Name: ________________________ Class: ___________________ Date: __________
ID: A
Algebra 2 - Final Review Multiple Choice Identify the choice that best completes the statement or answers the question. Multiple Choice Questions will require a Scantron. To which set of numbers does the number belong? ____
34
1. a. b. c. d.
rational numbers integers irrational numbers natural numbers
Which algebraic expression models the given word phrase? ____
2. 40 fewer than a number t a. b.
____
40t t 40
c. d.
40 t t 40
3. You had $199, but you are spending $3 each day. What algebraic expression models this situation? a. 199 3d c. 196d b. 199 3d d. 3 199d Write an algebraic model for the situation and evaluate it for the given information.
____
4. You are going shopping for some new sweaters, t-shirts, and pants. Sweaters (s) cost $30, t-shirts (t) cost $19, and pants (p) cost $18. What algebraic expression models the total cost of clothes that you buy? Suppose you bought 26 sweaters, 9 t-shirts, and 23 pairs of pants. How much did you spend? a. b.
30s 19t 18p ; $1,329 26s 9t 23p ; $1,329
c. d.
26s 9t 23p ; $1,365 30s 19t 18p ; $1,365
c. d.
14, –14 –4, 4
Solve the equation. ____
5. x 2 18x 81 25 a. 14, 4 b. –4, –14
16
Name: ________________________
ID: A
Solve the equation or formula for the indicated variable. ____
6. S 5r 2 t , for t a.
t
S r 5
b.
t
25r S
c.
t r 2 5S
d.
What inequality represents the sentence? ____
7. The product of a number and 5 is no more than 8. a. b.
5n 8 5n 8
c. d.
5n 8 5n 8
c.
b1
d.
no solutions
Solve the inequality. Graph the solution set. ____
8. 26 + 6b 2(3b + 4) a.
all real numbers
b.
b1
1 2
1 2
Solve the compound inequality. Graph the solution. ____
9. 9x – 5 < –41 or 3x + 13 > 7 1 a. x < 5 or x > –2 9
b.
1 2 x < 5 or x > 6 9 3
2 3
c.
x < –4 or x > 6
d.
x < –4 or x > –2
2
t
S 5r 2
Name: ________________________ ____ 10. 10 2x 4 6 a. 3 x 1
b.
1 x 7
ID: A
c.
3 x 5
d.
8 x 0
Solve the absolute value equation. Graph the solution. ____ 11. 2x 1 3 a. x = 1 or x = 4
c.
x = 1 or x = 1
x = 1 or x = 2
d.
x = 2 or x = 1
b.
Solve the equation. Check for extraneous solutions. ____ 12. 2 7 7x 2x 4 a. b.
3 5 or x = 2 6 3 5 x = or x = 2 8 x=
c. d.
5 8 3 x= 2 x=
Solve the inequality. Graph the solution. ____ 13. 2x 4 22 a.
x 13 or x 9
c.
x 13 or x 9
b.
x 9 or x 9
d.
x 26 or x 18
3
Name: ________________________
ID: A
____ 14. 2x 5 15 a.
x 5 or x 5
c.
–10 x 5
b.
–20 x 10
d.
–10 x 5
____ 15. A furniture maker uses the specification 21.88 w 22.12 for the width w in inches of a desk drawer. Write the specification as an absolute value inequality. a. w 0.24 22.12 c. w 22 0.24 b. w 0.12 22 d. w 22 0.12 ____ 16. Find the domain and range of the relation and determine whether it is a function.
–3 a. b. c. d.
domain: all real numbers; range: all real numbers; Yes, it is a function. domain: positive integers; range: positive integers; No, it is not a function. domain: x 0; range: y 3; No, it is not a function. domain: x > 3; range: y > 0; Yes, it is a function.
Is the relation a function? ____ 17. {(14, 9), (15, 8), (8, 7), (1, 9), (15, 2)} a. b.
yes no
4
Name: ________________________
ID: A
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation. ____ 18. x
y
5
20
15
60
45
180
135
540
a. b.
yes; k = 4; y =4x yes; k = 5; y =5x
c. d.
yes; k = 3; y =3x no
c. d.
yes; k = 2.33; y =2.33x no
____ 19.
a. b.
x
y
3
7
4
9
5
11
6
13 yes; k = 3; y =3x yes; k = 2.25; y =2.25x
Determine whether y varies directly with x. If so, find the constant of variation k. ____ 20. –3y = –5x a.
yes; –5
3 5
b.
yes;
b.
yes; 2
c.
yes;
5 3
d.
no
c.
yes; 1
d.
no
d.
81
____ 21. y + 2x = – 19 a.
yes; 2
Find the value of y for a given value of x, if y varies directly with x. ____ 22. If y = 44 when x = –264, what is y when x = –486? a.
–2916
b.
–81
c.
5
2916
Name: ________________________
ID: A
What is the slope of the line that passes through the given points? ____ 23. (6, 2) and (7, 4) a.
2
c.
1 2
b.
1 2
d.
2
What is an equation of the line in slope intercept form? ____ 24. m = a. b.
1 and the y-intercept is (0, –5) 2 1 y x5 2 1 y 5x + 2
c. d.
1 y x5 2 1 y 5x 2
Write the equation in slope-intercept form. What are the slope and y-intercept? ____ 25. 11x 9y 12 11 4 a. y x ; 9 3 11 4 slope: ; y-intercept: 9 3 b.
11 4 x 9 3 11 4 slope: ; y-intercept: 9 3
y
c.
d.
11 4 x ; 9 3 11 4 slope: ; y-intercept: 9 3
y
11 4 x ; 9 3 4 11 slope: ; y-intercept: 3 9
y
Write an equation of the line, in point-slope form, that passes through the two given points. ____ 26. points: (2,10), (10,14) a. b.
1 y 2 (x 10) 2 1 y 10 (x 2) 2
c.
y 10 2(x 2)
d.
y 2 2(x 10)
What is the equation of the given line in standard form? Use integer coefficients.
5 ____ 27. y x 12 7 a. b.
5x 7y 12 5x 7y 84
c. d.
6
5x 7y 84 5x 7y 84
Name: ________________________
ID: A
What are the intercepts of the equation? Graph the equation. ____ 28. 3x 4y 12 a.
x-intercept: (–3, 0) y-intercept: (0, 4)
c.
x-intercept: (4, 0) y-intercept: (0, –3)
b.
x-intercept: (4, 0) y-intercept: (0, –3)
d.
x-intercept: (–3, 0) y-intercept: (0, 4)
What is the equation of the line in slope-intercept form? ____ 29. the line parallel to y 8x 8 through (5, 2) a.
y 8x 38
c.
b.
y 8x 42
d.
7
1 y x 38 8 y 8x 38
Name: ________________________
ID: A
1 ____ 30. the line perpendicular to y x 5 through (2, 1) 3 1 a. y x 7 c. 3 b.
y 3x 7
d.
y 3x 7 1 y x7 3
____ 31. A candle is 18 in. tall after burning for 3 hours. After 5 hours, it is 16.5 in. tall. Write a linear equation to model the relationship between height h of the candle and time t. Predict how tall the candle will be after burning 8 hours. a. b.
h t 0.75t 20.25; 14.25 inches h t 0.75t 15.75; 9.75 inches
c. d.
h t 0.75t 15.75; 9.75 inches h t 0.75t 20.25; 14.25 inches
What are the solutions of the following systems?
x 2y 10 ____ 32. 3x 6y 11 a. infinitely many solutions b. (–5, 2)
c. d.
(5, –2) no solutions
x 3y 9 ____ 33. x 3y 9 a. (5, –6) b. no solutions
c. d.
(–5, 6) infinitely many solutions
____ 34. A group of 36 people attended a ball game. There were twice as many children as adults in the group. Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of adults and the number of children who were in the group. a. b.
a c a c
c 36 2a c 36
; 12 adults, 24 children ; 17 adults; 24 children
c. d.
a2
8
a a a a
c 36 c2 c 36 2c
; 24 adults; 17 children ; 24 adults, 12 children
Name: ________________________
ID: A
____ 35. Identify the maximum or minimum value and the domain and range of the graph of the function y 2(x 2) 2 3 . a. minimum value: 3 domain: all real numbers 3 range: all real numbers b. maximum value: –3 domain: all real numbers 3 range: all real numbers c. maximum value: 3 domain: all real numbers range: all real numbers 3 d. minimum value: –3 domain: all real numbers range: all real numbers 3 2 2 ____ 36. What steps transform the graph of y x to y (x 3) 5 ? a. translate 3 units to the right, translate down 5 units b. translate 3 units to the left, translate up 5 units c. reflect across the x-axis, translate 3 units to the left, translate up 5 units d. reflect across the x-axis, translate 3 units to the right, translate down 5 units
What are the vertex and the axis of symmetry of the equation? 2 ____ 37. y 2x 24x 16
a. b.
vertex: ( –6, –88) axis of symmetry: x 6 vertex: ( –6, 88) axis of symmetry: y 6
c. d.
vertex: ( 6, –88) axis of symmetry: x 88 vertex: ( –6, –88) axis of symmetry: x 88
What is the maximum or minimum value of the function? What is the range? 2 ____ 38. y 2x 28x 8
a. b.
minimum value: 7 range: y 7 minimum value: –7 range: y 7
c. d.
minimum value: –106 range: y 106 minimum value: –106 range: y 7
What is the vertex form of the equation? 2 ____ 39. y x 2x 8
a. b.
y (x 1) 2 7 y (x 1) 2 7
c. d.
9
y (x 1) 2 7 y (x 1) 2 7
Name: ________________________
ID: A
What is the expression in factored form? ____ 40. 9x 2 18x 9 a. (3x 3) 2
c.
(3x 3) 2
(3x 3)(3x 3)
d.
(3x 3) 2
____ 41. 16x 2 25 2 a. (4x 5) b. (4x 5)(4x 5)
c. d.
(4x 5)(4x 5) (4x 5)(4x 5)
b.
What are the solutions of the quadratic equation? ____ 42. x 2 11x 28 a. –4, –7 b. –4, 7
c. d.
4, 7 4, –7
2 ____ 43. The function y 16t 486 models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second. a. 7.79 seconds c. 0.25 seconds b. 11.02 seconds d. 5.51 seconds
What is the solution of each equation? ____ 44. 3x 2 21 a.
7
b.
7, –
c.
7
21
21
,
d.
3 7,
3
c. d.
two solutions cannot be determined
21
What is the number of real solutions? ____ 45. x 2 9x 7 0 a. b.
one solution no real solutions
Simplify the number using the imaginary unit i. ____ 46.
360 a. 6 10 b. 6i 10
c. d.
10
i 360 6 10
Name: ________________________
ID: A
What is the absolute value of each number? ____ 47. 1 3i . a.
2
c.
b.
–8
d.
10 3
____ 48. (3 i) (2 2i) a. 1 3i b. 5 i
c. d.
4i 1 3i
____ 49. (4 i)(2 5i) a. 2(4 9i) b. (13 18i)
c. d.
3 18i (8 18i)
Simplify the expression.
____ 50.
2 3i 6i a. b.
1 2 1 2
1 i 3 1 i 3
c. d.
1 2 1 2
1 i 3 1 i 3
____ 51. Find the solutions of the equation. 1 2 x x5 0 2 a. b.
1 9i 1 9i
c. d.
1 11i 1 11i
What is the solution of the quadratic system of equations?
y x 2 18x 35 ____ 52. 2 y x 2x 5 a. b.
(3, –10) (5, –30) (–3, –10) (–5, –30)
c. d.
11
(–3, 98) (–5, 150) (–10, –3) (–30, –5)
Name: ________________________
ID: A
What is the solution of the system of inequalities? ____ 53.
y x 2 6x 11 y x 2 8x 13
a.
c.
b.
d.
Find the values of the variables.
12 w 2 2k 81 ____ 54. 14 3 3 2f a. f = –7, k = 6, w = 9 or –9 b. f = –7, k = –6, w = 9 or –9
c. d.
12
f = –7, k = –6, w = 81 or –81 f = –7, k = –6, w = 9
Name: ________________________
ID: A
Solve the matrix equation.
2 8 4 ____ 55. 2X 2 2 4 2 0 5 a. 3 2 0 11 b. 3 6
6 8 c.
d.
0 5 4 5
5 6 5 2
Determine whether the product is defined or undefined. If defined, give the dimensions of the product matrix.
1 ____ 56. 5 a. b.
9 1 4 1 6 0 7 defined; 3 3 defined; 2 1
c. d.
defined; 2 3 undefined
c.
–136
Evaluate the determinant of the matrix.
4 5 4 ____ 57. 0 2 5 a. –104
6 4 4 b.
–72
d.
Does the given matrix, A, have an inverse? If it does, what is A 1 ?
7 25 ____ 58. A = 7 2 7 25 a. 2 7 7 25 b. 2 7
c.
7 2
d.
does not exist
13
25 7
136
Name: ________________________
ID: A
0 19 ____ 59. A = 0 1 0 19 a. 0 0 0 19 b. 0 1
c.
0 0
0 0
d.
does not exist
c.
10 24
What is the solution of the matrix equation?
5 ____ 60. 2 a.
2 2 X 1 4 2 4
b.
10 24
d.
10 24
Short Answer The following questions may require the display of work to receive credit. Graph the number on a number line. 1.
11 Solve the equation.
2. 2y 4 8 y 2 3. Identify the vertex and the axis of symmetry of the graph of the function y 2(x 2) 4 .
What value completes the square for the expression? 4. x 2 16x Use matrices A, B, and C. Find the sum or difference if you can. 5 4 2 7 3 5 3 1 B C A 8 2 1 6 0 3 0 6 5. B – A
14
Name: ________________________
ID: A
Evaluate the determinant of the matrix.
9 6. 6
9 6
What is the graph of each absolute value inequality? 7. y |x – 1| + 3 Solve the system by substitution.
2x y 14 8. 3x y 11 Solve the system using elimination.
4x 4y 8 9. x 4y 7 Solve the system of inequalities by graphing.
y 3x 1 10. y 3x 2 Solve the system of inequalities by graphing.
y 4 11. y x 1 What is the graph of the equation? 2 12. y x 2x 3
What is the expression in factored form? 13. x 2 14x 48 Solve the quadratic equation by completing the square. 14. x 2 10x 14 0
15
Name: ________________________
ID: A
Use the Quadratic Formula to solve the equation. 15. 2x 2 5x 5 0 Find the product.
5 16. 2
5 4 3 8
9 7
What is the graph of each inequality? 17. –4x + 4y 4 Evaluate the expression for the given value of the variable(s). 18. 4b 4 3 b 2 2b 3 ; b = 2 Combine like terms. What is a simpler form of each expression? 19. 3(4y 3) 7y For each function, what is the output of the given input? 20. For f x 3x 6 , find f 2 .
16
