Download Algebra 2x

Algebra 2x
Semester 1 Review
Name_____________________________________
1) Solve: 17 < 3x + 2 < 23
a) {x: -5 < x < 7}
b) {x: 5 < x < 7}
c) {x: 19/3 < x < 25/3} d) Ø e) none of these
2) Determine the solution of 7x – 2 > 26 or -3x + 5 > 11
a) {x: x > 4}
b) {x: x > -2}
c) Ø
d) {x: -2 < x < 4}
e) {x: x < -2 or x > 4}
3) The solution set of │x – 2 │< 4 is:
a) {x: -2 < x < 2}
b) {2,6}
d) {x: x < 6 or x > -2}
c) {x: -2 < x < 6}
e) none of these
4) Find the slope of the line through the points (-2, 7) and ( 5, -3).
a) -10
7
b) 7
10
c) -12
5
5) Find the y-intercept of the equation
a) 0
b) -½
d) -7
10
e) none of these
3x + 6y = 12
c) 3
d) 4
e) 2
6) Find the equation of the line with a y-intercept of 6 and parallel to the graph of
a) y = x + 6 b) y = 2x + 6
e) none of these
7)
d) y = -½x + 6
2x + 2y = 9
If the system: 2x – y = -3 is solved, the value of x is
a) -2
8)
c) y = 2x + 3
b) ½
c) 2
d) 5
2
e) -3
2
__1__
Simplify: 3 - √2
__
a) 3 - √2
7
__
b) - √2
__
c) 3 + √2
Page 1 of 6
__
d) 3 + √2
7
y = 2x – 15.
9) Which graph shows the correct solution for │y│< 3 ?
10)
a)
b)
d)
e)
c)
What is the solution of the system graphed at the right:
a) all real numbers
b) no solution
c) {(0,0)}
d) None of the above
11) Perform the indicated operation: (5x² - 3xy – 4y²) – (3y² - 2x² + 4xy)
12)
a) 2x² + xy – 2y²
b) 3x² - xy – 4y²
d) 7x² - 7xy – 2y²
e) none of these
c) 7x² - xy – 2y²
Determine the remainder when 2x² - 3x + 7 is divided by x – 1.
a) -2
b) 0
c) 6
d) 2
e) none of these
13) Factor completely 4x² – 100
a) (2x + 10)(2x – 10)
c) 4(x – 5)(x + 5)
b) 4(x² - 25)
d) 4(x – 25)
14) Perform the operation and simplify: (4 + 3i)(2 – i)
a) 5 + 2i
b) 11 – 10i
c) 8 + 5i
Page 2 of 6
d) 11 + 2i
e) none of these
15) Factor:
8x³ - 1
a) (2x – 1)³
b) (8x – 1)(64x² + 8x + 1)
d) (8x – 1)(8x + 1)
c) (2x – 1)(4x² + 2x + 1)
e) not factorable
16) Multiply: (x + 2)( x² - 3x + 5)
a) 2x² - 3x + 7
b) x³ + 5x² - 11x + 10
d) x³ - 5x² - 11x + 10
17) Solve:
c) x³ - x² - x + 10
e) none of these
x³ + 4x² - 21x = 0
a) {0, 3, -7}
b) {0, 3, 7}
c) {0, -3, -7}
d) {0, -3, 7}
e) none
12x² + 8x – 15
18) Factor:
a) (3x – 5)(4x + 3)
b) (6x – 5)(2x + 3)
d) (6x + 5)(2x - 3)
e) none of these
19) Solve:
c) (4x – 5)(3x + 3)
x² - 2x < 8
a) {x: -2 < x < 4}
b) {x: 0 < x < 2}
d) {x: x > 2 or x < 0}
e) none of these
c) {x: x < -2 or x > 4}
6x² + 23x – 18
20) Factor:
a) 3x(2x² + 7x - 6)
b) (2x – 9)(3x + 2)
d) (6x - 1)(x + 18)
e) (2x + 9)(3x – 2)
c) (3x + 6)(2x - 3)
21) Factor: 125x³ - 27y³
a) (5x–3y)(25x² - 15xy + 9y²)
b) (25x–9y)(5x² - 225xy + 81y²)
d) (5x – 3y)(25x² + 15xy – 9y²)
c) (5x+3y)(25x² - 15xy+ 9y²)
e) (5x – 3y)(25x² + 15xy + 9y²)
22) Solve 3x² – 12 = 0 for x.
a) ±6
23)
b) ±4
c) ±3
e) 2i
d) ±2
5i
equals
4  5i
a)
25
13
b) 5  4i
c)
25  21i
41
Page 3 of 6
d)
25  21i
9
e) none of these
24) Which of the following correctly describes {(1,3), (-2,7), (-5,3)}?
a) not a function;
Domain = {1,-2,-5},
Range = {3,7}
b) not a function;
Domain = {3,7},
Range = {1,-2,-5}
c) function;
Domain = {1,-2,-5},
Range = {3,7}
d) function;
Domain = {3,7},
Range = {1,-2,-5}
e) function;
Domain = {1,2,5}
Range = {3,7}
25) Solve by using the quadratic formula: 3 x 2  3 x  7  0
a) 3,
1
7
b)
3  5i 3
6
c)
3  5i 3
6
d)
3  5i 3
3
e) none of these
26) Determine the equation of the line of symmetry for y  ( x  3)2  4 .
a)
x = 4 b)
x = 3 c)
y = -3 d)
y = 4 e)
x = -3
 4 11
27) Find the inverse of the matrix A  

1 3 
 3 11
b) 

 1 4 
3 11
a) 

1 4 
a ) 7  15i
a)
7 3
12
 4 1
11 3 
11 3 d)  4 1 e) none of these




7i 10  2i 3  13i 55
28) Simplify:
29) Simplify
c)
b)  7  11i
c)  7  11i
d )  7  15i
7
12
b)
84
12
c)
7 3
6
d)
7 2
4
e) none of these
30) Write the equation of the line that passes through the point (2, -3) and is parallel to the line
2x – 3y =4.
a) 2x – 3y –13 = 0
31) Solve:
b) 2x + 3y + 5 = 0
c) 2x – 3y +13 = 0
d) y =
2
x 3
3
x2 - 6x - 6 > 0
a) x  3  15 or x  3  15
c) x<1 or x>6
b) x<6 or x>1
d) x  3  15 or x  3  15
Page 4 of 6
32) Find the discriminant and classify the roots of the equation
x
2
 3x  5  0
a ) -11; not real
b)
29 ;irrational and not equal
c) 29; irrational and not equal
d)
-11 ; not real
33)
Solve: 17  3x  2  23
(A) {x : 5  x  7}
(B) {x : 5  x  7}
34)Solve: x  2  4
a) x  6
b) x  2
35)


(C) x : 19  x  25
3
3
c) x  2 or 6
(D) 
d) x  2 or x  6
The set x : x  and  3  x  5 can be expressed using the interval notation:
a. (, 3] [5, )
b) [3,5]
c) (3,5]
d) (3,5)
36) Select the equation of a line parallel to y = 2x – 15.
1
1
a)y = 2x + 6
b)y = 15x + 2
c) y   x  6
d) y  2 x 
2
6
37) Which of the following represents a translation of the graph of f ( x)  x two units to the right?
a) g ( x)  x  2
b) g ( x)  x  2
c) g ( x)  x  2
d) g ( x)  x  2
c)28
d)14
38) If f ( x)  3x  7 , what is f (7) ?
a) 28
b) 14
 5 6 
39) What is the determinant of 
?
 7 2
a) -32
b) 52
40)
c)52
d) This matrix has no determinant
 1 1
What is the inverse of 
?
 2 3
1 1 
a)  1 1 
2 3
 3 1
 2 3
b) 
c) 


 1 1
 2 1 
41) Which system has an infinite number of solutions?
2 x  4 y  7
2 x  4 y  6
a) 
b) 
4 x  8 y  7
4 x  8 y  12
Page 5 of 6
d. This matrix has no inverse
x  2 y  3
c) 
x  2 y  3
x  5
d) 
y  5
42)
What is the vertex of the graph of the quadratic function f ( x)  x 2  4 x  3 ?
a) (2,9)
b) (4,29)
c) (2, 7)
d) (2, 15)
43)
What is the y-intercept of the graph of the quadratic function f ( x)  x 2  10 x  5 ?
a) (0,10)
44) Find the sum:
a) 7 + 9i
b) ( 5, 0 )
(2  3i)  (5  6i)
b) 3 – 3i
c) (0, 5)
d) (10,0)
c) 3+9i
d) -10 + 18i
c) 8 + 37i
d) 8 + 22i
45) Find the product: (2  3i )(4  5i )
a) 7  22i
b) 8 + 15i
46) f ( x)  x3  8 has three zeros, one of which is real. What is the function’s real zero?
a) 0
b) 2
c) 2
d) 8
47) In a system of linear equations, if the lines are parallel, the system is __________________.
48) A parabola has a vertex at (5, 1), and one of its x-intercepts is (3, 0). What is the other x-intercept?
a) (12, 0)
b) (7, 0)
c) (-7, 0)
Alg2X Semester 1 review –-answer key
1. b
2. e
3. c
5 e
6 b
7 b
9 b
10 b
11 e
13 c
14 d
15 c
17 a
18 b
19 a
21 e
22 d
23 c
25 b
26 e
27 b
29 c
30 a (also d)
31 d
33 b
34 c
35 c
37 c
38 d
39 b
41 b
42 c
43 c
45 a
46 b
47 inconsistent
d) (5, 0)
4.
8
12
16
20
24
28
32
36
40
44
48
Page 6 of 6
a
d
c
c
e
c
c
c
a
b
c
b