Download ALG I FINAL REVIEW 2010 Multiple Choice Identify the choice that

ALG I FINAL REVIEW 2010
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Match the equation with its graph.
____
1. 8x – 6y = –48
a.
–10 –8
–6
–4
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
10
–4
–6
–4
–2
–2
–4
–6
–6
–8
–8
–10
–10
y
–6
–10 –8
x
–4
b.
–10 –8
y
c.
y
10
8
8
6
6
4
4
2
2
2
4
6
8
10
x
4
6
8
10
x
2
4
6
8
10
x
y
d.
10
–2
–2
2
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
____
2. Which graph shows the best trend line for the following data.
a.
c.
Violin Competition
60
54
54
48
48
42
42
36
36
Score
Score
Violin Competition
60
30
30
24
24
18
18
12
12
6
6
2
4
6
8
10
12
14
16
18
20
2
4
Practice (weeks)
b.
d.
54
54
48
48
42
42
36
36
30
24
18
18
12
12
6
6
8
10
12
14
12
14
16
18
20
16
18
20
30
24
6
10
Violin Competition
60
Score
Score
Violin Competition
4
8
Practice (weeks)
60
2
6
16
18
20
2
Practice (weeks)
4
6
8
10
12
14
Practice (weeks)
Find the rate of change for the situation.
____
3. A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.
a.
c.
lb per person
lb per person
b. 4 lb per person
____
d. 36 people
4. A student finds the slope of the line between (1, 10) and (20, 4). She writes
. What mistake did she
make?
a. She should have added the values, not subtracted them.
b. She did not keep the order of the points the same in numerator and the denominator.
c. She mixed up the x- and y-values.
d. She used y-values where she should have used x-values.
____
5.
Plant Growth
6
Height (in.)
5
4
3
2
1
Plant 1 ___ Plant 2 - - 1
2
3
Plant 3 __ __
4
5
6
Time (Weeks)
Use the graph.
a. Which plant was the tallest at the beginning?
b. Which plant had the greatest rate of change over the 6 weeks?
a. plant 3; plant 3
b. plant 1; plant 2
c. plant 2; plant 3
d. plant 2; plant 1
Find the slope and y-intercept of the line.
____
6. 12x + 10y = 80
a. 6
; 8
5
b.
5
 ;8
6
c.
6
 ;8
5
d.
6 1
 ;
5 8
Write an equation of a line with the given slope and y-intercept.
____
7. m =
a.
1
4
,b=
5
3
4
3
b.
1
4
y= x–
5
3
y = 5x +
c.
4
y= x+
3
d.
1
y= x+
5
1
5
4
3
Write the slope-intercept form of the equation for the line.
____
8.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
a.
b.
____
y=x+
c.
3
2
3
y= x1
2
d.
2
y= x1
3
3
y= x1
2
9. The grocery store sells kumquats for $4.75 a pound and Asian pears for $2.25 a pound. Write an equation in
standard form for the weights of kumquats k and Asian pears p that a customer could buy with $22.
a. 4.75k + 2.25p = 22
c. 4.75k = 2.25p + 22
b. 4.75p + 2.25k = 22
d. 4.75 + 2.25 = k
____ 10. A line passes through (3, 6) and (5, 9).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in standard form using integers.
a.
c.
3
y – 6 = (x – 3); –3x + 2y = 3
y–3=
2
b.
d.
3
y – 6 = (x + 3); –3x + 2y = 3
y+6=
2
3
(x – 6); –3x + 2y = –12
2
3
(x – 3); –3x + 2y = –3
2
____ 11. The table shows the height of a plant as it grows.
a. Model the data with an equation.
b. Based on your model, predict the height of the plant at 12 months.
Time (months)
Plant Height (cm)
3
18
5
30
7
42
9
54
a. y – 18 = 3(x –3); 36 cm
b. y – 18 = 6(x –3); 72 cm
c.
d.
The relationship cannot be modeled.
y – 3 = 3(x –18); 66 cm
____ 12. The map shows Main Street and the construction site for the new library. Find the equation of a “street”that
passes through the building site and is parallel to Main Street.
y
10
e et
Main Str
9
8
7
6
5
4
3
library
2
1
1
2
3
4
5
6
7
8
9
10
11
x
c. y = 6x + 2
a.
1
y= x+2
6
b.
1
y= x–2
6
d.
1
y= x+2
6
Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
____ 13. 7x – 4y = 4
x – 4y = 3
a. perpendicular
b. parallel
c. neither
4
____ 14. y = x + 11
3
6x + 8y = 12
a. parallel
b. perpendicular
c. neither
____ 15. Giselle pays $190 in advance on her account at the athletic club. Each time she uses the club, $5 is deducted
from the account. Model the situation with a linear function and a graph.
Athletic Club Account
b
a.
280
560
240
480
200
400
160
320
120
240
80
160
40
80
1
2
3
4
5
6
7
8
9
x
1
b = 190 – 5x
b.
400
b
Athletic Club Account
b
c.
2
3
4
5
6
7
8
9
x
9
x
b = 185 + 5x
360
Athletic Club Account
b
d.
Athletic Club Account
280
320
240
280
200
240
200
160
160
120
120
80
80
40
40
1
2
b = 190 + 5x
3
4
5
6
7
8
9
x
1
2
b = 185 – 5x
3
4
5
6
7
8
____ 16. Use the slope and y-intercept to graph the equation.
1
y= x–4
4
y
a.
c.
–5
–4
–3
–2
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–3
–2
–4
–3
–2
–1
–1
–2
–3
–3
–4
–4
–5
–5
y
–4
–5
–2
b.
–5
y
5
4
4
3
3
2
2
1
1
1
2
3
4
5
x
2
3
4
5
x
1
2
3
4
5
x
y
d.
5
–1
–1
1
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
____ 17. Which graph represents the following system of equations?
y = –x + 2
y = 3x – 3
y
a.
c.
–4
–2
4
4
2
2
O
2
4
x
–2
O
–2
–4
–4
y
–2
–4
–2
b.
–4
y
4
2
2
2
4
x
4
x
2
4
x
y
d.
4
O
2
–4
–2
O
–2
–2
–4
–4
____ 18. Find a solution to the following system of equations.
a. (–4, 3)
b. (2, 3)
c. (0, 7)
d. (4, –1)
Solve the system of equations using substitution.
____ 19. 3y = – x + 2
y = –x + 9
a. (3, 6)
____ 20. 3x + 2y = 7
y = –3x + 11
a. (6, –3)
b. (20, –4)
c. (10, –1)
d. (–1, 8)
b. (6, –7)
c.
d. (5, –4)
____ 21. The sum of two numbers is 67. Their difference is 23. Solve by elimination to find the two numbers.
a.
c.
45 and 22
44 and 23
b.
d.
40 and 23
40 and 17
Solve the system using elimination.
____ 22. 2x = 1 + y
4y = 8 + 4x
a. (2, 4)
b. (5, 3)
c. (3, 4)
d. (3, 5)
____ 23. 3x – 4y = 9
–3x + 2y = 9
a. (3, 9)
b. (–27, –9)
c. (–3, –6)
d. (–9, –9)
____ 24. At the local ballpark, the team charges $4 for each ticket and expects to make $1,500 in concessions. The
team must pay its players $500 and pay all other workers $1,600. Each fan gets a free bat that costs the team
$1 per bat. How many tickets must be sold to break even?
a. 1,200
b. 150
c. 120
d. 200
Graph the inequality.
____ 25.
y
a.
–4
–2
4
4
2
2
O
2
4
x
–2
O
–2
–4
–4
y
–2
–4
–2
b.
–4
y
c.
4
2
2
2
4
x
4
x
2
4
x
y
d.
4
O
2
–4
–2
O
–2
–2
–4
–4
____ 26.
y
a.
–4
4
4
2
2
O
–2
2
x
4
–4
–2
O
–2
–2
–4
–4
y
b.
–4
y
c.
4
4
2
2
2
x
4
–4
–2
O
–2
–2
–4
–4
Write the linear inequality shown in the graph.
____ 27.
y
4
2
–4
–2
O
2
4
x
–2
–4
a.
b.
c.
4
x
2
4
x
y
d.
O
–2
2
d.
Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.
____ 28. y = 4x + 5
y = 4x + 4
a. no solutions
b. one solution
c. infinitely many solutions
____ 29. A jar containing only nickels and dimes contains a total of 60 coins. The value of all the coins in the jar is
$4.45. Solve by elimination to find the amount of nickels and dimes that are in the jar.
a. 30 nickels and 28 dimes
c. 29 nickels and 31 dimes
b. 31 nickels and 29 dimes
d. 30 nickels and 32 dimes
Find a solution of the system of linear inequalities.
____ 30.
a. (4, 1)
b. (2, 2)
c. (1, 2)
d. (5, 2)
Solve the system of linear inequalities by graphing.
____ 31.
y
a.
–4
4
4
2
2
O
–2
2
4
x
–4
O
–2
–2
–2
–4
–4
y
b.
–4
y
c.
4
2
2
O
2
4
–4
x
4
x
2
4
x
y
d.
4
–2
2
O
–2
–2
–2
–4
–4
____ 32. Which number is written in scientific notation?
a.
b.
c.
d.
____ 33. Which list shows the numbers in order from least to greatest?
a.
c.
b.
d.
Simplify the expression.
____ 34.
a. 625
b. –200
c. –6,250
d.
a. –20
b.
c. 100
d. 0
2
125
____ 35.
____ 36.
a.
b.
c.
d.
a.
b.
c.
d.
a. –5.7917
b. 17
c. 5.79
d. 1
c.
d. –16
____ 37.
____ 38.
for x = 2 and y = –4.
____ 39. Evaluate
b. –4
a. 16
Simplify the expression. Write the answer using scientific notation.
____ 40. Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one
year, or approximately 5,880,000,000,000 miles. Suppose a star is 17.6 light-years from Earth. In scientific
notation, how many miles away is it?
a. 5.88  1013 miles
c. 5.88  1012 miles
b. 1.76  1012 miles
d. 1.03488  1014 miles
____ 41.
a.
b.
c.
d.
a. 6.25  102
b.
c. 6.25  103
d.
____ 42.
____ 43. Last year a large trucking company delivered 9.5  105 tons of goods with an average value of $27,000 per
ton. What was the total value of the goods delivered? Write the answer in scientific notation.
a. 2.565  109 dollars
c. 2.565  1010 dollars
b. 2.565  1012 dollars
d. 2.565  1011 dollars
Evaluate the function rule for the given value.
____ 44.
for x = 5
a. 95
b. 30
c. 96
d. 192
Simplify the difference.
____ 45. (3w2 – 8w – 4) – (7w2 + 7w – 2)
a. –4w2 – 1w – 6
b. 10w2 – 1w – 6
c. 10w2 + 15w + 2
d. –4w2 – 15w – 2
Simplify the product.
____ 46. 8p(–3p2 + 6p – 2)
a. –5p3 + 14p2 – 6p
b. 48p2 – 16p – 24p3
c. 14p2 – 6p – 5p3
d. –24p3 + 48p2 – 16p
Simplify the product using FOIL.
____ 47.
a.
c.
b.
d.
____ 48. Find the area of the UNSHADED region. Write your answer in standard form.
x
x+ 5
a. –2x2 + 10x + 25
b. x2 + 8x + 25
c. 10x + 25
d. x2 + 10x + 25
Find the product.
____ 49. (8m2 – 4)(8m2 + 4)
a. 64m4 – 16
b. 64m2 – 16
c. 64m3 – 16
d. 64m4 + 16
Factor the expression.
____ 50. d2 + 15d + 50
a. (d – 5)(d + 10)
b. (d – 5)(d – 10)
c. (d + 5)(d + 10)
d. (d + 5)(d – 10)
____ 51. k2 + 2kf – 63f2
a. (k – 9f)(k – 7f)
b. (k – 9f)(k + 7f)
c. (k + 9f)(k + 7f)
d. (k + 9f)(k – 7f)
____ 52.
a. 2(5x – 2)(2x + 3)
b. 2(5x + 2)(2x – 3)
c. (10x – 2)(4x + 3)
d. 2(5x + 4)(2x – 3)
____ 53. 12x2 + 44x + 35
a. (2x – 5)(6x + 7)
b. (2x + 5)(6x – 7)
c. (2x – 5)(6x – 7)
d. (2x + 5)(6x + 7)
____ 54. 16m2 – 24mn + 9n2
a. (4m – 3n)(4m + 3n)
b. (16m – 3n)(m + 3n)
c. (4m – 3n)2
d. (4m + 3n)2
____ 55. 4x2 – 81y2
a. (2x + 9)(2x – 9)
b. (2x + 9y)(2x – 9y)
c. (2x + 9y)2
d. (2x – 9y)2
____ 56. k2 – 4h2
a. (k + 2h)(k + 2h)
b. (k + 2h)(k – 2h)
c. (k – 2h2)(k + 2)
d. h2(k + 2)(k – 2)
____ 57. 12g3 + 15g2 – 8g – 10
a. (3g2 + 2)(4g – 5)
b. (3g2 – 5)(4g + 2)
c. (3g2 – 2)(4g + 5)
d. (3g2 + 5)(4g – 2)
____ 58. Find the radius of a circle with an area of
a. 3x – 4
b. 9x – 16
c. 16x + 9
.
d. 4x + 3
Factor by grouping.
____ 59. a2 + 5ab – 24b2
a. (a + 8b)(a – 3b)
b. (a – 8b)(a – 3b)
c. (a – 8)(a + 3b)
d. (a + 8b)(a + 3b)
____ 60. 3x2 + 7x – 6
a. (3x – 2)(x – 3)
b. (3x – 2)(x + 3)
c. (x + 3)(3x + 2)
d. (3x + 2)(x – 3)
Find the degree of the monomial.
____ 61. 7m6n5
a. 5
b. 11
c. 6
d. 7
Solve the equation by factoring.
____ 62.
a. z = –6 or z = –4
b. z = –6 or z = 4
c. z = 6 or z = 4
d. z = 6 or z = –4
____ 63. The area of a playground is 135 yd2. The width of the playground is 6 yd longer than its length. Find the
length and width of the playground.
a. length = 21 yd, width = 15 yd
c. length = 15 yd, width = 9 yd
b. length = 15 yd, width = 21 yd
d. length = 9 yd, width = 15 yd
____ 64. The solutions given by the quadratic formula are ________ integers.
a. sometimes
b. always
c. never
Use any method to solve the equation. If necessary, round to the nearest hundredth.
____ 65.
a. 2.25, –7.12
b. 1.12, –7.12
c. 7.12, –1.12
d. 31, –37
ALG I FINAL REVIEW 2008
Answer Section
MULTIPLE CHOICE
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6-4 Standard Form
6-7 Scatter Plots and Equations of Lines
6-1 Rate of Change and Slope
6-1 Rate of Change and Slope
6-1 Rate of Change and Slope
6-2 Slope-Intercept Form
6-2 Slope-Intercept Form
6-2 Slope-Intercept Form
6-4 Standard Form
6-5 Point-Slope Form and Writing Linear Equations
6-5 Point-Slope Form and Writing Linear Equations
6-6 Parallel and Perpendicular Lines
6-6 Parallel and Perpendicular Lines
6-6 Parallel and Perpendicular Lines
6-3 Applying Linear Functions
6-2 Slope-Intercept Form
7-1 Solving Systems By Graphing
7-1 Solving Systems By Graphing
7-2 Solving Systems Using Substitution
7-2 Solving Systems Using Substitution
7-3 Solving Systems Using Elimination
7-3 Solving Systems Using Elimination
7-3 Solving Systems Using Elimination
7-4 Applications of Linear Systems
7-5 Linear Inequalities
7-5 Linear Inequalities
7-5 Linear Inequalities
7-1 Solving Systems By Graphing
7-3 Solving Systems Using Elimination
7-6 Systems of Linear Inequalities
7-6 Systems of Linear Inequalities
8-2 Scientific Notation
8-2 Scientific Notation
8-1 Zero and Negative Exponents
8-1 Zero and Negative Exponents
8-4 More Multiplication Properties of Exponents
8-5 Division Properties of Exponents
8-3 Mulitplication Properties of Exponents
8-1 Zero and Negative Exponents
8-2 Scientific Notation
8-3 Mulitplication Properties of Exponents
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8-4 More Multiplication Properties of Exponents
8-3 Mulitplication Properties of Exponents
8-7 Exponential Functions
9-1 Adding and Subtracting Polynomials
9-2 Multiplying and Factoring
9-3 Multiplying Binomials
9-4 Multiplying Special Cases
9-4 Multiplying Special Cases
9-5 Factoring Trinomials of the Type x^2 + bx + c
9-5 Factoring Trinomials of the Type x^2 + bx + c
9-6 Factoring Trinomials of the Type ax^2 + bx + c
9-6 Factoring Trinomials of the Type ax^2 + bx + c
9-7 Factoring Special Cases
9-7 Factoring Special Cases
9-7 Factoring Special Cases
9-8 Factoring by Grouping
9-7 Factoring Special Cases
9-8 Factoring by Grouping
9-8 Factoring by Grouping
9-1 Adding and Subtracting Polynomials
10-4 Factoring to Solve Quadratic Equations
10-4 Factoring to Solve Quadratic Equations
10-6 Using the Quadratic Formula
10-6 Using the Quadratic Formula