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WorksheetsChapter 4 Review
Total questions: 47
Worksheet time: 12hrs 45mins
Determine whether each statement is true or false. If it is false, give a counter example.
The sum of two imaginary numbers is an imaginary number.
True
False: i + i
False: (1 - i)+(1 + i)
False: 2i + (3 - 4i)
Determine whether each statement is true or false. If it is false, give a counter example.
The product of two pure imaginary numbers is a real number.
True
False: 2i(2i)
False: i(i)
False: i + i
Determine whether each statement is true or false. If it is false, give a counter example.
A pure imaginary number is an imaginary number
True
False: 2i
False: 1 + 2i
False: 3
Determine whether each statement is true or false. If it is true, give an example. If it is false, give a counter example.
A complex number is a real number.
True
False: 1 + 2i
False: 2i
False: 3 + 0i
Which student made a mistake and what is their mistake?
Solve by factoring.
x2 + 15x + 44 = 0
{-8, 2}
{-7, 5}
{-11, -4}
{-11}
Solve by factoring. (what do they have in common)
n² - 2n = 0
n = 2 and 0
n = -2 and 0
n = 2
n = 0
The solutions of the quadratic equation
x2+12x+35=0 are (hint: find the zeros) FACTOR
x = -5 or x = -7
x = 5 or x = 7
x = -35 or x = -1
x = -9 or x = -4
5m2 + 1 = 6
Solve x2− 4 = 0 (solve using square roots)
2 and -2
4 and -4
16 and -16
8 and -8
solve using square roots
±81
±9
±3
No real solution
What is standard form of a quadratic Equation?
Ax2 + Bx + C = 0
Ax2 + B + Cx = 0
Determine the values of a, b, and c for the quadratic equation:
4x2 – 8x = 3
a = 4, b = -8, c = 3
a = 4, b =-8, c =-3
a = 4, b = 8, c = 3
a = 4, b = 8, c = -3
Use the quadratic formula to solve 2x2 + 2x - 12.
-2, 3
2, 3
2, -3
-2, -3
Use the quadratic formula to find the solutions for
y = -x2 - 5x + 12
No Real Solution
a2 + 10a + 21 = 0
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
±
x2 + 6x = 5
x2 + 12x + ____
x2 + 12x = 5
For the function above, is the discriminant positive, negative, or zero?
For the function above, is the discriminant positive, negative, or zero?
For the function below, is the discriminant positive, negative, or zero?
___________
y = x² + 4x + 4
Positive
Negative
Zero
Not Sure
What is the discriminant of -2x2 − x − 1 = 0
76
-7
9
none of these
What is the discriminant for 5x2 + x − 2 = 0
-39
42
-41
none of these
If the discriminant is positive, then the solution will be
one real solution
two real solutions
no real solutions
one imaginary solution
A function has a discriminant of 25.
______________
How many real solutions does it have?
0
1
2
5
Determine the value of the discriminant and name the nature of the roots for the following:
x2 + 7x + 13
Remember: b2 - 4ac
400, 2 real root
0, 1 real root
-400, 2 imaginary roots
-3, 2 imaginary roots
(4 – 3i)(-7 – 2i)
(10+ 15i)-(48 - 30i)
How many solutions does this system of equations have?
one solution
two solutions
no solutions
All of the above
Solve the depicted system algebraically
(0,-7) and (1, 6)
(0,-7) and (1, -6)
(0, 7) and (1, -6)
(-7,0) and (1, -6)
The graph shows the height y (in feet) of an apple x sections after it is tossed in the air with an initial velocity of 32 ft per second. The linear function represents an arrow shot through the apple. After how many seconds does the arrow hit the apple? Check the reasonableness of the solution(s). You may use the model given below where v0 is the initial velocity and h0 is the initial height.
10 seconds
1.75 seconds
3 seconds
14.25 seconds
Which inequality is represented by the graph?
y > (x - 3)² - 3
y ≥ (x + 3)² - 3
y > (x + 3)² - 3
y ≥ (x - 3)² - 3
A
B
C
Have your attempted to complete the Quadratic Formula proof to practice reading math?
yes
no
