Deck 1: Preliminaries

Question 1

If the line passing through the points is parallel to the line passing through the points and , what is the value of a? ​

A)
B)
C)
D)
E)

Answer 1

Question 2

Find an equation of the horizontal line that passes through (-2, -7). ​

A)
B)
C) ​
D) ​
E) ​

Answer 2

​

Question 3

Find an equation of the line that parallel to the x-axis and 8 units below it. ​

A)
B)
C) ​
D) ​
E) ​

Answer 3

Question 4

Use the intercept form of an equation of a line to find an equation of a line with the x-intercept 3 and the y-intercept 4. ​

A)
B)
C) ​
D) ​
E) ​

Question 5

Determine whether the line through each pair of points is parallel. ​ ​

A) not parallel
B) parallel

Question 6

Find an equation of the line that passes through the point (1, -9) and has the indicated slope m = 8. ​

A)
B) ​
C) ​
D) ​
E) ​

Question 7

Determine whether the points A(-2, 9), B(4, -1), and C(7, -6) lie on a straight line. ​

A) yes
B) no

Question 8

If the line passing through the points (2, a) and (4, -5) is parallel to the line passing through the points (7, 9) and (2, a + 11), what is the value of a? ​

A) -3
B) -8
C) -7
D) -5
E) -4

Question 9

Find an equation of the line in general form that passes through the point (5, 8) and is perpendicular to the line . ​

A)
B)
C)
D) ​
E) ​

Question 10

Given that the point lies on the line , find k. ​

A)
B)
C) ​
D) ​
E) ​

Question 11

Given the equation , if x decreases by 2 units, what is the corresponding change in y? ​

A)
B)
C) ​
D) ​
E) ​

Question 12

Find an equation of the line that passes through the points (1, 3) and (3, 13). ​

A)
B)
C) ​
D) ​
E) ​

Question 13

Find an equation of the line in general form that passes through the point (-6, 6) and is parallel to the line . ​

A)
B)
C)
D) ​
E) ​

Question 14

Determine whether the line through each pair of points is perpendicular. ​
A(3, 9), B(7, 4) and C(-4, -13), D(1, -8)
​

A) not perpendicular
B) perpendicular

Question 15

Find an equation of the line that has slope and y-intercept . ​

A)
B)
C) ​
D) ​
E) ​

Question 16

Writing the equation in the slope intercept form, find the slope of the line. ​

A)
B)
C) ​
D) ​
E) ​

Question 17

If the slope of the line L​₁ is negative, then the slope of a line L​₂ perpendicular to L​₁ may be positive or negative? ​

A) negative
B) positive

Question 18

Write the equation in the slope-intercept form and then find the slope and -intercept of the corresponding line. ​ ​

A)
B)
C)
D)

Question 19

Using data compiled by the Admissions Office at Faber University, college admissions officers estimate that 54% of the students who are offered admission to the freshman class at the university will actually enroll. If the desired freshman class size for the upcoming academic year is 810 students, how many students should be admitted? ​

A) 1,650
B) 900
C) 1,950
D) 1,200
E) 1,500

Question 20

Determine whether lie on a straight line. ​

A) no
B) yes

Question 21

Find the slope of the line shown in the figure. ​
​ ​

A) ​
B)
C) ​2
D) ​-1
E) ​1

Question 22

Find an equation of the line that passes through the point and is parallel to the line

Question 23

Find the slope of the line that passes through points and . m = __________

Question 24

Find an equation of the line that is parallel to the x-axis and 1 units below it.

Question 25

Given the graph of a line, which of the following statements is true? ​ ​

A) The slope of the line is negative, and its y-intercept is positive.
B) The slope of the line is negative, and its y-intercept is negative.
C) The slope of the line is positive, and its y-intercept is positive.
D) The slope of the line is positive, and its y-intercept is negative.
E) The slope of the line is zero.

Question 26

Find an equation of the horizontal line that passes through (-4, -3).

Question 27

Use the intercept form of an equation of a line to find an equation of a line with the x-intercept 5 and the ​y-intercept 2.

Question 28

Find the slope of the line shown in the figure.
​

Question 29

Find an equation of the line that has slope m = 9 and y-intercept b = 1.

Question 30

If the line passing through the points (1, a) and (2, -8) is parallel to the line passing through the points (9, 8) and (2, a + 10), what is the value of a?
​a = __________

Question 31

Find the slope of the line shown in the figure.
​
m = __________

Question 32

Find the slope of the line that passes through points and . ​

A) 5
B) 2
C) 3
D) 7
E) 6

Question 33

Find an equation of the line that passes through the point (6, 7) and is perpendicular to the line

Question 34

Find the slope of the line shown in the figure. ​ ​

A) ​
B) ​
C) ​3
D) -3
E) 1

Question 35

Find an equation of the line that passes through the point (3, -5) and has the slope m = 8.

Question 36

Find the slope of the line that passes through points and . ​

A) 5
B) 6
C) 2
D) 4
E) 1

Question 37

If the line passing through the points (a, 1) and (5, 7) is parallel to the line passing through the points (1, 6) and (a + 1,3), what is the value of a? a = __________

Question 38

Find an equation of the line that passes through the points (2, 9) and (-1, -12).

Question 39

Given that the point lies on the line , find k.
k = __________

Question 40

Find the slope of the line that passes through points and . m = __________

Question 41

Determine whether the statement is true or false.​
The point ( -n, 0b) is symmetric to the point (n, 0b) with respect to the y-axis.

Question 42

Find the distance between the points and . ​

A) 11
B)
C) 61
D)
E) 37

Question 43

Find the coordinates of the points that are 5 units away from the origin and have a y-coordinate equal to -3. ​

A) and
B) and
C) and
D) and
E) and

Question 44

Find the coordinates of the points that are 10 units away from the origin and have an x-coordinate equal to 8. ​

A)
B)
C) and
D) and
E) and

Question 45

A grand tour of four cities begins at city A and makes successive stops at cities B, C, and D before returning to city A. If the cities are located as shown in the following figure, find the total distance covered on the tour. ​
​ ​

A) 2,300 mi
B) 2,200 mi
C) 2,100 mi
D) 2,000 mi
E) 1,600 mi

Question 46

If the slope of the line L​₁ is positive, then the slope of a line L​₂ perpendicular to L​₁ may be positive or negative?

Question 47

Find an equation of the circle with radius 2 and center (-3, -5). ​

A)
B)
C)
D)
E)

Question 48

Find an equation of the circle with center at (-a, 0a) and radius 5a. ​

A)
B)
C)
D)
E)

Question 49

Determine whether A(-2, 1), B​(1, 7), and C(4, 14) lie on a straight line. Answer yes or no.

Question 50

Determine whether the points A(-2, 5), B(2, -3), and C(8, -14) lie on a straight line. Answer yes or no.

Question 51

Determine whether the statement is true or false The circle with equation lies inside the circle with equation provided

Question 52

Determine whether the line through each pair of points is perpendicular. Answer perpendicular or not perpendicular. A(3, 9), B(11, 5) and C(-3, -9), D(2, 1)

Question 53

Find an equation of the circle that satisfies the conditions. ​
Center and passes through .
​

A)
B)
C)
D)
E)

Question 54

Plot point (8, -7) on the set of coordinate axes. ​

A)
B)
C)
D)
E)

Question 55

Determine whether the line through each pair of points is parallel. Answer parallel or not parallel.
​A(1, -2), B(-3, -10) and C(1, 2), D(-1, -8)

Question 56

The circle with equation lies out side the circle with equation means. ​

A) k ≥ 1
B) k > 1
C) k < 1
D) k ≤ 1
E) these curves are intersecting

Question 57

Refer to the following figure and determine the coordinates of point and the quadrant in which it is located. ​ ​

A) (3, -4) and first quadrant
B) (2, -2) and first quadrant
C) (2, -2) and fourth quadrant
D) (-4, 0) and fourth quadrant
E) (3, -4) and fourth quadrant

Question 58

Find an equation of the circle with center at the origin that passes through (2, 1). ​

A)
B)
C)
D)
E)

Question 59

A furniture store offers free setup and delivery services to all points within a 23-mi radius of its warehouse distribution center. If you live 19 mi east and 14 mi south of the warehouse, will you incur a delivery charge? ​

A) No
B) Yes

Question 60

Ship A leaves port sailing north at a speed of 25 mph. A half hour later, ship B leaves the same port sailing east at a speed of 16 mph. Let t (in hours) denote the time ship B has been at sea. Find an expression in terms of t giving the distance between the two ships and use this expression to find the distance between the two ships 3 hours after ship A has left port. Round the answer to the nearest tenth. ​

A) 86.0 mi
B) 78.0 mi
C) 83.5 mi
D) 83.0 mi
E) 85.0 mi

Question 61

Refer to the following figure. Which point has a y-coordinate that is equal to zero? ​ ​

A) G
B) B
C) E
D) C
E) A

Question 62

Find the distance between the points (-2, -3) and (6, 10). ​

A)
B)
C)
D)
E)

Question 63

Refer to the following figure. Which points have a negative x-coordinate and a negative y-coordinate?
​

Question 64

Find an equation of the circle with center at the origin that passes through (1, 2).

Question 65

Find an equation of the circle that satisfies the conditions.
​
Center and passes through .

Question 66

Refer to the following figure. Which point has an x-coordinate that is equal to zero? ​ ​

A) C
B) A
C) B
D) E
E) F

Question 67

Refer to the following figure. Which point has coordinates (-8, 3)? ​

A) C
B) A
C) B
D) E
E) F

Question 68

A grand tour of four cities begins at city A and makes successive stops at cities B, C, and D before returning to city A. If the cities are located as shown in the following figure, find the total distance covered on the tour.
​
​ ​
__________mi

Question 69

Refer to the following figure. What are the coordinates of point B? ​ ​

A) (10, -6)
B) (14, 14)
C) (4, 10)
D) (-3, 3)
E) (-9, -13)

Question 70

Refer to the following figure. Which points have negative y-coordinates?
​

Question 71

Find an equation of the circle with center at (-a, 0a) and radius 2a.

Question 72

Determine which statements are true.
​
a. The point (-(a), (b)) is symmetric to the point (0(a), (b)) with respect to the origin.
b. The point (-(a), 0(b)) is symmetric to the point (0(a), -(b)) with respect to the origin.
c. The point ((a), -(b)) is symmetric to the point ((a), 0(b)) with respect to the x-axis.
d. The point (-(a), 0(b)) is symmetric to the point (0(a), -(b)) with respect to the y-axis.
e. The point (-(a), (b)) is symmetric to the point (0(a), (b)) with respect to the y-axis.

Question 73

Find the coordinates of the points that are 13 units away from the origin and have an x-coordinate equal to 5.

Question 74

Refer to the following figure. What are the coordinates of point C?
​

Question 75

Find the distance between the points and .

Question 76

Refer to the following figure. Which points have negative y-coordinates? ​ ​

A) E, B, C
B) A, B, D
C) F, A, E, C
D) F, A, D, G
E) G, D, B

Question 77

Refer to the following figure. Which points have a negative x-coordinate and a negative y-coordinate? ​ ​

A) B
B) D, F
C) E, A
D) G, C
E) A, C, B

Question 78

Find the coordinates of the points that are 5 units away from the origin and have a y-coordinate equal to -3.

Question 79

Find an equation of the circle with radius 5 and center (1, 1).

Question 80

Refer to the following figure. Which point has coordinates (-3, 4)? ​ ​

A) D
B) G
C) C
D) A
E) B