Free Printable Topic 6 Review

1.

Consider the function -2x² − x − 1 = 0. How many and what type of roots does the equation f(x)=0 have?

a)

Two distinct real roots

b)

Two distinct non-real complex roots

c)

One distinct real root

d)

One distinct non-real complex root

e)

None

2.

Which set of numbers includes the number 5 + 7i?

a)

Complex numbers

b)

real numbers

c)

Imaginary numbers

d)

Irrational numbers

e)

This is not a number; it is an algebraic expression

3.

Multiply:
(4 – 3i)(7 + 2i)

a)

A. 22 - 13i

b)

B. 28 - 19i

c)

C. 34 - 13i

d)

D. -34 - 29i

4.

a)

4x - 2

b)

4x + 2

c)

4x - 2 + (1/3x - 1)

d)

4x + 2 + (1/3x - 1)

5.

Consider the equation $f\left(x\right)=x^2+4x+7.$ How many and what type of roots does $f\left(x\right)=0$ have?

a)

Two distinct real roots

b)

One distinct real root

c)

One distinct non-real complex root

d)

Two distinct non-real complex roots

e)

None

6.

Which of the following are solutions to the cubic equation $x^3+4x^2+4x=0?$ Select all that apply.

a)

$x=0$

b)

$x=2i$

c)

$x=-2i$

d)

$x=-2$

e)

$x=2$

7.

What does i² = ?

a)

-1

b)

√-1

c)

1

d)

-√1

8.

a)

10

b)

-10

c)

10i

d)

-10i

9.

Simplify the expression:
$\left(8\ +\ 9i\right)\ +\ \left(4\ -\ 6i\right)$

a)

$17\ +\ 3i$

b)

$12\ +\ 3i^2$

c)

$17\ -2i$

d)

$12\ +\ 3i$

10.

Simplify the expression:
$\left(5\ +\ 14i\right)\ -\ \left(10\ +\ 2i\right)$

a)

$5\ -16i$

b)

$-5\ +\ 16i$

c)

$5\ -\ 12i$

d)

$-5\ +\ 12i$

11.

$Simplify:\ \ \ \ 2i\left(4\ +\ 3i\right)$

a)

$-6\ +\ 8i$

b)

$6\ +\ 8i$

c)

$-6i\ +\ 8i$

d)

$-1\ +\ 8i$

12.

$Simplify:\ \ \left(-2\ +\ 7i\right)\left(4\ -\ 2i\right)$

a)

$6+\ 32i$

b)

$-6\ +\ 32i$

c)

$22+32i$

d)

$6\ +\ 24i$

13.

What letter represents an imaginary number?

a)

a

b)

i

c)

j

d)

x

14.

If you are adding two complex numbers you should

a)

add all the numbers together then divide by 2

b)

add only the real numbers and subtract the complex numbers

c)

add only the complex numbers and subtract the real numbers

d)

add only the real numbers together and then add only the complex numbers together then stop

15.

A complex number can be expressed as a + bi. What does a represent?

a)

the real part of the complex number

b)

the imaginary part of the complex number

c)

depends on the sign of the number

d)

the square root of the complex number

16.

What does the discriminant tell us about a quadratic function?

a)

The maximum or minimum value

b)

The y-intercept

c)

The number and type of solutions

d)

The axis of symmetry

17.

What is the formula for the discriminant of a quadrartic equation?

a)

$\frac{-b}{2a}$

b)

$b^2-4ac$

c)

$ax^2+bx+c$

d)

$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

18.

If the discriminant is equal to -2, how many real solutions are there?

a)

None

b)

One

c)

Two

d)

Infinite

19.

If the discriminant of the quadratic equation is equal to 4, how many real solutions are there?

a)

None

b)

One

c)

Two

d)

Infinite

20.

What is the discriminant of this equation?

3x² + 8x = 0

a)

64

b)

52

c)

9

d)

0

21.

Complete the quadratic formula

Black question mark (a)

Blue question mark (b)

Red question mark (c)

Choose from the below words

$-b$

$b^2-4ac$

$2a$

$b$

$2b-4ac$

$b^2-4c$

$2$

$a^2$

$b^2-ac$

$2b$

22.

a)

This is correct

b)

This is incorrect

23.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

24.

Identify the missing term to complete the solution.

a)

4

b)

-4

c)

5

d)

-5

25.

Determine the quotient.

$\frac{10x^2-93x-70}{x-10}$

26.

Determine the quotient.

$\frac{x^2-13x+42}{x-7}$

27.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

28.

What is the proper way to write the answer for the following problem? If the dividend was a quartic.

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

29.

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

a)

Cam wrote the remainder incorrectly.

b)

Cam did not use a zero place holder for the x³ term.

c)

Cam added instead of subtracting the rows.

d)

Cam should have used -2 as his division since the factor was x-2.

30.

What is the first thing we do?

a)

Bring down the 5 below the line.

b)

Add all the coefficients

c)

Divide 5 by -2

d)

Multiply the 5 and 2

31.

What goes next to the 5 below the line?

a)

4

b)

-16

c)

16

d)

-4

32.

What goes under the -28?

a)

32

b)

-32

c)

-20

d)

20

33.

What is the final answer?

a)

$5x^{4\ }-16x^3+4x^2-10x$

b)

$5x^3-16x^2+4x-10$

c)

$5x^2-16x+4+\frac{10}{x+2}$

d)

$5x^2-16x+4-\frac{10}{x+2}$

34.

Factor
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

35.

Factor
x²+12x+35

a)

(x+5)(x+7)

b)

(x+4)(x+3)

c)

(x+7)(x-5)

d)

Prime

36.

Order the following steps for solving quadratic equations by factoring.

a)

Set the quadratic equation equal to zero.

b)

Factor the left side.

c)

Set each factor equal to zero, and solve each for the variable.

d)

Write the answer using curly braces in set notation.

1)

2)

3)

4)

37.

Solve the equation:

x² - 7x + 10 = 0

a)

x = 2, -5

b)

x = -2, 5

c)

x = 2, 5

d)

x = -2, -5

38.

Solve
x² + 13x + 12 = 0

a)

x = -12, -1

b)

x = 12, 1

c)

x = 13, 1

d)

x = -13, -1

39.

Solve using the Quadratic Formula:

$b^2+b-56=0$

a)

$b=-8,\ 7$

b)

$b=-7,\ 8$

c)

$b=-1.4,\ 1.8$

d)

$b=-0.5,\ 2.5$

40.

Solve using the Quadratic Formula:

$x^2+6x+9=0$

a)

$x=-3,\ 3$

b)

$x=-3$

c)

$x=3$

d)

No Solution

41.

What is the quadratic formula?

a)

$x=\frac{b-\sqrt{\left(b\right)^2-4\left(a\right)\left(c\right)}}{2\left(a\right)}$

b)

$x=\frac{-\left(b\right)\pm\sqrt{\left(b\right)^2-4\left(a\right)\left(c\right)}}{2\left(a\right)}$

c)

$x=\frac{\left(b\right)\pm\sqrt{\left(b\right)^2-4\left(a\right)\left(c\right)}}{2a}$

d)

$x=-\left(b\right)\pm\sqrt{b\pm4\left(a\right)\left(c\right)}$

Topic 6 Review

Total questions: 41

Worksheet time: 3hrs 24mins

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