Math Practice Test 2 (Untimed) – Outschool

1. The goal of a classroom fundraiser is $350. The class has already raised $110 and plans to raise $20 each week. What is the minimum number of weeks needed to reach the goal?

2. Similar polygons must have equal:

3. [latex](\dfrac{1}{27})^{-\dfrac{1}{3}}=?[/latex]

4. Which expression is equivalent to [latex](2x-5)^2[/latex]?

5. Three containers hold a total of 240 liters of water. The amounts in the containers are in the ratio 4:3:1. How many liters of water are in the container with the largest amount?

6. In a group of 60 customers at a cafe, 35 ordered coffee, 28 ordered tea, and 12 ordered both coffee and tea. How many customers ordered neither coffee nor tea?

7. A technician earns $18 per hour for the first 40 hours worked in a week and earns time-and-a-half for any additional hours. Which expression represents the technician’s total pay for working 46 hours?

8. When written in decimal form, which of the following is a terminating decimal?

9. If the side length x of a square garden satisfies the equation [latex]\sqrt{x}+5 = 7[/latex], what is the area of the garden?

10. Which of the following is a solution to [latex]x^2=-16[/latex]?

11. A grocery store freezer contains 28 tubs of chocolate ice cream, 23 tubs of vanilla, and 37 tubs of specialty flavors. Three tubs have to be removed to make room for a different frozen dessert. If the first tub removed is chocolate and the second tub removed is vanilla, what is the probability that the third tub removed will be a specialty flavor tub?

12. A factory models the total number of items produced using the linear equation P = 120 + 45t, where P is the total number of items produced and t is the number of hours the factory has been operating. The initial value represents items completed before the timed shift began.

Actual production totals are shown in the table below.

For which time was the absolute error between the model and the actual production the greatest?

13. The graph below shows the remaining fuel in a tank, in gallons, as a function of time, in minutes. Which of the following intervals represents the range of the function?

14. If [latex]i=\sqrt{-1}[/latex], then [latex]\mbox{$\dfrac {i^2+i^3+i^4}{i^4+i^5+i^6}$}[/latex] =?

15. What is the value of [latex]x+y[/latex]?

[latex]2x+3y = 13[/latex]

[latex]4x-y=5[/latex]

16. The function [latex]y=3\cos{(2\pi x)}[/latex] is graphed in the standard x,y coordinate plane for x in radians in the interval [latex]0\leq x \leq 1[/latex]. What are the period and amplitude of the function?

17. Solve for x:

[latex]a(x-4)=b[/latex]

18. A triangular sail [latex]\triangle ABC[/latex] has side lengths AB = 7ft, BC = 5ft, and AC=9ft. Which angle of the sail is the largest?

19.b if [latex]f(x) = 4x+1[/latex], what is its inverse[latex]f^{-1}(x)[/latex]?

20. The profit P in dollars, from selling x custom notebooks is modeled by:

[latex]P(x)=-2x^2+120x-800[/latex]

For what number of notebooks sold is the maximum profit achieved?

21. Triangle ABC has vertices A(0,0), B(6,0) and C(6,8).

Triangle DEF is similar to triangle ABC and has a base DE of length 9. What is the length of the corresponding height?

22. A temperature, T_x, in Town X ranges from -5^o to 7^o, and a temperature, T_y, in Town Y ranges from -8^o to 4^o. What is the greatest possible value of |T_x-T_y|?

23. For what value(s) of [latex]x[/latex] is the expression [latex]\dfrac{x+4}{x^2-16}[/latex] undefined?

24. A jar contains 4 red marbles and 6 blue marbles. Two marbles are drawn without replacement. What is the probability that both are red?

25. A student modeled a set of paired data with the equation [latex]f(x) = ax^2[/latex] where [latex]a = 2[/latex]. The student’s model and a scatterplot of the paired data are graphed in the standard (x,y) coordinate plane. Among the following possible changes to the student’s equation, which one will most improve the fit to the paired data?

26. In the figure below, a square lies inside a circle with center C and a radius of 6. All four vertices of the square touch the circle. Which is closest to the area of the shaded region?

27. A certain translation maps the point (2,4) to (0,4) and the point (7,-6) to (5,-6). This translation maps the point (-3, -5) to the point:

28. A certain game offers three possible payouts: $0, $50, and $200, each with a known probability. Which calculation gives the expected value of a game?

29. The number of bacteria in a culture decreases by the same percent each hour. Which type of model best represents this situation?

30. If [latex]n[/latex] is an even, rational number, which of the following statements about the number [latex]\sqrt{7} – \frac{n}{2}[/latex] must be true?

31. In the repeating decimal [latex]0.\overline{375}[/latex], which digit is in the 200th place?

32. One of the following is the equation of this graph in the standard (x,y) coordinate plane. Which one?

33. Event A consists of 18 simple outcomes. Event B consists of 12 simple outcomes. Exactly 5 simple outcomes are common to both events A and B.
Let:

• C = the intersection of A and B
• D = the union of A and B

Which of the following statements is true?

34. A solid cube has side length s. A second cube is constructed so that each edge is ¾ the length of the original cube. A third cube is constructed so that each edge is ¾ the length of the second cube. What is the ratio of the volume of the original cube to the volume of the third cube?

35. Line L₁ passes through the points (2,-1) and (6,7). Line L₂ is perpendicular to L₁. Which equation could represent L₂?

36. A population is modeled by [latex]P(t) = 500(1.08)^t[/latex], where [latex]t[/latex] is in years. When will the population first exceed 750?

37. If [latex]x+3[/latex] is a factor of [latex]2x^2+kx-15[/latex], what is the value of k?

38. A four-letter security code is formed using the letters A, B, C, D, and E. No letter may be repeated, and the first letter must be a vowel. How many different codes are possible?

39. If 25% of m equals a and b = 2a, what is 150% of m in terms of b?

40. What is the sum of the first 50 positive integers?

41. Find all asymptotes of [latex]y=\dfrac{5x^2}{x^2-4}[/latex].

42. How many terms are there when [latex](x+2y)^4[/latex] is expanded and like terms are combined?

43. A satellite dish is modeled by the equation [latex]\dfrac{x^2}{16} – \dfrac{y^2}{9} = 1[/latex]. The graph has an x-intercept at which of the following points?

44. A cone has a height of 8 and a slant height of 10 as shown below. What is its volume?

45. A normal distribution models the number of miles driven per week by employees at a company. The mean is 500 miles and the standard deviation is 50 miles.

A diagram of the distribution is shown below:

Which of the following is the value of P(450<X<600) to the nearest whole percent?