Deck 1: Fundamentals

Question 1

Find both the x-intercept and the y-intercept for the equation defined as follows: $3 x + 4 y = 12$ Choose the correct graph of this straight line equation.

A) 3
B) 1b
C) 1a
D) 2
E) 1

Answer 1

1

Question 2

Use a calculator to determine all x-intercepts and all y-intercept accurate to two decimal places.

A) x-intercept: - 2.00; y-intercept: - 0.86
B) x-intercepts: 1.46, 5.16; y-intercept: - 2.00
C) x-intercept: 2.00; y-intercepts: 1.16, - 4.16
D) x-intercept: - 2.00; y-intercepts: - 1.16, 5.16
E) x-intercepts: 0, - 2.00; y-intercept: - 1.46

Answer 2

x-intercept: - 2.00; y-intercepts: - 1.16, 5.16

Question 3

Find the midpoint of the line segment joining P and Q. P ( - 3, 9) and Q ( 21, - 13)

A) (11,0)
B) (10,-1)
C) (8,-3)
D) (7,-3)
E) (9,-2)

Answer 3

(9,-2)

Question 4

Solve for x in terms of the other letters. $\frac { x } { a } + \frac { x } { b } = 3$

A) $x = \frac { 3 a b } { b + a }$
B) $x = \frac { b - a } { b + a }$
C) $x = \frac { b - a } { a b }$
D) $x = 3 ( a + b )$
E) $x = \frac { - 3 - a b } { b - a }$

Question 5

Draw a number line showing the location of the indicated number 9/8.

A)
B)
C)
D)
E)

Question 6

Given the following three points, (-14, 8), (-7, 8), (-7, 16),
Which of the following statements is true?

A) The points are not the vertices of any triangle.
B) The points are the vertices of an equilateral triangle.
C) The points are the vertices of a right triangle.
D) The points are the vertices of a triangle that is neither right nor isosceles nor equilateral.
E) The points are the vertices of an isosceles triangle.

Question 7

Rewrite using absolute value notation. The distance between x and 1 is at least 1/4.

A) $| x - 1 | > \frac { 1 } { 4 }$
B) $| x - 1 | \geq \frac { 1 } { 4 }$
C) $| x - 4 | \leq 1$
D) $| x + 1 | < \frac { 1 } { 4 }$
E) $| x - 4 | \geq \frac { 1 } { 4 }$

Question 8

Find the midpoint of the line segment joining P and Q. $$P ( 19 , \pi )$$ and $Q ( 9,11 \pi )$

A) $( 15,7 \pi )$
B) $( 14,6 \pi )$
C) $( 15 , \pi )$
D) (14,6)
E) (15,7)

Question 9

Determine whether the given point lies on the graph of the equation. $( 4,3 ) ; y = \frac { 1 } { 2 } x + 3$

A) True
B) Flase

Question 10

Use a calculator to graph the equation. Then approximate the x-intercepts accurate to three decimal places. y = x ⁵ - 8x ⁴ + 3

A) - 0.765, 0.804, 8.001
B) - 0.765, 0.804, 7.999
C) 4.000, 0.804, 0.265
D) 0.904, 0.765, 4.000
E) - 0.765, 0.904, 4.000

Question 11

Which of the following points is closest to the origin?

A) (-4,12)
B) (-12,-8)
C) (-8,12)
D) (-5,-14)
E) (8,-11)

Question 12

Draw a number line showing the approximate location of the indicated number π/3.

A)
B)
C)
D)
E)

Question 13

Use a calculator to determine all x-intercepts and all y-intercept accurate to two decimal places.

A) x-intercepts: $$0,5.87,1.87$$ y-intercepts: $$0,1$$
B) x-intercepts: $0 , - 5.87,0.87$ y-intercept: $0$
C) x-intercepts: $0 , - 5.87,1.87$ y-intercepts: $0 , - 1$
D) x-intercepts: $0 , - 5.87,1.87$ y-intercept: $0$
E) x-intercepts: $0 , - 6.87,1.87$ y-intercept: $0$

Question 14

Find the distance between the given points. (4, 9) and (7, 13)

A) 8
B) 6
C) 5
D) 4
E) 2

Question 15

Find the equation of the line with the given slope and $y$ -intercept. $\text { slope } = 3 ; y - \text { intercept } = \frac { 3 } { 2 }$

A) $y = 3 x + \frac { 3 } { 2 }$
B) $y = \frac { 1 } { 3 } x + \frac { 3 } { 2 }$
C) $y = 3 x + \frac { 2 } { 3 }$
D) $y = 3 x - \frac { 2 } { 3 }$
E) $y = \frac { 1 } { 3 } x + \frac { 2 } { 3 }$

Question 16

Evaluate. | 3 | + | - 3 |

A) $\overline { 9 }$
B) $\overline { 6 }$
C) 9
D) 6
E) 0

Question 17

Solve for x in terms of the other letters. $\frac { b - x } { b - a } - 2 = \frac { c - x } { a - c }$

A) x=2b
B) x=a
C) x=2a
D) x=c
E) x=1/2a

Question 18

Rewrite using absolute value notation. The distance between x and 4 is at least 8.

A) $| x - 4 | \leq 8$
B) $| x - 4 | \geq 8$
C) $| x - 8 | < 4$
D) $| x + 4 | < 8$
E) $| x - 8 | > 4$

Question 19

Solve for x. $\frac { x - 1 } { 2 } + \frac { 3 x + 4 } { - 1 } = 0$

A) x=-9/5
B) x=-5/7
C) x=11/5
D) x=9/7
E) x=-7/5

Question 20

Rewrite expression without using absolute value notation. | x - 8 | given that x < 8

A) x - 8
B) 8 - x
C) - x - 8
D) x + 8
E) 8 + x

Question 21

Find the equation of the line described below. $x \text {-intercept } 5 ; y \text {-intercept } 4$

A) $y = - \frac { 4 } { 5 } x - 4$
B) $y = - \frac { 4 } { 5 } x + 5$
C) $y = - \frac { 4 } { 5 } x + 4$
D) $y = - \frac { 5 } { 4 } x - 4$
E) $y = - \frac { 5 } { 4 } x + 5$

Question 22

Find the intercepts and determine what type of symmetry the graph possesses. $y = x ^ { 2 } - 6 x + 9$

A) Symmetry about the y-axis.
B) No symmetry.
C) Symmetry about the y-axis.
D) No symmetry.
E) Symmetry about the x-axis.

Question 23

Find the intercepts and determine what type of symmetry the graph possesses. $x = y ^ { 2 } - 4$

A) Symmetry about the x-axis.
B) Symmetry about the y-axis.
C) Symmetry about the y-axis.
D) Symmetry about the x-axis.
E) Symmetry about the x-axis.

Question 24

Find the intercepts and determine what type of symmetry the graph possesses. $y = - 4 + x ^ { 2 }$

A) Symmetry about the y-axis.
B) Symmetry about the y-axis.
C) Symmetry about the x-axis.
D) Symmetry about the y-axis.
E) Symmetry about the y-axis.

Question 25

Find the center of the circle. $$x ^ { 2 } + y ^ { 2 } + 8 x - 4 y = - 16$$

A) (4,2)
B) (-4,2)
C) (-4,-2)
D) (-8,4)
E) (4,-2)