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Practice Test 31 - ACT Math

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

  1. Evaluate log⁡2(32)\log_{2}(32).
  2. What is the area of a circle with radius 3?
  3. A class has 10 students: 6 are wearing glasses and 4 are not. One student is chosen at random. What is the probability the student is not wearing glasses?
  4. What is the sum of the interior angles of a 9-sided polygon (nonagon)?
  5. What is f(0)f(0) for the function f(x)=7x+3f(x) = 7x + 3?
  6. A doctor wants to study whether people who drink coffee daily have different average blood pressure than people who do not. She reviews existing medical records and compares blood pressure for patients who already report drinking coffee daily versus those who do not. Is this an experiment or an observational study?
  7. Lines mm and nn are parallel (⇒) and a transversal tt intersects them. At line mm, an interior angle is labeled 115∘115^\circ. m ⇒ ─────────────── 115∘115^\circ\ \ \ t \ n ⇒ ─────────────── xx If lines mm and nn are parallel, what is the measure of angle xx?
  8. Which equation represents a line with a slope of -2 and a y-intercept of 4?
  9. Order the following numbers from least to greatest: −4-4, −2-2, 00, 22.
  10. A model rocket's height in feet after tt seconds is modeled by h(t)=−16t2+96th(t) = -16t^2 + 96t. What is the height, in feet, 4 seconds after launch?
  11. A class compares two 2×2 data matrices by subtracting them. What is A−BA-B if A=[4−201]A=\begin{bmatrix}4 & -2\\ 0 & 1\end{bmatrix} and B=[−132−4]B=\begin{bmatrix}-1 & 3\\ 2 & -4\end{bmatrix}?
  12. Which of the following values is closest to 4⋅103+3⋅10−24 \cdot 10^3 + 3 \cdot 10^{-2}
  13. A data table is doubled to reflect two weeks instead of one. If A=[5−1−32]A=\begin{bmatrix}5 & -1\\ -3 & 2\end{bmatrix}, what is 2A2A?
  14. In the standard (x,y)(x, y) coordinate plane, the graph of y=x2y = x^2 is shifted 3 units to the right and 2 units up. Which of the following is the equation of the new graph?
  15. If f(x)=x2+1f(x)=x^2+1, what is the value of f(2x)f(2x)? f(x)=x2+1f(x)=x^2+1, so f(2x)=(2x)2+1f(2x)=(2x)^2+1.
  16. What is log⁡10(100)\log_{10}(100)?
  17. For the function f(x)={x3,x<02x−4,0≤x<3(x−3)2−2,x≥3f(x)=\begin{cases} \dfrac{x}{3}, & x<0\\ 2x-4, & 0\le x<3\\ (x-3)^2-2, & x\ge 3 \end{cases} what is f(3)f(3)?
  18. A regular polygon has each interior angle measuring 120°. How many sides does it have?
  19. A scatterplot shows four points: (5, 2), (6, 4), (7, 3), and (8, 5). The x-axis is x (units) and the y-axis is y (units). Which point on the graph represents the condition x=8x=8?
  20. What type of triangle has one angle measuring more than 90°?

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