Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
Find the mode for the group of data items. If there is no mode, so state.
1)
1)
5, 9, 75, 3, 2, 8, 39, 1, 4, 16
A)
8
B)
no mode
C)
15.6
D)
9
Solve the problem.
2)
2)
The equation of a line passing through two distinct points (x1, y1) and (x2, y2) is given by
x y 1
x1y11
x2y21= 0. Use the determinant to write an equation for the line passing through (5, 9) and
(–6, –4). Express the line‘s equation in standard form.
A)
–13x + 11y + 34 = 0
B)
13x – 11y + 34 = 0
C)
9x – 6y – 20 = 0
D)
–4x + 5y – 54 = 0
Write the augmented matrix for the system of equations.
3)
4x + 9y + 7z = –2
9x + 7z = 4
3x + 8y = 2
3)
A)
4 9 7 –2
9 1 7 4
3 8 1 2
B)
4 9 7 2
9 0 7 4
3 8 0 2
C)
4 9 7 2
9 1 7 4
3 8 1 2
D)
4 9 7 –2
9 0 7 4
3 8 0 2
4)
x = –8
y =4
z = –2
4)
A)
[–8 4 –2 1]
B)
1 0 0 –8
0 1 0 4
0 0 1 –2
C)
[–8 4 –2 0]
D)
–8 0 0 1
0 4 0 1
0 0 –2 1
Use Cramer’s rule to solve the linear system.
5)
8x+2z =42
–5x +4y –2z = –1
–6x –4y = –50
5)
A)
{(8, 9, 8)}
B)
{(4, 6, 9)}
C)
{(3, –8, –9)}
D)
{(3, 8, 9)}
Find the mean for the group of data items. If necessary, round the answer to nearest tenth.
6)
6)
6, 4, 10, 5, 14, 9
A)
8.5
B)
8
C)
6.5
D)
9.6
7)
7)
70, 43, 70, 100, 43
A)
81.5
B)
64.7
C)
65.2
D)
65.7
Use Cramer’s rule to solve the system or to determine that the system is inconsistent or contains dependent equations.
8)
3x +2y = –1
2x +y= –2
8)
A)
{(4, –3)}
B)
dependent equations; infinitely many solutions
C)
{(–3, 4)}
D)
inconsistent; no solution or
Evaluate the determinant.
9)
1
6–1
12
12 6
9)
A)
–2
B)
2
C)
0
D)
5
2
Use matrices to determine whether the system is inconsistent, dependent, or neither.
10)
4x + y =1
–4y + 4z = –4
–4x + 7y – 8z =7
10)
A)
neither
B)
dependent
C)
inconsistent
Find the mean for the group of data items. If necessary, round the answer to nearest tenth.
11)
11)
24, 17, 77, 32, 121, 95
A)
61
B)
61.5
C)
60.5
D)
73.2
Use Cramer’s rule to solve the system or to determine that the system is inconsistent or contains dependent equations.
12)
7x +8y =4
2x +3y =2
12)
A)
inconsistent; no solution or
B)
6
5, –4
5
C)
–4
5, 6
5
D)
dependent equations; infinitely many solutions
Solve the problem.
13)
The three points (x1, y1), (x2, y2), and (x3, y3) are collinear if
x1y11
x2y21
x3y31= 0. Are the points (–1, 6),
(0, –8), and (–4, 50) collinear?
13)
A)
Yes
B)
No
Solve the system using matrices. If there is no solution or if there are infinitely many solutions and a system’s
equations are dependent, so state.
14)
x–7y =3
–4x +28y = –12
14)
A)
{(3, 0)}
B)
{(0, 0)}
C)
no solution or
D)
infinitely many solutions; dependent equations
Find the mode for the group of data items. If there is no mode, so state.
15)
15)
1.3, 0.7, 0.9, 1.3, 0.5, 1.5, 0.5, 1.6, 2
A)
1.3
B)
0.5 and 1.3
C)
1.1
D)
0.5
Evaluate the determinant.
16)
–2 4 5
–2 0 3
2 0 –4
16)
A)
56
B)
8
C)
–56
D)
–8
Use Cramer’s rule to solve the linear system.
17)
2x +6y –z=12
x–5y –9z = –27
–3x +y+z=1
17)
A)
{(2, 0, 2)}
B)
{(1, 2, 2)}
C)
{(2, 2, 2)}
D)
{(1, –2, –2)}
Solve the system using matrices. If there is no solution or if there are infinitely many solutions and a system’s
equations are dependent, so state.
18)
x–y+3z =5
5x +z=0
–x+y–3z = –20
18)
A)
no solution or
B)
{(3, –5, 0)}
C)
infinitely many solutions; dependent equations
D)
{(0, 0, –5)}
Find the mode for the group of data items. If there is no mode, so state.
19)
19)
89, 25, 89, 13, 25, 29, 56, 89
A)
no mode
B)
51.9
C)
89
D)
42.5
Use Cramer’s rule to solve the system or to determine that the system is inconsistent or contains dependent equations.
20)
–5x + 7y= –40
–10x = –42 – 14y
20)
A)
{(6, 8)}
B)
dependent equations; infinitely many solutions
C)
{(1, –5)}
D)
inconsistent; no solution or