MATHEMATICS TEST—NO CALCULATOR 6

There is no penalty for wrong answers, so it makes sense to give the best answer you can to every question, even if it is just your best guess.

The time is up. Section 2 is done, you have a 5-minute break period, then you be redirected to Section 3: Mathematics Test—Calculator 2

Math – No Calculator Tests

Mathematics Test—No Calculator 6

20 Questions. 25 Minutes to Complete

Directions

For questions 1 through 15, solve each problem, choose the best answer from the choices provided, and indicate your answer choice on your answer sheet. For questions 16 through 20, solve the problem and indicate your answer, which is to be recorded in the spaces provided on the answer sheet. Please refer to the directions before question 16 on how to record your answers in the spaces provided. You may use scratch paper for scratch work.

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1. Directions

Notes

1. The use of a calculator is not permitted.

2. All variables and expressions used represent real numbers unless otherwise indicated.

3. Figures provided in this test are drawn to scale unless otherwise indicated.

4. All figures lie in a plane unless otherwise indicated.

5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for which f (x) is a real number.

Reference

Begin skippable figure descriptions.

The figure presents information for your reference in solving some of the problems.

Reference figure 1 is a circle with radius r. Two equations are presented below reference figure 1.

A equals pi times the square of r.

C equals 2 pi r.

Reference figure 2 is a rectangle with length ℓ and width w. An equation is presented below reference figure 2.

A equals ℓ w.

Reference figure 3 is a triangle with base b and height h. An equation is presented below reference figure 3.

A equals onehalf b h.

Reference figure 4 is a right triangle. The two sides that form the right angle are labeled a and b, and the side opposite the right angle is labeled c. An equation is presented below reference figure 4.

c squared equals a squared plus b squared.

Special Right Triangles

Reference figure 5 is a right triangle with a 30degree angle and a 60degree angle. The side opposite the 30degree angle is labeled x. The side opposite the 60degree angle is labeled x times the square root of 3. The side opposite the right angle is labeled 2 x.

Reference figure 6 is a right triangle with two 45degree angles. Two sides are each labeled s. The side opposite the right angle is labeled s times the square root of 2.

Reference figure 7 is a rectangular solid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 7.

V equals ℓ w h.

Reference figure 8 is a right circular cylinder whose base has radius r and whose height is h. An equation is presented below reference figure 8.

V equals pi times the square of r times h.

Reference figure 9 is a sphere with radius r. An equation is presented below reference figure 9.

V equals fourthirds pi times the cube of r.

Reference figure 10 is a cone whose base has radius r and whose height is h. An equation is presented below reference figure 10.

V equals onethird times pi times the square of r times h.

Reference figure 11 is an asymmetrical pyramid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 11.

V equals onethird ℓ w h.

End skippable figure descriptions.

Additional Reference Information

The number of degrees of arc in a circle is 360.

The number of radians of arc in a circle is 2 pi.

The sum of the measures in degrees of the angles of a triangle is 180.

Question 1 refers to the following equation.

3x + x + x + x – 3 – 2 = 7 + x + x

Question 1.

In the preceding equation, what is the value of x?

$https://latex.codecogs.com/svg.image?\inline -\frac{5}{7}$

$https://latex.codecogs.com/svg.image?\inline \frac{12}{7}$

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2. The preceding graph shows the distance traveled d, in feet, by a product on a conveyor belt m minutes after the product is placed on the belt. Which of the following equations correctly relates d and m ?

d = 2m

$https://latex.codecogs.com/svg.image?\inline d=\frac{1}{2}m$

d = m + 2

d = 2m + 2

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3. Question 3 refers to the following information.

The following formula is often used by project managers to compute E, the estimated time to complete a job, where O is the shortest completion time, P is the longest completion time, and M is the most likely completion time.

$https://latex.codecogs.com/svg.image?\inline E=\frac{O+4M+P}{6}$

Question 3.

Which of the following correctly gives P in terms of E, O, and M ?

P = 6E – O – 4M

P = -6E + O + 4M

$https://latex.codecogs.com/svg.image?\inline P=\frac{O+4M+E}{6}$

$https://latex.codecogs.com/svg.image?\inline P=\frac{O+4M-E}{6}$

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4. Question 4 refers to the following figure.

Begin skippable figure description.

The figure presents triangle R T U, with R U horizontal, and U to the right of R. A point V is on R U, such that V is closer to R than it is to U. Vertex T is above R U. The angle at T is labeled 114 degrees. Side U T is extended to point S, above vertex R, and line segment S V is drawn. The angle to the right of S V and below S T is labeled 31 degrees. The angle to the left of S V and above R V is labeled x degrees.

End skippable figure description.

Question 4.

In the preceding figure, R T = T U. What is the value of x?

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5. The width of a rectangular dance floor is w feet. The length of the floor is 6 feet longer than its width. Which of the following expresses the perimeter, in feet, of the dance floor in terms of w ?

2w + 6

4w + 12

$https://latex.codecogs.com/svg.image?\inline w^{2}+6$

$https://latex.codecogs.com/svg.image?\inline w^{2}+6w$

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6. Which of the following consists of the ycoordinates of all the points that satisfy the preceding system of inequalities?

y > 6

y > 4

$y>\frac{5}{2}” title=”https://latex.codecogs.com/svg.image?y>\frac{5}{2}” /></label><label for='ays-answer-3570-25' class='ays_answer_image ays_empty_before_content'></label> </div> <div class='ays-field ays_list_view_item'> <input type='hidden' name='ays_answer_correct[]' value='0'/> <input type='radio' name='ays_questions[ays-question-939]' id='ays-answer-3571-25' value='3571'/> <label for='ays-answer-3571-25' class=' ays_position_initial '><img decoding=$

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7. Question 7 refers to the following equation.

$https://latex.codecogs.com/svg.image?\inline \sqrt{2x+6}+4=x+3$

Question 7.

What is the solution set of the preceding equation?

$https://latex.codecogs.com/svg.image?\inline \left\{-1 \right\}$

$https://latex.codecogs.com/svg.image?\inline \left\{5 \right\}$

$https://latex.codecogs.com/svg.image?\inline \left\{-1,5 \right\}$

$https://latex.codecogs.com/svg.image?\inline \left\{0,-1,5 \right\}$

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8. Question 8 refers to the following functions.

$https://latex.codecogs.com/svg.image?\inline f(x)=x^{3}-9x$
$https://latex.codecogs.com/svg.image?\inline g(x)=x^{2}-2x-3$

Question 8.

Which of the following expressions is equivalent to $https://latex.codecogs.com/svg.image?\inline \frac{f(x)}{g(x)}$ , for x > 3?

$https://latex.codecogs.com/svg.image?\inline \frac{1}{x+1}$

$https://latex.codecogs.com/svg.image?\inline \frac{x+3}{x+1}$

$https://latex.codecogs.com/svg.image?\inline \frac{x(x-3)}{x+1}$

$https://latex.codecogs.com/svg.image?\inline \frac{x(x+3)}{x+1}$

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9. Question 9 refers to the following equation.

$https://latex.codecogs.com/svg.image?\inline (x-6)^{2}+(y+5)^{2}=16$

Question 9.

In the x yplane, the graph of the preceding equation is a circle. Point P is on the circle and has coordinates (10, -5). If line segment P Q is a diameter of the circle, what are the coordinates of point Q?

(2, -5)

(6, -1)

(6, -5)

(6, -9)

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10. them. Some of the tents held 2 people each, and the rest held 4 people each. Assuming all the tents were filled to capacity and every person got to sleep in a tent, exactly how many of the tents were 2person tents?

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11. Question 11 refers to the following figure.

Begin skippable figure description.

The figure presents the graph of a curve in the x yplane with the origin labeled O. The numbers negative 3 through 3 appear along the xaxis. The numbers negative 10 and 10 appear on the yaxis. The curve begins to the left of the yaxis and above the xaxis, moves downward and to the right, crossing the xaxis at negative 3, continues to go down until it reaches a minimum point. Then it starts going upward and to the right, reaches the origin, and then it curves downward again to another minimum point. The curve goes up again, crossing the xaxis at 2, and extends to the right of the yaxis above the xaxis.

End skippable figure description.

Question 11.

Which of the following could be the equation of the preceding graph?

y = x(x – 2)(x + 3)

y = x²(x – 2)(x + 3)

y = x(x + 2)(x – 3)

y = x²(x + 2)(x – 3)

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12. If $https://latex.codecogs.com/svg.image?\inline \frac{2a}{b}=\frac{1}{2}$ , what is the value of $https://latex.codecogs.com/svg.image?\inline \frac{b}{a}$ ?

$https://latex.codecogs.com/svg.image?\inline \frac{1}{8}$

$https://latex.codecogs.com/svg.image?\inline \frac{1}{4}$

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13. Oil and gas production in a certain area dropped from 4 million barrels in 2000 to 1.9 million barrels in 2013. Assuming that the oil and gas production decreased at a constant rate, which of the following linear functions f best models the production, in millions of barrels, t years after the year 2000?

$https://latex.codecogs.com/svg.image?\inline f(t)=\frac{21}{130}t+4$

$https://latex.codecogs.com/svg.image?\inline f(t)=\frac{19}{130}t+4$

$https://latex.codecogs.com/svg.image?\inline f(t)=-\frac{21}{130}t+4$

$https://latex.codecogs.com/svg.image?\inline f(t)=-\frac{19}{130}t+4$

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14. Question 14 refers to the following system of equations.

$https://latex.codecogs.com/svg.image?\inline y=x^{2}+3x-7$

y – 5x + 8 = 0

Question 14.

How many solutions are there to the preceding system of equations?

There are exactly 4 solutions.

There are exactly 2 solutions.

There is exactly 1 solution.

There are no solutions.

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15. Question 15 refers to the following functions.

g(x) = 2x – 1

h(x) = 1 – g(x)

Question 15.

The preceding functions g and h are defined. What is the value of h(0)?

-2

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16. Directions

For questions 16 through 20, solve the problem and record your answer in the spaces provided on the answer sheet, as described in the following directions and examples.

1. Although not required, it is suggested that your answer be recorded in the boxes at the top of the columns to help fill in the circles accurately. You will receive credit only if the circles are filled in correctly.

2. Mark no more than one circle in any column.

3. No question has a negative answer.

4. Some problems may have more than one correct answer. In such cases, indicate only one answer.

5. Mixed numbers such as $https://latex.codecogs.com/svg.image?\inline 3\frac{1}{2}$ must be recorded as 3.5 or 7/2.

( is recorded in the spaces provided on the answer sheet, it will be interpreted as $https://latex.codecogs.com/svg.image?\inline \frac{31}{2}$ not $https://latex.codecogs.com/svg.image?\inline 3\frac{1}{2}$ )

6. Decimal answers: If you obtain a decimal answer with more digits than the spaces on the answer sheet can accommodate, it may be either rounded or truncated, but it must fill all four spaces.

The following are four examples of how to record your answer in the spaces provided. Keep in mind that there are four spaces provided to record each answer.

Examples 1 and 2

Begin skippable figure description.

Example 1: If your answer is a fraction such as seventwelfths, it should be recorded as follows. Enter 7 in the first space, the fraction bar (a slash) in the second space, 1 in the third space, and 2 in the fourth space. All four spaces would be used in this example.

Example 2: If your answer is a decimal value such as 2.5, it could be recorded as follows. Enter 2 in the second space, the decimal point in the third space, and 5 in the fourth space. Only three spaces would be used in this example.

End skippable figure description.

Example 3

Begin skippable figure description.

Example 3: Acceptable ways to record twothirds are: 2 slash 3, .666, and .667.

End skippable figure description.

Example 4

Note: You may start your answers in any column, space permitting. Columns you don’t need to use should be left blank.

Begin skippable figure description.

Example 4: It is not necessary to begin recording answers in the first space unless all four spaces are needed. For example, if your answer is 201, you may record 2 in the second space, 0 in the third space, and 1 in the fourth space. Alternatively, you may record 2 in the first space, 0 in the second space, and 1 in the third space. Spaces not needed should be left blank.

End skippable figure description.

Question 16 refers to the following equation.

$https://latex.codecogs.com/svg.image?\inline x^{2}+x-12=0$

Question 16.

If a is a solution of the preceding equation and a > 0, what is the value of a?

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17. The sum of $https://latex.codecogs.com/svg.image?\inline -2x^{2}+x+31$ and $https://latex.codecogs.com/svg.image?\inline 3x^{2}+7x-8$ can be written in the form $https://latex.codecogs.com/svg.image?\inline ax^{2}+bx +c$ , where a, b, and c are constants. What is the value of a + b + c?

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18. Question 18 refers to the following system of equations.

-x + y = -3.5

x + 3y = 9.5

Question 18.

If (x, Y)satisfies the preceding system of equations, what is the value of y?

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19. A startup company opened with 8 employees. The company’s growth plan assumes that 2 new employees will be hired each quarter (every 3 months) for the first 5 years. If an equation is written in the form y = a x + b to represent the number of employees, y, employed by the company x quarters after the company opened, what is the value of b ?

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20. Question 20 refers to the following figure.

Begin skippable figure description.

The figure presents a circle with the center labeled A. A line segment extends from A, horizontally right to the circle at a point labeled C. Another line segment extends from A, upward and left, to the circle at a point labeled B. Line segment B C is drawn, and the angle at A is labeled x degrees. The figure is not drawn to scale.

End skippable figure description.

Question 20.

In the preceding circle, point A is the center and the length of arc BC is two fifths of the circumference of the circle. What is the value of x?

MATHEMATICS TEST—NO CALCULATOR 6

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