Download Math Level 3 Answer Key

Keystone National High School Placement Exam
1. Graph the equation y = x + 4 .
Answer:
y
Math Level III
− 3 0  − 4 2
2. Simplify 
+

 5 − 7  − 1 8 
Answer:
− 7 2
1
16
c. 
4
12
8
4
–8
–4
O
4
8
x
–4
3.
Graph the equation
4. Identify the vertex and the y-intercept of
the graph of the function
y = −2( x − 2) − 4 .
2
y = −3( x + 2) + 5 .
2
Answer:
y
8
6
Answer: a. vertex: (–2, 5); y-intercept:
–7
4
2
–8 –6 –4 –2 O
–2
2
4
–4
–6
–8
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6
8
x
Keystone National High School Placement Exam
5. Write the number in the form a + bi.
− 4 + 10
Answer: 10 + 2i
Write 7. Write the expression (x + 6)(x – 4) as a
polynomial in standard form.
Answer: c. x2 + 2x – 24
6. Simplify the expression (− 6i )(− 6i ) .
Answer: b. -36
8. Divide using synthetic division.
(x
4
)
+ 15x 3 − 77 x 2 + 13x − 36 ÷ ( x − 4)
Answer:
d.
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Math Level III
x 3 + 19 x 2 − x + 9
Keystone National High School Placement Exam
Math Level III
Find
the
real-number
root.
10.
Solve
the
equation
9.
x + 10 − 7 = −5
− 125
3
343
Answer: d. −
5
7
11. Solve the equation
3y + 20 = 3 + 2 y
Answer: y = -17
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Answer: d. x = -6
12. Solve the equation 3x + 5 = 1 .
1
Answer: x = −1 or x = −2
3
Keystone National High School Placement Exam
Math Level III
14. Write the equation in logarithmic form.
13. Solve the equation
6 4 = 1,296
3(y + 6) = 30
Answer: c. 4
Answer:
a.
16. Solve the following
15. Simplify
5
−2
4
=
x+4 x+3
2
4a 2b
×
7b4 2a4
Answer:
log 6 1,296 = 4
4a
7b 2
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−
Answer:
11
3 or
−3
2
3
Keystone National High School Placement Exam
Math Level III
con18. A bag contains 6 red marbles, 6 white
17. Evaluate the expression A5abag
+ 5b
given a = -6 and b = -5.
marbles, and 4 blue marbles. Find P(red or
blue).
Answer: a. -55
Answer: c. 5/8
0
19. Simplify (-2.7)
20. Find a solution to the following
system of equations.
Answer: c. 1
-5x + y = -5
-4x + 2y = 2
Answer: d. (2, 5)
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Keystone National High School Placement Exam
Math Level III
21. Solve the inequality –5x – 7 < 28
22. Write a compound inequality that
the graph could represent.
–5
Answer: a. x > –7
( )−2
23. Simplify 4
Answer:
1
16
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–4
–3
–2
–1
0
Answer: d. -4<x<2
24. Simplify 7a-5b3
7b 3
Answer:
a5
1
2
3
4
5
Keystone National High School Placement Exam
(
25. Simplify 3xy
) ( xy)
3 2
8 12
Answer: 9 x y
Math Level III
14
6
26. Simplify
x
x7
Answer:
x7
27. Solve
3
7
x+5=8
Answer: x=7
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28. Solve
3p – 1 = 5(p – 1) – 2(7-2p)
Answer: p=3
Keystone National High School Placement Exam
29. Find the zeros of y = x(x - 3)(x – 2)
30. Add
Answer: 0, 3, 2
Math Level III
3
8
+ 2
m + 5 m − 25
3m − 7
Answer: (m − 5)(m + 5)
31. Evaluate the expression
4b − 4 + 3 − b 2 + 2b 3
32. Solve s = 5r t , for t.
2
using
b=2
Answer: 21
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Answer: t =
s
5r 2
Keystone National High School Placement Exam
Math Level III
33. Solve 2r – 9 ≥ –6.
34. Solve 2 x + 10 < 26
Answer: r ≥ 1
1
3
or r ≥
2
2
p 2 − 4 p − 32
35. Simplify
p+4
Answer: p-8
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Answer: –18 < x < 8
36. Simplify
3
128a 13b 6
. Assume
that all variables are positive
Answer:
4a 4 b 2 3 2a
Keystone National High School Placement Exam
Math Level III
2
38.
Factor
the
expression
37. Solve 3x = 21 .
8 x 2 + 12 x − 16
Answer:
7, – 7
39. Factor the expression
x + 14 x + 48
2
Answer: (x + 6)(x + 8)
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2
Answer: 4(2 x + 3x − 4)
40. Factor the expression
x 2 − 6x + 8
Answer: (x – 2)(x – 4)
Keystone National High School Placement Exam
Math Level III
2
42. Solve by factoring
41. Factor 9 x − 16
4 x 2 + 28 x − 32 = 0
Answer: (3x+4)(3x-4)
43. Use the Quadratic Formula to
2
solve 5x + 9 x − 2 = 0
Answer:
1
5
Answer: –8, 1
44. Find the value for x and y in
 4 3 4 y 
− 1 2 =  x 2 

 

, −2
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Answer: x = –1, y = 3
Keystone National High School Placement Exam
Math Level III
46.Solve the system by graphing
45. Solve the system
y < -3x - 1
5x – y = 5
y > 3x - 2
5x – 3y = 15
Answer:
y
Answer: (0, –5)
4
2
–4
–2
O
2
4
x
–2
–4
47. f(x)=5x+2, find f(-4).
Answer: –18
48. Graph the equation y = −
1
x − 3.
4
Answer:
y
4
2
–4
–2
O
–2
–4
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2
4
x
Keystone National High School Placement Exam
Math Level III
Simplify
(-1
+
6i)
+
(-4
+ 2i).
49. Write in standard form an equation of
50.
the line passing through the point (-2,-2)
with the slope of -8.
Answer: -5 + 8i
Answer: 8x + y = –18
51. Divide 3x 3 − 3x 2 − 4 x + 3 by x + 3.
Answer: 3x − 12 x + 32 , R –93
− 93
or 3 x 2 − 12 x + 32 +
x+3
52. Write the exponential expression in
radical form
3x
2
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Answer:
38 x 3
3
8
Keystone National High School Placement Exam
Math Level III
4
4
53.Multiply and Simplify
54. Simplify 2 2 x + 6 2 x .
7− 2 8+ 2
4
Answer: 8 2 x
(
)(
)
Answer:
54 − 2
55. Multiply and simplify
Answer: 2 3
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6⋅ 2 .
56. Solve
4
=2
−x
Answer: x = -2