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Practice Test 1 - 0312-Chap. 2.4,2.7, 3.1-3.6,4.1,5.4,5.5
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write an inequality statement involving the letter x that describes the given graph or interval notation.
1)
-7 -6 -5 -4 -3 -2 -1 0
A) x ≥ 3
1
2
3
4
5
6
7
B) x < 3
C) x > 3
D) x ≤ 3
2) (2, 6)
A) 2 < x ≤ 6
B) 2 ≤ x < 6
C) 2 < x < 6
D) 2 ≤ x ≤ 6
3) [-6, -2)
A) -6 ≤ x ≤ -2
B) -6 < x ≤ -2
C) -6 ≤ x < -2
D) -6 < x < -2
Solve the equation.
4) 6m + 5 = 6
1 11
A) - , 6 6
2)
3)
4)
1
11
, - 6
6
B) ∅
C)
3
10
B)
, - 7
7
3
11
C) - , - 7
7
D)
1
11
, - 5
5
5) 8s - 7 = s - 4
A) ∅
1)
5)
3 11
D)
, 7 9
An equation that defines y as a function of x is given. Solve for y in terms of x, and replace y with the function notation
f(x).
6)
6) 5x - 6y = 5
5x
5
5 - 5x
B) f(x) = 5 - C) f(x) = -5x - D) f(x) = 5 - 5x
A) f(x) = 6
6
-6
1
Graph the linear function. Give the domain and range.
7) h(x) = -1
7)
y
6
4
2
-6
-4
-2
2
6 x
4
-2
-4
-6
A) Domain: (-∞, ∞)
Range: {-1}
B) Domain: {-1}
Range: (-∞, ∞)
y
-6
-4
y
6
6
4
4
2
2
-2
2
4
x
6
-6
-4
-4
-4
-6
-6
A) (-∞, -7)
-14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
3
4
5
6
7
8
9
10 11 12
-14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
4
5
6
7
8
9
10 11 12
B) (-∞, 5]
-1
0
1
2
C) (-7, ∞)
-1
0
D) [5, ∞)
-2
-1
0
1
2
-2
Solve the inequality. Give the solution set in both interval and graph forms.
8) -7a - 7 ≤ -8a - 2
-2
-2
-2
2
3
2
4
6
x
8)
9) -6(4a - 3) < -30a - 6
9)
A) (-4, ∞)
-11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
B) (-∞, -30)
-37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23
C) (-∞, -4)
-11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
D) (-30, ∞)
-37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23
10) -21 < 5a + 4 ≤ -1
10)
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
A) [-5, -1]
B) [-5, -1)
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
C) (-5, -1)
D) (-5, -1]
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
Solve the problem.
11) A car rental company has two rental rates. Rate 1 is $30 per day plus $.12 per mile. Rate 2 is $60
per day plus $.06 per mile. If you plan to rent for one day, how many miles would you need to
drive to pay less by taking Rate 2?
A) more than 250 miles
B) more than 1000 miles
C) more than 600 miles
D) more than 500 miles
3
11)
Use the graph to answer the question.
12)
12)
In which months was the percent of tropical storms at most 5%?
A) February, March, April
B) May, June, July
C) May, October
D) May
Solve the problem.
13) Behemoth Back Packs, Inc. finds that the cost to make x back packs is C = 142x + 6639, while the
revenue produced from them is R = 197x (C and R are in dollars). What is the smallest whole
number of back packs, x, that must be sold for the company to show a profit?
A) 121
B) 2,250,621
C) 365,145
D) 20
13)
The graph shows sales in thousands of dollars for 1989 and 1990. Use it to answer the question.
14) If the ordered pair (x, y) represents a point on the graph, what does x represent? What does y
represent?
A) y represents the month; x represents the sales in thousands of dollars.
B) x represents the year 2006; y represents the year 2007.
C) x represents the month; y represents the sales in thousands of dollars.
D) x represents the year 2006; y represents the sales in thousands of dollars
Name the quadrant, if any, in which the point is located.
15) (17, -16)
A) II
B) III
14)
15)
C) I
4
D) IV
Plot the point on the rectangular coordinate system provided. Write the corresponding letter as your answer.
6
A
B
y
D
4
E
C
2
G
-6
-4
F
-2
H
I
2
4
6 x
-2
J
K
-4
L
-6
16) (0, 2)
A) F
16)
B) B
C) K
D) C
Complete the table for the equation.
17) y = -x - 3
17)
x y
3
-3
0
A) -6; 0; -3
B) 1; -6; -3
C) 1; 0; -3
Find the x- and y-intercepts. Then graph the equation.
18) 6x - 12y = 24
18)
y
10
5
-10
-5
5
10
D) -6; 0; 0
x
-5
-10
5
A) (2, 0); (0, -4)
B) (-4, 0); (0, 2)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C) (-2, 0); (0, 4)
x
5
10
x
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
19) y = -6
19)
y
10
5
-10
10
D) (4, 0); (0, -2)
y
-10
5
-5
5
10
x
-5
-10
6
A) None; (0, -6)
B) (-6, 0); none
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C) None; (0, -6)
10
x
5
10
x
D) (-6, 0); none
y
-10
5
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
Find the midpoint of the segment with the given endpoints.
20) (-8, -6) and (-7, -2)
A) -15, -8
20)
15
C) - , - 4
2
B) -1, -4
1
D) - , - 2
2
Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates of
the other endpoint Q.
3
21) P(0, -9) and M - , 0
21)
2
A) Q 3, -18
C) Q -3, 0
B) Q(-3, 9)
D) Q
3
, - 9
2
Solve the problem.
22) Suppose y = mx + b is a linear model for actual time as a function of estimated time, where y
represents actual time and x represents estimated time and m and b are constants. If m = 3.1 and
b = -2.7, find y when x is 15 min.
A) 49.2 min
B) 6.63 min
C) 43.8 min
D) 23.37 min
7
22)
Find the slope of the line through the pair of points.
23) (-5, -6) and (7, -4)
1
B) - 6
A)
6
23)
1
C) - 6
D) 6
Find the slope of the line.
24)
24)
y
10
5
-10
-5
5
10
x
-5
-10
A) -1
B) -2
C) 2
Find the slope of the line and sketch the graph.
25) 2x + 5y = 21
25)
y
10
5
-10
-5
5
10
D) 1
x
-5
-10
8
A) Slope: 2
5
B) Slope: 5
2
y
-10
C) Slope: - y
10
10
5
5
-5
5
10
x
-10
-5
5
-5
-5
-10
-10
2
5
D) Slope: - y
10
x
5
2
y
10
15
5
10
-10
-5
5
10
x
5
-5
5
10
15
x
-10
Graph the line described.
26) Through (0, 5); m = 1
6
26)
y
10
5
-10
-5
5
10
x
-5
-10
9
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
x
5
10
x
D)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
Decide whether the pair of lines is parallel, perpendicular, or neither.
27) 3x - 2y = 12 and 2x + 3y = -3
A) Parallel
B) Perpendicular
27)
C) Neither
Solve the problem.
2
28) If the slope of the road shown is , find the value for h if v = 3 ft.
3
A) 6 ft
B) 3 ft
C)
9
ft
2
Find the equation in slope-intercept form of the line satisfying the conditions.
29) m = -8, passes through (-3, 4)
A) y = -8x - 20
B) 8x + y = 20
C) y = -8x + 27
28)
D) 9 ft
29)
D) y = 8x - 18
4
30) m = - ; y-intercept (0, 8)
3
4
A) y = - x - 8
3
30)
4
B) y = x - 8
3
4
C) y = x + 8
3
10
4
D) y = - x + 8
3
Write the equation in slope-intercept form.
31) 7x - 6y = 4
7
2
7
2
A) y = x + B) y = x - 6
3
6
3
31)
6
4
C) y = x + 7
7
Find the slope and the y -intercept of the line.
32) 4x + 9y = 26
26
4
A) Slope ; y-intercept 0, 9
9
D) y = 7x - 4
32)
4
26
B) Slope - ; y-intercept 0, 9
9
9
9
C) Slope ; y-intercept 0, 4
26
9
9
D) Slope - ; y-intercept 0, 4
26
Find an equation of the line that satisfies the conditions. Write the equation in standard form.
2
33) Through (0, 3); m = - 7
A) 7x + 2y = -21
B) 2x + 7y = -21
C) 2x + 7y = 21
D) 2x - 7y = 21
Find an equation of the line passing through the two points. Write the equation in standard form.
34) (-2, -6) and (-7, 0)
A) -6x + 5y = -42
B) 4x - 7y = 28
C) 6x + 5y = -42
D) -4x + 7y = 28
Find an equation of the line satisfying the conditions. Write the equation in slope -intercept form.
35) Through (-6, 7); parallel to 3x + 7y = 3
31
7
7
3
31
3
3
3
B) y = - x + C) y = x - D) y = x + A) y = - x + 7
3
3
7
7
7
7
7
36) Through (-3, 8); perpendicular to -3x + 4y = -23
23
4
3
B) y = x + 12
A) y = - x + 4
3
4
33)
34)
35)
36)
4
C) y = - x + 4
3
3
41
D) y = x + 4
4
Solve the problem.
37) It costs $17 per hour plus a flat fee of $28 for a plumber to make a house call. What is an equation
of the form y = mx + b for this situation?
A) y = 28x + 17
B) y = 28x
C) y = 17x
D) y = 17x + 28
38) Using a phone card to make a long distance call costs a flat fee of $0.54 plus $0.14 per minute
starting with the first minute. What is an equation of the form y = mx + b for this situation?
A) y = 0.14x + 0.54
B) y = 0.14x
C) y = 0.54x
D) y = 0.54x + 0.14
11
37)
38)
Graph the linear inequality in two variables.
39) 2x + y ≤ -2
39)
y
10
5
-10
-5
5
10
x
-5
-10
A)
B)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
C)
5
10
5
10
x
D)
y
y
-10
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
12
x
Decide whether the relation is a function, and give the domain and range.
40)
40)
y
10
5
-10
-5
5
10
x
-5
-10
A) Not a function; domain: (-∞, -2] ; range: (-∞, ∞)
B) Function; domain: (-∞, -2] ; range: (-∞, ∞)
41)
41)
y
10
5
-10
-5
5
10
x
-5
-10
A) Function; domain: (-∞, ∞); range: (-∞, 0)
B) Not a function; domain: (-∞, ∞); range: (-∞, 0)
Decide whether the relation is a function.
42) {(2, -9), (2, -2), (5, -7), (7, -3), (11, -9)}
A) Not a function
42)
B) Function
Determine whether the relation defines y as a function of x. Give the domain.
43) y2 = 4x
A) Function; domain: (-∞, ∞)
C) Not a function; domain: [0, ∞)
43)
B) Not a function; domain: (-∞, 0]
D) Function; domain: (-∞, 0]
Solve the problem.
44) Find f(0) when f(x) = x2 + 4x - 5.
A) 5
B) -5
44)
C) -1
D) 25
Determine whether the relation defines y as a function of x. Give the domain.
45) y = 2x - 6
A) Not a function; domain: -∞, 3
B) Function; domain: 3, ∞
C) Not a function; domain: 3, ∞
D) Function; domain: (-∞, ∞)
13
45)
Solve the problem.
46) Find f(k - 1) when f(x) = 4x2 + 5x + 6.
A) 4k2 + 29k + 15
B) 4k2 - 3k + 5
46)
C) 4k2 - 3k + 15
D) -3k2 + 4k + 5
Decide whether the ordered pair is a solution of the given system.
47) 4x + y = 14
2x + 4y = 14 ; (3, 2)
A) No
B) Yes
47)
Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
48) x = -28 - 7y
7x + 6y = 19
B) {(-7, -4)}
A) {(7, -5)}
D) ∅; inconsistent system
C) {(6, -4)}
Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.
49) x + 4y = 13
2x + 3y = 6
A) {(-4, 5)}
B) {(-3, 4)}
C) {(3, 5)}
D) ∅; inconsistent system
Tell how many solutions the system has. Do not actually solve.
50) 3x - y = 10
x + 2y = 8
A) No solution
B) One solution
51) 5x + 4y = -1
25x + 20y = -5
A) No solution
52) x - 3y = 6
3y + 1 = x
A) Infinitely many
C) Infinitely many
51)
B) Infinitely many
C) One solution
52)
B) No solution
C) One solution
53)
4 2 7
- = y x 4
1 1
, 8 2
49)
50)
Solve the system of equations.
5 6 13
53) + = y x
4
A)
48)
C) ∅
B) {(8, 2})
14
D) {(-8, 2})
Choose the inequality that best matches the given calculator graph.
54)
A) y ≤ 2x + 2
B) y ≤ -2x - 2
54)
C) y ≥ 2x + 2
Decide whether the pair of lines is parallel, perpendicular, or neither.
55) 9x + 3y = 12 and 15x + 5y = 23
A) Parallel
B) Perpendicular
Find the product.
56) (-3x - 3y)(3x + 11y + 1)
A) -9x2 - 9xy - 3x - 33y2 - 3y
D) y ≥ -2x - 2
55)
C) Neither
56)
B) -9x2 - 42xy - 42y2
C) -9x2 - 33xy - 3x - 33y2
D) -9x2 - 42xy - 3x - 33y2 - 3y
57) (7p - 1)(49p2 + 7p + 1)
A) 343p3 + 56p2 - 1
B) 49p3 - 1
C) 343p3 + 1
D) 343p3 - 1
57)
58) 3x(4x - 1)(4x + 9)
A) 48x3 + 96x2 - 27x
58)
B) 44x3 + 98x2 - 25x
C) 46x2 + 97x - 27
D) 16x3 + 32x2 - 9x
59) (7a - 5)2
A) 7a 2 + 25
B) 49a 2 - 70a + 25
C) 49a 2 + 25
D) 7a 2 - 70a + 25
60) (-4x - 1)2
A) 16x2 + 1
B) -4x2 + 8x + 1
C) -4x2 + 1
D) 16x2 + 8x + 1
59)
60)
For the pair of functions, find the product (fg)(x).
61) f(x) = 5x + 4, g(x) = -x2 + 5x + 7
61)
A) -5x3 - 22x2 + 55x - 28
C) -10x2 + 21x2 - 55x + 28
B) 5x3 + 21x2 - 55x - 28
D) -5x3 + 21x2 + 55x + 28
15
Express the area of the figure as a polynomial in descending powers of the variable x.
62)
3x - 3
62)
x + 7
A) 3x2 + 18x - 21
Find the product.
63) (x - 7)(4x + 7)
A) x2 - 21x - 21
B) -3x2 + 17x + 21
C) 3x2 + 24x - 14
D) 2x2 - 24x + 21
63)
B) 4x2 - 22x - 49
C) 4x2 - 49x - 21
D) 4x2 - 21x - 49
C) 570
D) 374
Find the requested value.
64) If f(x) = x2 + 9x + 9 and g(x) = 8x - 2, find (fg)(-4).
A) -1866
64)
B) -37
Divide.
65)
-40x7 + 15x5 - 15x3
-5x5
A) 8x - 3 + 66)
B) 8x - 3 + 3
x
C) 8x2 - 3 + 3
x
D) 8x2 - 3 + 3
x2
x2 + 8x + 9
x + 6
A) x + 2 + 67)
3
x2
65)
66)
3
x + 6
B)
x + 2
x + 6
C) x + 3
D) x + 2 - 3
x + 6
9y4 + 12y3 + 4y - 1
3y2 + 1
A) 3y2 - 1
67)
B) 3y2 + 4y
C) 3y2 - 4y + 1
16
D) 3y2 + 4y - 1
Answer Key
Testname: PTEST1‐0312‐FALL‐2013
1) A
2) C
3) C
4) C
5) D
6) A
7) A
8) B
9) C
10) D
11) D
12) C
13) A
14) C
15) D
16) D
17) A
18) D
19) C
20) C
21) B
22) C
23) A
24) A
25) C
26) D
27) B
28) C
29) A
30) D
31) B
32) B
33) C
34) C
35) A
36) C
37) D
38) A
39) B
40) A
41) A
42) A
43) C
44) B
45) B
46) B
47) B
48) A
49) B
50) B
17
Answer Key
Testname: PTEST1‐0312‐FALL‐2013
51) B
52) B
53) B
54) A
55) A
56) D
57) D
58) A
59) B
60) D
61) D
62) A
63) D
64) D
65) D
66) D
67) D
18