ACT-aligned practice

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  1. A phone plan costs 37 dollars a month plus 15 cents per text. Maya wants a model for her monthly bill. Which is the best definition of the variable?
    1. Let n be the number of texts Maya sends in one month
    2. Let n be texts
    3. Let n be the cost of one text
  2. Solve 3x+3=−183x + 3 = -18. x=  ?x = \;?
  3. A survey asked 145 people whether they exercise weekly. Under 30: 22 yes, 43 no. Age 30 or over: 27 yes, 53 no. What proportion of the under-30s exercise weekly?
  4. f(x)=2x2+3f(x) = 2x^2 + 3. Find f(−3)f(-3).
  5. A table gives x=0,1,2,3x = 0, 1, 2, 3 and y=4,12,36,108y = 4, 12, 36, 108. What kind of relationship is it?
    1. Exponential: yy is multiplied by 3 at each step
    2. Linear: yy goes up by 8 at each step
    3. Neither
  6. A tile pattern has 6, 9, 14 and 21 tiles in steps 1 to 4 (a square of tiles plus 5 extra). How many tiles are in step 10?
  7. Solve x2=100x^2 = 100. Enter all solutions.
  8. Put the steps for constructing the perpendicular bisector of a segment AB of length 7 cm in order.
    • With the compass point on A, draw an arc with a radius of more than half of AB
    • Keep the same opening; with the point on B, draw an arc that crosses the first one twice
    • Label the two crossing points P and Q
    • Draw the line through P and Q with the straightedge
  9. △ABC≅△DEF\triangle ABC \cong \triangle DEF with AB=3AB = 3, BC=11BC = 11 and CA=18CA = 18. Find DEDE.
  10. Dilate A(3,1)A(3, 1) about the origin with scale factor 2. Tap its image.
  11. An isosceles right triangle has legs of length 8. Find the hypotenuse (exact).
  12. A cylinder of radius 4 is sliced by a plane parallel to its base. What shape is the cross section?
    1. A circle of radius 4
    2. A rectangle
    3. An ellipse
  13. Find the distance between (−1,−3)(-1, -3) and (2,1)(2, 1).
  14. A central angle measures 49∘49^\circ. Find an inscribed angle that intercepts the same arc (degrees).
  15. Two fair dice are rolled. Find the probability that the sum is 2.
  16. a1=3a_1 = 3 and an+1=2an−7a_{n+1} = 2a_n - 7. Find a3a_3.
  17. Expand (x+6)(x+9)(x + 6)(x + 9). What is the coefficient of xx?
  18. Evaluate 365236^{ \frac{ 5 }{2} }.
  19. A culture starts with 7 grams of algae. Each week, the amount is multiplied by 3. How many grams are there after 3 weeks?
  20. Evaluate log⁡1020+log⁡105\log_{ 10 } 20 + \log_{ 10 } 5 without a calculator.
  21. f(x)={x+3if x<53xif x≥5f(x) = \begin{cases} x + 3 & \text{if } x < 5 \\ 3x & \text{if } x \ge 5 \end{cases}. Find f(5)f(5).
  22. What kind of function is f(x) = 9 · 3^x?
    1. Exponential
    2. Polynomial
    3. Linear
  23. Convert 225∘225^\circ to radians. Give the exact value.
  24. The vector ⟨2,1⟩\langle 2, 1 \rangle starts at the point (1,1)(1, 1). Tap the point where it ends.
  25. A researcher measures the sleep of 376 randomly chosen teenagers and finds a mean of 7.1 hours. What is 7.1?
    1. A statistic: it describes the sample
    2. A parameter: it describes all teenagers
    3. The population
  26. A random variable X takes the values 0, 1 and 2, with P(X = 0) = 29/100 and P(X = 1) = 13/100. Find P(X = 2).
  27. What is the domain of f(x)=x−9f(x) = \sqrt{x - 9}? Give it as an interval.
  28. Describe the end behavior of f(x)=7x3f(x) = 7x^{ 3 }.
    1. As x→∞x \to \infty, f(x)→∞f(x) \to \infty; as x→−∞x \to -\infty, f(x)→−∞f(x) \to -\infty
    2. As x→±∞x \to \pm\infty, f(x)→∞f(x) \to \infty
    3. As x→∞x \to \infty, f(x)→−∞f(x) \to -\infty; as x→−∞x \to -\infty, f(x)→∞f(x) \to \infty
  29. Evaluate log⁡416\log_{ 4 } 16.
  30. Find the exact value of cos⁡(π6)\cos\left(\frac{\pi}{6}\right).
  31. sin⁡θ=15\sin\theta = \frac{1}{5} and θ\theta is in quadrant II. Find the exact value of cos⁡θ\cos\theta.
  32. Find the exact magnitude of v⃗=⟨6,−5⟩\vec{v} = \langle 6, -5 \rangle.
  33. Let A = (3−375)\begin{pmatrix} 3 & -3 \\ 7 & 5 \end{pmatrix} and B = (−4−4−55)\begin{pmatrix} -4 & -4 \\ -5 & 5 \end{pmatrix}. What is the entry in row 1, column 2 of A + B?
  34. x(t)=t+1x(t) = t + 1 and y(t)=t2y(t) = t^2. Tap the point where the curve is at t=1t = 1.
  35. What is the radius of the circle (x−9)2+(y+1)2=16(x - 9)^2 + (y + 1)^2 = 16?
  36. An arithmetic sequence has a1=14a_1 = 14 and common difference 2. Find a43a_{ 43 }.
  37. A distribution of incomes has mean 54 thousand dollars and median 43 thousand dollars. What is its most likely shape?
    1. Skewed right: a long tail of high values pulls the mean up
    2. Skewed left
    3. Symmetric
  38. How many inches are in 5 feet? (1 foot = 12 inches)
  39. Solve 7x+9y=237x + 9y = 23 for yy. y=  ?y = \;?
  40. Of 40 drivers who texted, 30 had a near-miss; of 40 who did not text, 10 had one. Is there an association between texting and near-misses in these data?
    1. Yes: 75% of texters vs 25% of non-texters had a near-miss
    2. No: both groups have 40 drivers
    3. Yes, and it proves texting causes near-misses
  41. Find the average rate of change of f(x)=3x2f(x) = 3x^2 from x=0x = 0 to x=6x = 6.
  42. A geometric sequence has a1=3a_1 = 3 and ratio 3. Find a4a_{ 4 }.
  43. Write (x+2)(x−3)(x + 2)(x - 3) in standard form ax2+bx+cax^2 + bx + c.
  44. Solve x(x−3)=0x(x - 3) = 0. Enter all solutions.