Name———————————————————————— ChapterS
1–5
Date —————————————
Cumulative Test 1
1. Graph y 5 2x 2 2 4x 1 1. Identify the vertex and axis
of symmetry.
Answers
y
1.
See left.
1
1
x
2.
2. Factor 25x 2 2 121.
3.
2
3. Solve x 2 9x 2 22 5 0 by factoring.
4. Solve the equation 4x 2 2 5x 2 6 5 0 by factoring.
5. Solve 5(x 2 3)2 5 75 by finding square roots.
4.
6. Write the product as a complex number in standard form.
5.
(3 1 2i)(4 2 5i)
7. Write the quotient as a complex number in standard form.
21i
 
 ​ 
​ }
3 2 4i
6.
7.
8. Solve x 2 2 5x 1 2 5 0 by completing the square.
10. Find the value of the discriminant and give the number and type of
solutions of the equation 4x2 – 8x 1 3 5 0.
9.
11. A rectangular picture 16 inches by 20 inches has a frame of uniform
10.
width. Find the width of the frame if the total area of the picture and
the frame is 672 square inches.
11.
12. Solve x 2 2 5x 2 24 ≤ 0 algebraically.
13. Evaluate 3222/5.
76
8.
Algebra 2
Assessment Book
12.
13.
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
9. Use the quadratic formula to solve the equation 3y 2 1 7y 1 3 5 0.
Name———————————————————————— Date —————————————
Cumulative Test 1
ChapterS
1–5
1  2
22x3 4
​  22  
​  ​ .
14. Evaluate ​}
3y
Answers
14.
15. Simplify (23x25y 2)22.
16. Multiply (2x 2 1)(3x 2 2 5x 1 4).
15.
17. Subtract (3x2 1 8x 2 2) 2 (5x2 2 x 1 6).
16.
18. Factor completely 7x3 2 56.
17.
19. Find all the real zeros of f(x) 5 x3 2 4x 2 2 11x 1 30.
3
18.
2
20. Find all the zeros of f(x) 5 x 2 2x 1 x 2 2.
19.
21. Divide (x5 2 3x3 2 2x 1 3) 4 (x 1 2).
20.
y
22. Use a graphing calulator to graph f (x) 5 x 3 1 5x 2 1 2x 2 8.
Identify the x-intercepts and the
points where the local maximums
and local minimums occur.
21.
2
2
x
22.
See left.
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
2
__
23. Simplify ​8​ ​3 ​.​
}
Ï
24. Simplify ​ 4  81x6y8 ​ 
.
23.
25. Find f(g(4)) if f(x) 5 3x 2 5 and g(x) 5 7x 2 1.
24.
2
26. Find f (x) 1 g(x) if f (x) 5 x 2 2x and g(x) 5 4x 1 9
2
3
27. Write the equation for the inverse of y 5 ​ } ​ x 1 1.
}
28. Graph y 5 2​Ï x ​.  State the domain and range.
y
25.
26.
27.
28.
See left.
1
1
x
29.
29. Solve 3x
3/4
5 375.
}
30. Solve x 2 5 5 ​Ï 16x ​ 
.
30.
Algebra 2
Assessment Book
77
Name———————————————————————— ChapterS
1–5
Date —————————————
Cumulative Test 1
31. Graph y 5 3 p 2x 2 1 1 4. State the domain and range.
31.
See left.
y
32.
2
33.
x
34.
32. Evaluate log2 64.
33. Evaluate ln e23.
35.
34. Use log8 5 5 0.7740 and log8 4 5 0.6667 to evaluate log8 20.
36.
4x 2
35. Expand log3 }
​  }  ​.
​Ï y ​ 
37.
36. Use the change-of-base formula to evaluate log6 15.
38.
37. Condense the expression 3(log3 14 2 log3 7) 1 2 log3 5.
39.
38. Solve log2x 1 log2(x 1 7) 5 3.
40.
39. Solve log7x 1 log72 5 log7(x 1 6).
41.
40. Solve 5x 1 2 5 12.
41. You deposit $3000 in an account that pays 6% annual interest.
Find the balance after 2 years if the interest is compounded quarterly.
42. Find the domain of f (x) 5 log(x 1 3) 2 1.
43. Write an equation relating x, y, and z given that z varies jointly with
42.
43.
44.
x and y and z 5 20 when x 5 23 and y 5 4. Then find z when x 5 8
and y 5 9.
44. The variables x and y vary inversely. Write an equation relating x and
y when x 5 5 and y 5 2. Then find y when x 5 1.
3
45. Graph y 5 ​ }
   ​ 2 2. x11
State the domain and range.
y
2
2
78
Algebra 2
Assessment Book
x
45.
See left.
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
2
Name———————————————————————— ChapterS
1–5
Date —————————————
Cumulative Test 1
3x 1 1
​. 46. Graph y 5 ​ }  
2x 2 4
y
46.
See left.
State the domain and range.
2
2
x
47.
x
47. Write the equations of the asymptotes of y 5 ​ }
   ​  
.
(x 2 5)2
x2 1 3x 2 18 . 2x2 2 2x
48. Multiply ​ }
   
​ ​ }
  
​
x21
x3 2 3x2
x 2 1 2x 2 35
x 2 2 13x 1 40
49. Divide ​ }
  
​4 }}
​ 
  
  ​. 
2
x 2 7x 1 12
3x 2 2 12x
49.
50.
3
1
50. Add }
​ x 1 2 ​ 1 }
​ x 2 2 ​ 
.
51.
4
8x 2 1
51. Perform the indicated operation and simplify ​ }
  ​ 
2}
​ x 2 2 ​. 
x2 1 x 2 6
52.
3
6
52. Solve ​ }
   ​ 
5}
​ x 1 3 ​. 
x2 2 9
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
48.
2x 2 7
x25
53. Solve ​ }  
​2 }
​  x 1 3  
​5 1.
x13
53.
54.
See left.
55.
54. Sketch a graph of h(t) where h represents altitude and t represents
time for the given situation. Label local minima and maxima and
intervals where h(t) is increasing or decreasing.
A plane flying at a constant altitude is avoiding a storm. It goes up
slowly then back down below its original altitude. It then rises back
to its original altitude, and later slowly descends to a landing.
55. Tell if the function f (x) 5 2x4 1 2x2 1 6 is even, odd, or neither.
Algebra 2
Assessment Book
79
Answers
Cumulative Test 1
y
35. log3 4 1 2 log3 x 2 0.5 log3 y 36. 1.5114
; vertex: (1, 21),
axis of symmetry: x 5 1
37. log3 200 38. 1 39. 6 40. 20.456
41. $3379.48 42. x . 23
1
1
5
43. z 5 2​ } ​ xy; 2120 44. xy 5 10; y 5 10
3
y
45.
; domain: all real numbers
x
3
2. (5x 1 11)(5x 2 11) 3. 22, 11 4. 2, 2 }
​ 4 ​
2
22
}
}
56Ï
​ 17 ​ 
2 1 11i
5. 3 6 Ï
​ 15 ​  6. 22 2 7i 7. }
​  25   
​  8. ​ }
   
​ 
2
}
27 6 Ï
​ 13 ​ 
9. }
​ 
 
 
​ 10. 16; 2 rational solutions
6
11. 4 in. 12. 23 ≤ x ≤ 8
x
46.
; domain: all real numbers
except 2, range: all real
numbers except 1.5
y
16x12 y8
1
13. }
​ 4 ​ 14. ​ }
   
​ 
81
4
4
x10
15. }
​  4 ​  16. 6x 3 2 13x 2 1 13x 2 4
9y
x
17. 22x2 1 9x 2 8
47. x 5 5, y 5 0
18. 7(x 2 2)(x 2 1 2x 1 4) 19. 5, 23 , 2
2x 1 12
48. }
​  x   
​ 
20. 2, i, 2i
3x(x 1 7)
49. }}
​ 
  
 
 ​
(x 2 3)(x 2 8)
1
21. x 4 2 2x 3 1 x 2 2 2x 1 2 2 }
​ x 1 2 ​ 
22.
; x-intercepts: (24, 0),
(22, 0), (1, 0);
x maximum: (23.12, 4.06);
minimum: (20.21, 28.21)
y
2
2
except 21, range: all real
numbers except 22
4x 1 4  
50. }}
​ 
   ​
(x 1 2)(x 2 2)
1
4x 2 13
7
51. }}
​ 
  
  ​ 52. ​ } ​ 53. 2​ } ​
2
2
(x 1 3)(x 2 2)
54.
Decreasing
Increasing
Increasing Decreasing
h(t)
}
23. 4 24. 3xy 2​Ï x ​  25. 76 26. x2 1 2x 1 9
3
2
3
2
27. y 5 }
​   ​ x 2 }
​   ​
; domain: x ≥ 0, range: y ≥ 0
y
28.
1
1
x
29. 625 30. 25
31.
; domain: all real numbers,
range: y > 4
y
2
2
A14
Algebra 2
Assessment Book
x
O
Local
Local
Local maximum
maximum
Local
minimum
minimum
55. neither
t
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
answers
1.
32. 6 33. 23 34. 1.4407