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Practice Test 49 - ACT Math

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

  1. Simplify: 4(2y−3)−y4(2y - 3) - y.
  2. To study the health effects of smoking, researchers follow smokers and non-smokers for 10 years. Is this an experiment or an observational study?
  3. In a circle with radius 1010 m, arc ABAB subtends a central angle of 45∘45^\circ. What is the length of arc ABAB?
  4. Solve by factoring: What are the solutions to x2−1=0x^2-1=0?
  5. A small club recorded the number of members who attended 8 weekly meetings: 20, 21, 22, 22, 23, 23, 23, 24. If one additional meeting had 32 attendees added to the data set, how would the mean change?
  6. A line has equation y=32x−6y=\dfrac{3}{2}x-6. A student says the slope is −6-6 because it is the number at the end. What is the actual slope of the line?
  7. A signal is modeled by the complex number −7+2i-7 + 2i. To compute a reciprocal later, you first need its complex conjugate. What is the complex conjugate of −7+2i-7 + 2i?
  8. If A=[[3,−2],[0,5]]A=[[3,-2],[0,5]] represents a simple linear transformation, what is 2A2A?
  9. If a $50 shirt is on sale for 30% off, what is the sale price?
  10. In simplifying a polynomial with complex coefficients, you multiply two binomials. What is (1−6i)(−3−2i)(1 - 6i)(-3 - 2i)? Use FOIL and apply i2=−1i^2=-1 to write the result as a+bia + bi.
  11. A line represents a constant change in a bank balance. The line has slope m=−1m=-1 and passes through the point (6,2)(6,2). What is the equation of the line in the form y=mx+by=mx+b?
  12. What is the value of xx if 2x=322^x=32?
  13. What is v+w\mathbf{v} + \mathbf{w} if v=⟨−2,5⟩\mathbf{v} = \langle -2, 5 \rangle and w=⟨3,7⟩\mathbf{w} = \langle 3, 7 \rangle?
  14. A gardener measured the heights (in inches) of 7 plants: 9, 10, 10, 11, 11, 11, 12. What is the mean of the data set?
  15. What is the solution set of the inequality 5−x≤25 - x \leq 2?
  16. A solution's acidity is measured on the pH scale, where pH=−log⁡10([H+])\text{pH}=-\log_{10}([H^+]). If [H+]=10−5[H^+]=10^{-5}, what is the pH?
  17. Which of the following represents f(x+2)f(x + 2) if f(x)=3x−1f(x) = 3x - 1?
  18. Simplify: 44\sqrt{44}
  19. A set of values is {2,2,3,4,4,4,5,5,6}\{2, 2, 3, 4, 4, 4, 5, 5, 6\}. Which best describes the shape of the distribution?
  20. What is the range of xx if ∣x−5∣<3|x - 5| < 3?

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