Name: ________________________ Class: ___________________ Date: __________
ID: A
Algebra 1CP Final- REVIEW
Short Answer
ÏÔÔ
ÔÔ 3x + 3y = 15
1. Tell whether the ordered pair (3, 2) is a solution of the system ÌÔ
.
ÔÔ −x − 3y = −9
Ó
ÏÔÔ
ÔÔ x − y = −4
by substitution. Express your answer as an ordered pair.
2. Solve ÌÔ
ÔÔ x = 2y − 12
Ó
ÏÔÔ
ÔÔ −3x − y = 15
3. Solve ÌÔ
by elimination. Express your answer as an ordered pair.
ÔÔ −x − y = −11
Ó
4. At the local pet store, zebra fish cost $2.25 each and neon tetras cost $1.95 each. If Marsha bought 11 fish for
a total cost of $23.55, not including tax, how many of each type of fish did she buy?
5. An airplane travels 900 miles from Houston to Miami in 6 hours against the wind. On its return trip, with the
wind, it takes only 5 hours. Find the rate of the airplane with no wind. Find the rate of the wind.
6. A paint mixer wants to mix paint that is 15% gloss with paint that is 30% gloss to make 6 gallons of paint
that is 25% gloss. How many gallons of each paint should the paint mixer mix together?
7. Tell whether (6, 1) is a solution of y > 3x − 2 .
8. Write an inequality to represent the graph.
9. Simplify 2 −2 .
10. Simplify 3 0 .
11. Find the value of the power 10−3 .
12. Find the value of the expression 166 × 10−3 .
13. Simplify (−2) 2 ⋅ (−2) 4 .
1
Name: ________________________
ID: A
14. Simplify n 7 ⋅ m6 ⋅ n 8 .
15. Simplify (x 4 ) −7 x 2 .
16. Simplify
33
.
3
ÁÊÁ 2x 8
17. Simplify ÁÁÁÁ 3 5
Áx y
Ë
3
˜ˆ˜
˜˜ .
˜˜
˜
¯
2
3
18. Simplify the expression 64 .
19. Tell whether the number 2 is a root of 2r 2 − 7r − 15.
20. Add or subtract.
5z − 10z 4 − 12z − 6z 4
21. Subtract.
(7e 2 − e ) − (e 2 + 4e − 2)
22. Multiply.
Ê
ˆ
3a b 3 ÁÁ 3a 4 b 5 + 3a 2 b 5 ˜˜
Ë
¯
23. Multiply.
(z − 3)(z − 4)
24. Multiply.
(p − 3) 2
25. Multiply.
(e + 9)(e − 9)
26. Factor the polynomial 10x 3 + 24x 2 − 6x .
27. Factor the trinomial b 2 − 2b − 8.
28. Factor 3x 2 − 11x + 6.
29. Without graphing, tell whether the point (–8, 2) is on the graph of y = −2x 2 − 6 .
30. Graph y = x 2 − 3x + 4 . Find the axis of symmetry and the vertex.
31. Solve the quadratic equation z 2 + 2z − 15 = 0 by factoring.
32. Solve x 2 = 9 by using square roots.
33. Solve 49x2 – 9 = 0 by using square roots.
34. Complete the square for x 2 + 4x + ? to form a perfect square trinomial.
35. Solve 2x 2 − x − 4 = 0 by using the Quadratic Formula.
2
Name: ________________________
ID: A
36. Simplify the rational expression
2r 2 − 4r
. Identify any excluded values.
r −2
37. Multiply. Simplify your answer.
x2 − x − 6
x2 + x
⋅
.
2x 2 − 6x x 2 + 4x + 4
38. Divide. Simplify your answer.
1 n−4
÷
n
4n
39. Add. Simplify your answer.
3x + 8
4
+ 2
2
x − 16 x − 16
40. Add. Simplify your answer.
3y
3y
−
2
18y
9y
41. Divide. Simplify your answer.
(12x 4 − 18x 3 + 36x 2 ) ÷ 6x 3
42. Divide.
(2x 2 + 3x − 15) ÷ (x − 3 )
43. Solve
3
2
=
. Check your answer.
q − 3 5q
44. Solve
6 5 −7
+ =
. Check your answer.
t 4
4
48 .
45. Simplify the expression
46. Simplify
x 11
. The variable represents a nonnegative number.
25x
47. Simplify
160
.
49
8x + 4 50x −
48. Simplify the expression
18x .
49. Multiply. Write the product in simplest form.
4h
14h
50. Simplify the quotient
7
10
.
3
Name: ________________________
51. Solve the equation
52. Solve
ID: A
a = 16. Check your answer.
3z + 7 = 4. Check your answer.
4
ID: A
Algebra 1CP Final- REVIEW
Answer Section
SHORT ANSWER
1.
2.
3.
4.
5.
6.
7.
8.
yes
(6, 6)
(–13, 24)
7 zebra fish, 4 neon tetras
The airplane flies at 165 mi/h with no wind. The rate of the wind is 15 mi/h.
The paint mixer should use 2 gallons of 15% gloss paint and 4 gallons of 30% gloss paint.
No, (6, 1) is not a solution of y > 3x − 2 .
y ≤ 2x + 3
9.
1
4
10.
11.
12.
13.
1
0.001
0.166
64
14. n 15 ⋅ m6
1
15. 26
x
16. 9
17.
8x 15
y 15
18. 16
19. No
20. −7z − 16z 4
21. 6e 2 − 5e + 2
22. 9a 5 b 8 + 9a 3 b 8
23. z 2 − 7z + 12
24. p 2 − 6p + 9
25. e 2 − 81
26.
27.
28.
29.
2x (5x 2 + 12x − 3)
(b − 4)(b + 2)
(x − 3)(3x − 2)
No
1
ID: A
30.
Ê3 7ˆ
3
The axis of symmetry is x = 2 . The vertex is ÁÁÁ 2 , 4 ˜˜˜ .
Ë
¯
31. –5 and 3
32. The solutions are 3 and –3.
3
33. ± 7
34. x 2 + 4x + 4
35. x =
36.
37.
38.
39.
40.
1±
33
4
2r; r ≠ 2
x+1
2x + 4
4
n −4
3
x−4
y−2
6y
41. 2x − 3 +
6
x
42. 2x + 9 +
12
x−3
6
43. q = − 13
44. t=-2
45. 4
3
5
46.
x
5
47.
4 10
7
48. 19 2x
49. 2b
50.
15
70
10
2
ID: A
51. a = 256
52. No solution.
3