Download dm065 review 2r (6/00) - City Tech

2R
NEW YORK CITY COLLEGE OF TECHNOLOGY
of the City University of New York
DEPARTMENT OF MATHEMATICS
Revised 09/08
MAT063 AND MAT065 FINAL EXAM REVIEW – FORM 2R
Evaluate:
6x  3 y 2
1.
when x = 5, y = – 4, z = 6
3z
Solve and Check:
4x  1 2x  1 3
13.


3
6
2
Simplify:
Write an equation that expresses the word sentence
and solve:
14.
If ten times a number is increased by four,
the result is twelve more than nine times the
number. Find the number.
Solve for r:
mv 2
15.
F
gr
2.
(5x2 – 6x + 3) + (4x2 + 5x – 4) – (3x2 + x – 8)
Multiply and Combine:
3.
– 3xy(4x2y2 – 6xy) + 10x3y3
Factor Completely:
4.
25a2b – 35ab2  40ab
Solve:
16.
1.05y + .6y = – 4.95
Divide:
Reduce:
 10a 4 b 3  15a 3b 2  5a 2 b
17.
5a 2 b
6 3 2
5.
45 x y z
 9 xy 3 z 3
Multiply:
30a 2 6b

6.
18b 5a
Multiply:
18.
(2x – 7)(x – 9)
Evaluate:
7.
Is x = 7 the solution to 5x – 4 = 3x + 10?
Solve:
x 2  4 x  21  0
19.
Solve:
8.
3(x – 2) – 2 = 5(x + 3) – 7(x – 1)
Factor Completely:
20.
24x5y3 – 16x7y2 + 8x2y2
Divide:
Factor and Reduce:
y2  y  6
21.
y2  9
9.
7 xy 2 14 y 2

 10rs 5r 3 s 3
Combine:
8
5
 2
10.
3x 6 x
Multiply:
 2a  5b  6c 
22.
    

 3b  4c  35a 2 
Factor Completely:
11.
49 - 64 y 2
Solve:
23.
2f + 1.3f = – .7f + 32
Reduce:
10 y 4  5 y 3  15 y 2
12.
 5y2
Factor Completely:
24.
16 x 2 - 81
2R
Page 2 Factor and reduce:
5 x 2  15 x
25.
x2  9
Multiply and combine:
Solve and Check:
26.
5( x  3)  ( x  2)  11
Solve and Check:
38.
2y – 3 – 4y = 5 – 6y – 4
Combine:
2a  1 4a  2
27.

5a
4a
Evaluate:
Divide:
Combine:
4
7
 2
40.
9 y 3y
28.
9b
3b
4 
y
14y 2
2
37.
39.
2cd(c2d + d2) – 7cd3
Is x = – 5 the solution to 9x – 4 = 12 + 5x?
Solve Graphically:
5 x  3 y  9
29.
3x  4 y  12
Solve Algebraically:
3r  7 s  4
41.
2r  5s  3
Solve:
30.
7.4 = 1.8y – 16
Solve for t:
42.
a = p – rt
Solve for M:
M V
u
31.
V
Solve:
18x 2  9 x  0
43.
Multiply:
Write an equation that expresses the word
sentence and solve:
44.
Five times a number decreased by eighteen
equals three times the number increased
by six. Find the number.
32.
3c(5c  7)(4c  3)
Solve and Check:
33.
y2 – y – 12 = 0
Solve and Check:
34.
– 2y – 3 + 5y = 8 – 3y + 7
Solve and Check:
45.
13 – (2x – 5) = 2(4x – 1)
Solve:
46.
m2 – 8m + 15 = 0
Write an equation that expresses the word sentence
and solve:
35.
A 25–foot board is cut into two pieces so that
the longer piece is one foot more than twice
the measure of the shorter piece. Find the
measurement of each piece.
Multiply:
Evaluate:
Evaluate:
36.
4x2 + 3x – 5 when x = – 2
47.
48.
 8 x 2 y 2  39d 4 f 9  12ab 




  13d  40 x  27d 3 f 9 x 




c 2  b 2 when b = 9, c = 15
2R
Page 3 Factor completely:
49.
Divide:
25x3 – 25x2 – 50x
61.
Evaluate:
50.
9 y3
2 x 3  20 x 2  48x
62.
2(y – 3) + 17 = 13 – 3(y + 2)
Solve Graphically:
3x  2 y  3
63.
 x  y 1
Solve:
a2 – 64 = 0
64.
17 3a 4a


4
8
5
Solve Algebraically:
3r  4s  17
53.
2r  3s  0
Solve:
Solve:
Multiply:
54.
20 x 4
6 – 3(2 – 4)2
Solve:
52.
27 y 2

Factor Completely:
Solve:
51.
8x 3
3x2
65.
+x=0
66.
k2 – 144 = 0
(7x + 5y)(7x + 5y)
Factor and Reduce:
4x
55.
2
4 x  16 x
Solve:
Evaluate:
Combine:
3
7

68.
2
10 x
5x
56.
67.
Is (3, 5) the solution to y = 3x – 12?
Evaluate:
Solve:
a 2  b 2 when a = 6, b = 8
57.
Reduce:
12 x y
y  8x y
3 2
 4x
2
2
4x y
Evaluate:
c  2d
2x
3
59.
12 3 1
 
5t t 15
70.
(2) 5  6
2
Multiply and Combine:
2
when c = – 2, d = 4, x = 5
Evaluate:
60.
69.
Evaluate:
2 2
58.
2x2 – 3x = 0
a 2  b 2 when a = 4, b = 3
71.
– 4xy(2x2 – 5y – 7xy2) + 3xy2
Solve for y:
72.
12x – 3y = 6
2R
Page 4 Multiply and Simplify:
Multiply and Simplify:
73. 2 3a 5 3a 6a 4b
77.  5 y 12 z 2 4 z 5 2 y11



State the slope and y-intercept and sketch the
graph of the equation:
74.
 7 x  2 y  10
2.2 10 
4 10 1.110 
3
Evaluate:
2.4 10 7.7 10 
1.110 1.2 10 
5
76.
2
5 10 3.9 10 
1.3 10 
1
6
79.
12
Evaluate:
3
7
 5x  3 y  4
Evaluate:
7
15

State the slope and y-intercept and sketch the
graph of the equation:
78.
Evaluate:
75.


2.8 10 2.5 10 
3.5 10 8 10 
11
80.
2
3
6
2R
Page 5 ANSWERS
1.
–1
2.
6x2 – 2x + 7
4.
5ab(5a – 7b + 8)
5.

7.
Yes, because 31 = 31
8.
16 x  5
10.
6x
2
3.
– 2x3y3 + 18x2y2
6.
2a
x=6
9.
 xr 2 s 2
xr 2 s 2
OR 
4
4
11.
(7 + 8y)(7 - 8y)
12.
– 2y2 + y – 3
5x 5
 5x 5
OR
z
z
mv 2
fg
13.
x=1
14.
n=8
15.
r
16.
y = –3
17.
– 2a2b2 + 3ab – 1
18.
2x2 – 25x + 63
19.
x = 3, x = –7
20.
8x2y2(3x3y – 2x5 + 1)
21.
1
7a
5x
x3
42b
 42b
OR
–
2
y
y2
23.
f=8
24.
(4x + 9)(4x – 9)
26.
x=6
27.
 6a  7
10a
29.
(0, – 3)
30.
y = 13
31.
M = V(u – 1) OR uV – V
32.
60c3 – 39c2 – 63c
33.
y = 4, y = –3
34.
y=3
35.
8 ft., 17 ft
36.
5
37.
2c3d2 – 5cd3
4 y  21
38.
y=1
39.
41.
(1, 1)
42.
No, because – 49  – 13
pa
a p
 r
OR
r
44.
n = 12
45.
x=2
48.
12
22.
25.
28.
40.
9y2
y2
y 3
43.
1
x = 0, x = 2
46.
m = 3, m = 5
47.
 4aby 2
4aby 2
OR 
15
15
49.
25x(x – 2)(x + 1)
50.
–6
51.
4
y=–5
52.
a = 8, a = – 8
53.
r = 3, s = – 2
54.
x = 0, x = –
55.
1
x4
56.
No, because 5 –3
57.
10
3y – xy + 2
2y
15 x
59.
–4
60.
5
62.
2x(x – 6)(x – 4)
63.
(– 1, 0)
a = 10
65.
k = 12, k = – 12
66.
49x2 + 70xy + 25y2
58.
61.
64.
1
3
2R
Page 6 -
6  7x
67.
3
x = 0, x = 2
68.
70.
13
71.
73.
18a5 2ab
74. y 
76.
1.4 102
77.  40 y 6 z 6 6 y
79.
1.5 10 6
80.
10 x 2
– 8x3y + 23xy2 + 28x2y3
7
x 5
2
2.5 103
m=
7
, b = -5
2
69.
t=–9
72.
y = 4x – 2
75.
5104
5
4
5
4
78. y   x 
m=  ,b=
3
3
3
3