Math Practice Test 1(New Format)

1.  A 20-sided die is rolled once. What is the probability that the die will land on a number that is a multiple of 4?

2. Which of the following expressions is equivalent to \( 3x^2 + 12x + 12\)?

3. When \(x=\frac{2}{3}\), what is the value of \(\frac{6x+2}{x}\)?

4. If \(\left|3x-7 \right|=8\), which of the following are the possible values of \(x\)?

5. The expression \((6a + 5b)(3a – b)\) is equivalent to:

6. 240 participants were asked their favorite cupcake flavor. 2⁄3 of the participants chose vanilla, 1⁄5 chose chocolate, and the rest chose “other.” How many participants chose a cupcake flavor in the “other” category?

7. Two gyms offer different membership plans. Gym A charges a $50 monthly fee and $5 per class attended. Gym B charges a $30 monthly fee and $7 per class attended. For both gyms, how many classes must be attended in one month for the total costs to be the same?

8. The perimeter of a rectangle is 42 inches, and the width of the rectangle is 8 inches. What is the length of the rectangle?

9. The distance from Dallas to Houston is 239 miles. Dana’s car averages 26 miles per gallon, and the gas station she stopped at before her trip charged $3.67 per gallon for gas. How much would it cost in gas for Dana to travel from Dallas to Houston?

10. In the standard (x,y)-coordinate plane, point D is the reflection of the point (4,3) over the y-axis. What are the coordinates of point D?

11. In the figure shown below, DE || FG, DE = 6, FG = 12, and DF = 8. What is the length of FH?

12. To get from her car to the park, Julia chose to walk along the paved path, which took her 6 yards west, 7 yards south, 18 yards west, and 3 yards south. How many fewer yards would she have walked if she had cut through the grass to go directly from the car to the park?

13. Which of the following expressions is equivalent to \((\frac{x}{16})^\frac{-3}{4}\)?

14. Ella paints her fence at a rate of 5 square meters per hour. If her fence is 35 square meters, how many minutes will it take her to paint the entire fence?

15. Carter is counting the money he earned at his lemonade stand. In his jar, he counted 12 quarters, 6 dimes, and 12 nickels. How many additional dimes would he need so the probability of randomly drawing a dime is 2⁄5 ?

16. What is the slope of a line, in the standard (x,y)-coordinate plane, that is perpendicular to y – 3x = -7?

17. \(\frac{2.14 \times 10^{42}}{4 \times 10^{53}} =?\)

18. The average height of a group of 6 students is 160 cm. If a new student is added to this group and the new average height becomes 162 cm, what is the height of the new student?

19. Line segment AB is a diameter of a circle. The coordinates of the center of the circle, O, are (3,-2), and the coordinates of point B are (6,4). What are the coordinates of point A?

20. Jordan is paving a rectangular patio that measures 12 feet wide by 15 feet long. He plans to use square pavers that measure 18 inches on each side. What is the minimum number of pavers Jordan must purchase to cover the entire patio?

21. What is the least common multiple of the first eight positive integers?

22. In trapezoid ABCD shown below, AD || BC and AB = CD. The measure of <ABC is 105^o. What is the measure of <ADC?

23. In the standard (x,y)-coordinate plane, the point (-2, 5) is on circle C, which is centered at (3, -1). What is the radius of circle C?

24. A water balloon is launched into a fenced-in pool area. The fenced area is a 35-foot by 50-foot rectangle, and the pool is a 14-foot by 28-foot rectangle. To the nearest percent, what is the probability that the water balloon lands in the pool?

25. What is the 275th digit after the decimal point in the repeating decimal \(0.\overline{2357}\)?

26. Given that \(f(x) = x^2 – 4\) and \(g(x) = x+ 3\), what are all the values of \(x\) such that \(f(g(x)) = 0\)?

27. At a school cafeteria, a student gets to choose one of five entrees, one of three vegetables, and one of two desserts. How many different combinations of meals are possible?

28. In the figure below, point E is the intersection of line segments AD and CB, AC || BD, and two angle measures are given. What is the measure of <BED?

29. In the complex number system where \(i^2 = -1, \mbox{$\frac {i}{3+i}$} \cdot \mbox{$\frac {i}{3-i}$}\) = ?

30. A mixing tank contains 75 liters of a mixture that is 80% hydrochloric acid by volume. How many liters of pure water should be added to the mixture so that the resulting solution is 60% hydrochloric acid by volume?

31. For all \(x\neq0\) and \(y\neq0\), \(\frac{x+y}{xy}=\) ?

32. A line through the origin and point (12, -5) is shown in the standard (x,y)-coordinate plane below. What is the value of sinθ?

33. If \( 81^{x-5} = \sqrt{3}^{(-4x+8)}, x = ?\)

34. A pizzeria defines its pizza sizes by the diameter of a pizza. If the pizzeria’s 10-inch pizza is cut into 8 equal slices, what is the arc length of each slice (the distance along the crust of each piece of pizza)?

35. A ball with a diameter of 6 centimeters is packed inside a cubic container with side lengths of 8 centimeters. What volume of the container, in cubic centimeters, is empty space?

36. A data analyst is studying the monthly sales (in thousands of dollars) of a small business over the past 8 months. The sales are recorded as follows:

12, 15, 20, 20, x, y, 35, and 40, where x and y are missing values.

• The mean of the dataset is 25.
• The median is 22.5.

What is the value of y?

37. A company sells a product and has a fixed cost of $2000 to operate plus a variable cost of $10 per item. The price per item sold is $50. What is the number of items that must be produced and sold for the company to break even?

38. A triangular plot of land has sides measuring 120 meters, 80 meters, and 100 meters. What is the measure of the angle opposite the 100-meter side, rounded to the nearest degree?

39. The 4th and 5th terms of an arithmetic sequence are 20 and 26, respectively. What is the 30th term of the sequence?

40. In the standard (x,y) coordinate plane, the solution set to a system of inequalities is shaded. What is the system of inequalities that corresponds to the graph?

41. In the figure below, a circle is centered at point O and AB is a diameter of the circle. Point C lies on the circle such that <ABC = 60 degrees. Point D lies on the circle in the same semicircle as C, and <AOD = 60 degrees.

What is the measure of <ACD?

42. A cosine function is shown in the standard (x,y)-coordinate plane below.

Which of the following equations represents this function?

43. Simplify the following expression: \(\frac{\frac{x}{x-3}-\frac{2x}{x+6}}{\frac{1}{x-3}+\frac{1}{x+6}}\)

44. Matrix A is defined as:

\(A = \begin{bmatrix} 3 & x \\ 2 & 4\end{bmatrix}\)

Matrix B is defined as:

\( B = \begin{bmatrix}1 & 2 \\ -1 & 0\end{bmatrix}\)

The product of A and B is:

\(AB = \begin{bmatrix} 7 & 6 \\ -2 & 4 \end{bmatrix}\)

What is the value of x?

45. A carnival game involves rolling a fair six-sided die and flipping a fair coin. The payouts are as follows:

1. If the coin lands on heads, the payout is equal to 3 times the number rolled on the die (in dollars).
2. If the coin lands on tails, the payout is equal to 2 times the number rolled on the die (in dollars).

What is the expected payout of the game?