Practice Test 8 - PSAT Math

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

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1. A model car is built at a scale of $1:24$ (model:actual). The model's length is 18.5 cm. What is the actual length of the car, in centimeters?
2. The parabola $y=-2x^2+8x-3$ is graphed on the coordinate plane. What is the axis of symmetry of this parabola? Do not confuse the axis of symmetry with the $y$-intercept or with the vertex's $y$-coordinate.
3. Refer to the figure. From point $P$ outside circle $O$, secants $PAB$ and $PCD$ are drawn with points $A$ and $C$ on the circle and $B$ and $D$ on the far side of the circle. If $PA=3$, $AB=9$, and $PC=4$, what is the length of $CD$?
4. Solve the compound inequality $2x-7<-1$ AND $x+4\ge 6$. Which set of values satisfies both conditions?
5. A factory produces $2.16\times10^{6}$ bolts each day. About how many bolts does the factory produce each second? (1 day = 86,400 seconds)
6. A line has slope $-4$ and passes through the point $(3, 2)$. Which equation is the line written in point-slope form?
7. On a coordinate plane, a line passes through the points $(-2,3)$ and $(4,-9)$. Which equation represents the line in slope-intercept form $y=mx+b$? Several options have the correct slope but an incorrect intercept.
8. Solve the system algebraically: $y=x^2-4x+1$ and $y=-x+3.$ How many real solutions does the system have?
9. Consider the polynomial $p(x)=(x-4)^2(x+1)$. Which statement correctly identifies the zeros and the total number of x-intercepts the graph can have, accounting for multiplicity?
10. A radioactive sample has mass $M(t)=50(0.8)^t$ grams after $t$ days. What is $M(3)$? Compute using the exponential decay factor.
11. The function $f$ is linear and satisfies $f(1)=9$ and $f(5)=1$. What is the value of $f(3)$? Incorrect approaches often compute the slope correctly but apply it from the wrong starting point.
12. A recipe uses 2.5 cups of flour to make 20 muffins. At this rate, how many cups of flour are needed to make 32 muffins?
13. Which of the following is an equation of the line perpendicular to $y=-4x+7$ that passes through the point $(3,1)$ ?
14. A cross-country team recorded the number of minutes each runner took to finish a short course: 18, 19, 19, 20, 21, 22, 60. The coach wants a single measure of center that best represents a "typical" finishing time for the group. Which statement is true about the mean and median of this data set, and which measure is less affected by the outlier 60?
15. A delivery service charges a base fee plus a constant amount per mile. The relationship between miles $m$ and cost $C$ is shown by the line on the graph passing through $(0, 6)$ and $(10, 26)$. What is the base fee?
16. A number line shows closed circles at $-1$ and $3$ with shading outside the interval (left of $-1$ and right of $3$). Which compound inequality matches the graph?
17. Refer to the figure. From point $T$ outside the circle with center $C$, two segments $TA$ and $TB$ are drawn tangent to the circle at $A$ and $B$, respectively. If $TA=12\text{ cm}$, what is the length of $TB$?
18. Solve for $x$: $\dfrac{3}{5}x+\dfrac{1}{2}=\dfrac{1}{10}x+\dfrac{7}{2}$. What is the value of $x$?
19. A principal compares attendance rates before and after installing new hallway posters encouraging attendance. Attendance rose from 93% to 95%. No other data were collected, and the change happened during a month with fewer illnesses. Which conclusion is most appropriate?
20. A circular track has radius $50$ meters. A runner completes $\tfrac{3}{5}$ of a lap. What distance did the runner travel, in meters?

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