance–time graph. During which time interval was the runner at rest?

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