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2018 April(A09) Math Question 1

Equation of a Line

- Equations that Describe a Line

1. A line in the standard (x,y) coordinate plane passes through the points (-2,-6) and (5,3). The slope of the line:

Choice A

$s l o p e = \frac{3 - (- 6)}{5 - (- 2)} > 0$

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2018 April(A09) Math Question 2

Number Types & Properties

- Complex Number

Choice J

(3 - 4i) + (5 + 3i) = 8 - I

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2018 April(A09) Math Question 3

Ratios, Proportions, Percentages, Fractions

- Proportions & Ratios

3. Last year at RT University, the ratio of the number of students accepted to the number of students applying for admission was 2 to 7. RT University accepted 630 students last year. Flow many students applied to RT University last year?

Choice C

$\frac{630}{x} = \frac{2}{7}$ $x = \frac{630 \times 7}{2} = 2205$

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2018 April(A09) Math Question 4

Angles

- Collinear Points & Triangles

Choice K

x = 40 + (180-150) = 70

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2018 April(A09) Math Question 5

Perimeter, Area, Volume

- Triangles, Squares, Rectangles, Circles

5. A carnival game is played using an open box with a rectangular bottom measuring 6 inches by 13 inches. A square with side lengths of 4 inches is painted on the bottom of the box. The game is played by dropping a small bead into the open box. if the bead conies to rest in the painted square, the player wins a prize. Assuming a bead dropped into the box comes to rest at a random spot on the bottom of the box, which of the following is closest to the probability that the bead comes to rest in the painted square?

Choice C

$p = \frac{4 \times 4}{6 \times 13} \approx 0.21$

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2018 April(A09) Math Question 6

Equation of a Line

- Equations that Describe a Line

6. What is the slope-intercept form of 9x — y 5 = 0 ?

Choice H

$9 x - y - 5 = 0$ $\Rightarrow 9 x - 5 = y$ $\Rightarrow y = 9 x - 5$

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2018 April(A09) Math Question 7

Ratios, Proportions, Percentages, Fractions

- Proportions & Ratios

Choice A

$X Y = 5 k$ $Y Z = 9 k$ $\Rightarrow X Z = 14 k$ $\Rightarrow \frac{X Y}{X Z} = \frac{5 k}{9 k} = \frac{5}{9}$

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2018 April(A09) Math Question 8

Inequalities

- Inequality Expressions

8. The solution set of 2x + 4 —8 is the set of all real values of .v such that:

Choice G

$2 x + 4 \geq - 8$ $\Rightarrow 2 x \geq - 8 - 4$ $\Rightarrow x \geq \frac{- 8 - 4}{2}$ $\Rightarrow x \geq - 6$

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2018 April(A09) Math Question 9

Exponents, Radicals, & Scientific Notation

- Exponent Expressions

9. Which of the following is equivalent to (a3)2′ ?

Choice E

$(a^{3})^{21} = a^{3 \times 21} = a^{63}$

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2018 April(A09) Math Question 10

Algebraic & Function Expressions

- Solve Function Expressions

10. If f(x) 3×2 + 7x — 8, then f(-3) = ?

Choice G

$f (- 3) = 3 (- 3)^{2} + 7 (- 3) - 8 = - 2$

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2018 April(A09) Math Question 11

Perimeter, Area, Volume

- Triangles, Squares, Rectangles, Circles

11. Two sides of a triangle are equal in length. The third side is 3 centimeters longer than either of the other 2 sides. Given that the perimeter of the triangle is 93 centimeters, what is the length, in centimeters, of the longest side?

Choice D

$2 a + (a + 3) = 93$ $a = 30$ $a + 3 = 33$

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2018 April(A09) Math Question 12

Sequences and Patterns

- Arithmetic Sequences

12. The 220 graduating seniors of Madison- High School will sit in the center section of the school auditorium at the graduation ceremony. How many rows of seats will be needed to seat all of the graduating seniors if the first row has 10 seats and each succeeding row has 2 more seats than the previous row?

Choice G

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2018 April(A09) Math Question 13

Equation of a Line

- Distance & Midpoint

13. In the standard (x,y) coordinate plane, the point (3,-7) is the midpoint of the line segment with endpoints (9, -11) and:

Choice B

$\frac{9 + x}{2} = 3$ $\frac{- 11 + y}{2} = - 7$ $\Rightarrow x = - 3, y = - 3$

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2018 April(A09) Math Question 14

Word Problems

- 2 Variable Addition

14. A community theater group performed at 5 local schools. For each school, the table below shows the total number of tickets sold and the total dollar amount collected from ticket sales. At School A, only 2 types of tickets were sold: premium tickets for $10 each and value tickets for $6 each. How many value tickets were sold at School A ?

Choice J

$t + v = 200$ $10 t + 6 v = 1400$ $\Rightarrow t = 50, v = 150$

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2018 April(A09) Math Question 15

Word Problems

- Fixed Cost + Variable Cost

15. The theater group had to pay each school a facility charge. For use of its facility, School C charged the theater group 10% of the ticket sales and a fixed fee of $200. How much money did School C charge the theater group for use of its facility?

Choice E

$10 % \times 1800 + 200 = 380$

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2018 April(A09) Math Question 16

Statistics

- Mean, Median, Mode Combinations

16. What is the difference between the median and the mean number of tickets sold at the 5 schools?

Choice K

$m e d i a n = 250$ $m e a n = \frac{200 + 250 + 300 + 150 + 275}{5} = 235$ $\Rightarrow m e d i a n - m e a n = 250 - 235 = 15$

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2018 April(A09) Math Question 17

Perimeter, Area, Volume

- Triangles, Squares, Rectangles, Circles

17. What is the area, in square decimeters, of a right triangle with side lengths of 10 dm, 26 dm, and 24 dm ?

Choice E

$A r e a = \frac{10 \times 24}{2} = 120 d m^{2}$

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2018 April(A09) Math Question 18

Statistics

- Mean, Median

18. The mean of a list of 7 numbers is 85. The first 6 numbers on the list are 82, 93, 68, 93, 70, and 98. What is the 7th number on the list?

Choice J

$M e a n = \frac{82 + 93 + 68 + 93 + 70 + x}{7} = 85$ $\Rightarrow x = 91$

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2018 April(A09) Math Question 19

Trigonometry

- Pythagorean Theorem & sin cos tan

19. Which of the following is the sine of the smallest angle in a right triangle with side lengths 7, 24, and 25 inches, respectively?

Choice A

$\sin A = \frac{7}{25}$

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2018 April(A09) Math Question 20

Perimeter, Area, Volume

- Triangles, Squares, Rectangles, Circles

20. In the figure shown below, all angles are right angles, and the side lengths given are in feet. What is the area, in square feet, of the figure?

Choice G

The longer length of the smaller rectangle (S2) = 12-5=7

$T o t a l a r e a = S 1 + S 2 = 10 \times 5 + 3 \times 7 = 71$

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2018 April(A09) Math Question 21

Perimeter, Area, Volume

- Triangles, Squares, Rectangles, Circles

21. A triangle has a perimeter of 26 cm and sides of length x cm, (x + 3) cm, and (x + 5) cm. What is the value of x?

Choice A

x+(x+3)+(x+5)=26 => x=6

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2018 April(A09) Math Question 22

Word Problems

- Distance, Speed, Time

22. A truck sprang a leak in its radiator, which held 480 ounces of fluid when it started to leak. Assuming the truck continues at 35 mph and its radiator leaks 4 ounces of fluid per minute, how many miles will the truck travel before the radiator is empty?

Choice J

$$t=\frac{480}{4}=120 \ minutes = 2 …

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2018 April(A09) Math Question 23

Algebraic & Function Expressions

- Systems of Equations

23. An ice cream shop sells ice cream cones with exactly 1 of 3 ice cream flavors in the cone. The 3 flavors are vanilla, chocolate, and strawberry. Last Saturday, the shop sold 42 cones. It sold I 1 more with chocolate than with vanilla and 2 more with vanilla than with strawberry. How many cones with strawberry ice cream did the shop sell that Saturday?

Choice A

v+c+s=42

c=v+11

v=s+2

=> c=s+13 …

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2018 April(A09) Math Question 24

Similar Triangles & Types of Triangles

- Similar Triangles

24. In ABC below, D is the midpoint of CB, ZABC is a right angle, AB = 8 m, and AC = 10 m. What is AD, in meters?

Choice G

$B C = \sqrt{A C^{2} - A B^{2}} = \sqrt{10^{2} - 8^{2}} = 6$ $B D = \frac{B C}{2} = 3$ $\Rightarrow A D = \sqrt{B D^{2} + A B^{2}} = \sqrt{3^{2} + 8^{2}} = \sqrt{73}$

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2018 April(A09) Math Question 25

Graphing Properties

- Interpret Graphs or Figures

25. Lyman has plotted 5 points in the standard (.v,y) coordinate plane below. He then plots a new point as follows: the x-coordinate of the new point is the mean of the .v-coordinates of the 5 points already plotted; the y-coordinate of the new point is the mean of the y-coordinates of the 5 points already plotted. Which of the following ordered pairs gives the coordinates of Lyman’s new point?

Choice C

$x = \frac{(- 2) + (- 1) + (- 2) + 1 + 4}{5} = 0$ $y = \frac{4 + 1 + (- 2) + (- 1) + (- 2)}{5} = 0$

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2018 April(A09) Math Question 26

Sequences and Patterns

- Geometric Sequences

26. The 1st and 2nd terms of a certain geometric sequence are 10 and —5, respectively. What is the 5th term of the geometric sequence?

Choice H

$$10, -5, \frac{5}{2}, -\frac{5}{4}, \frac{5}{8}, …

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2018 April(A09) Math Question 27

Word Problems

- 1 Variable Equations

27. Alani works 8 hours per day 5 days each week at a custom embroidery shop. Each day Alani is paid either $1.00 per shirt that she stitches or $10.00 per hour, whichever daily amount is higher. Alani stitched the following numbers of shirts: 60 on Monday, 52 on Tuesday, 85 on Wednesday, 80 on Thursday, and 90 on Friday. What is Alani’s total pay for these 5 days?

Choice C

Monday:

The daily amount for …

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2018 April(A09) Math Question 28

Quadratic Equations

- Factoring

28. Which of the following most precisely describes the roots of the equation 5×2 + 7x + 2 = 0 ?

Choice H

To find the roots of …

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2018 April(A09) Math Question 29

Trigonometry

- Pythagorean Theorem & sin cos tan

29. Paula is planning a course for a bike race. The course is in the shape of a right triangle, as shown below. Participants will begin at A, ride directly to B, then directly to C, and directly back to A. Paula wants to put a rest stop at the halfway point on the course. How many miles past B will the rest stop be?

Choice D

$B C = \sqrt{A B^{2} + A C^{2}} = 13$

Total distance of the …

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2018 April(A09) Math Question 30

Ratios, Proportions, Percentages, Fractions

- Percents & Fractions

30. Adams High School has 120 students, and 1/3 of thestudents are taking Literature. Of the students NOT taking Literature, I are taking Composition. No students are taking both Literature and Composition. How many students are taking Composition?

Choice G

The number of students NOT …

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2018 April(A09) Math Question 31

Exponents, Radicals, & Scientific Notation

- Radical Expressions

Choice D

$\sqrt{x} + 3 = 6$ $\Rightarrow \sqrt{x} = 3$ …

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2018 April(A09) Math Question 32

Trigonometry

- Pythagorean Theorem & sin cos tan

32. In the right triangle AABC shown below, the length of

Choice H

$\sin A = \frac{3}{4} = \frac{B C}{A B} = \frac{12}{A B}$ …

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2018 April(A09) Math Question 33

Logarithms

- Logarithm Expressions

Choice A

$3 (\log_{2} 16) = 3 (\log_{2} 2^{4}) = 3 (4) = 12$

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2018 April(A09) Math Question 34

Probability

- One Event

34. A bag contains several marbles. On 3 successive draws with replacement, a red marble is drawn from the bag each time. Which of the following statements must be: true about the marbles in the bag?

Choice F

F. is apparently true, because …

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2018 April(A09) Math Question 35

Equation of a Line

- Distance & Midpoint

35. Students and adults from Western High School visited an amusement park on a field trip. The amusement park charged $25 for each adult ticket and $20 for each student ticket. Before the trip, the students were given this information about the Happy Dragon roller coaster: the average speed of the roller coaster is 50 miles per hour, and 1 ride on the roller coaster track is completed in 2.25 minutes. A graph showing the height above level ground, in feet, with respect to the time into the ride, in seconds, is given below. Which of the following values is closest to the total distance traveled, in miles, during 1. complete ride on the roller coaster track?

Choice B

Total distance travelled in 1 …

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2018 April(A09) Math Question 36

Ratios, Proportions, Percentages, Fractions

- Percents & Fractions

36. The roller coaster is at a height of at least 235 feet for a total of 5 seconds during each complete ride. Which of the following is closest to the percent of the time during a complete ride that the roller coaster is at a height of at least 235 feet?

Choice G

$$\frac{5 \ seconds}{2.25 \ minutes …

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2018 April(A09) Math Question 37

Equation of a Line

- Equations that Describe a Line

37. Which of the following values is closest to the average slope, in feet per second, of the graph on the interval between 40 seconds and 90 seconds?

Choice E

$$The\ slope \approx \frac{200\ ft}{50\ …

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2018 April(A09) Math Question 38

Exponents, Radicals, & Scientific Notation

- Scientific Notation

38. The value of x5(0.5×2+ 2.5x + 6) is between which of the following numbers when x T 10 ?

Choice J

$10^{5} (0.5 \times 10^{2} + 2.5 \times 10 + 6) = 10^{5} (50 + 25 + 6) = 81 \times 10^{5} = 8.1 \times 10^{6}$ $$\Rightarrow 8\times10^6<8.1\times10^6 …