Free Printable Pre Calc End of Q2 Review Fall 2024

1.

What does $i$ represent?

a)

$1$

b)

$-1$

c)

$\sqrt{1}$

d)

$\sqrt{-1}$

2.

What is $i^2$ equal to?

a)

$1$

b)

$-1$

c)

$\sqrt{1}$

d)

$\sqrt{-1}$

3.

What is $\sqrt{25}$ ?

a)

$5$

b)

$-5$

c)

$5i$

d)

$-5i$

4.

What is $\sqrt{-25}$ ?

a)

$5$

b)

$-5$

c)

$5i$

d)

$-5i$

5.

Which point represents $-2+4i$ ?

a)

A

b)

B

c)

C

d)

D

6.

Which complex number is represented by the point?

a)

$4+3i$

b)

$-4+3i$

c)

$3+4i$

d)

$3-4i$

7.

$\sqrt[]{4}\ x\ \ \ \sqrt[]{-6}$

a)

$2i\ \sqrt[]{6}$

b)

$4i\ \sqrt[\ ]{6}$

c)

-2+7i

d)

$6\sqrt[]{2}$

8.

Add the following together.

\left(3+5i\right)+\left(7+i\right)

a)

$4+4i$

b)

$10+6i$

c)

$21+5i$

d)

$10+5i$

9.

Add the following together.

\left(-4-3i\right)+\left(-3+2i\right)

a)

$-7-i$

b)

$-1-i$

c)

$12-6i$

d)

$-1-5i$

10.

Subtract the following.

\left(4+7i\right)-\left(1+i\right)

a)

$5+8i$

b)

$-3+11i$

c)

$3+6i$

d)

$3+7i$

11.

Subtract the following.

\left(-3-6i\right)-\left(4-5i\right)

a)

$-7-i$

b)

$7+i$

c)

$1-i$

d)

$12+30i$

12.

Multiply the following together.

\left(2+i\right)\left(3+2i\right)

a)

$8+7i$

b)

$12+12i$

c)

$4+7i$

d)

$4+i$

13.

Multiply the following together.

\left(2+3i\right)\left(4-6i\right)

a)

$26$

b)

$26i$

c)

$26+24i$

d)

$62$

14.

Simplify

\frac{4+3i}{2i}

a)

$\frac{3}{2}-2i$

b)

$-2+\frac{3}{2}i$

c)

$-5-2i$

d)

$2+0i$

15.

Simplify

\frac{1+i}{2-3i}

a)

$\frac{1}{13}-\frac{5}{13}i$

b)

$-\frac{1}{13}+\frac{5}{13}i$

c)

$-1+5i$

d)

$1-5i$

16.

Simplify

\frac{4-5i}{2+4i}

a)

$-3-13i$

b)

$-5-10i$

c)

$-\frac{3}{5}-\frac{13}{10}i$

d)

$\frac{3}{5}+\frac{13}{10}i$

17.

Find the modulus of the complex number.

z=3+i

a)

$\left|z\right|=10$

b)

$\left|z\right|=\sqrt{10}$

c)

$\left|z\right|=2$

d)

$\left|z\right|=\sqrt{2}$

18.

Find the modulus of the complex number.

z=2+5i

a)

$\left|z\right|=\sqrt{29}$

b)

$\left|z\right|=5$

c)

$\left|z\right|=2\sqrt{7}$

d)

$\left|z\right|=7\sqrt{2}$

19.

(3x² + 4x - 2) - (5x + 7)

a)

3x² - x - 9

b)

2x² - 9

c)

3x² + 9x - 5

d)

3x² - x + 5

20.

(x+3)(x+1)

a)

x²+3x+3

b)

2x+4x+3

c)

x²+4x+3

d)

5x + 3

21.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

22.

Simplify the expression:
(p³ - 6p⁴ + 1) - (8p⁴ - 8p³ + 7)

a)

-14p⁴ + 9p³ - 6

b)

-14p⁴ + 9p³ + 6

c)

-14p⁴ + 9p³ - 1

d)

-15p⁴ + 9p³ + 6

23.

(x-3)(x²+2x+7)

a)

x³-x²+x-21

b)

x³+5x+13x-21

c)

x³-3x²+7x-21

d)

x²+2x-3

24.

(5x⁴- 4x³- 2x² + x - 19) - (x⁴+ 5x³ + 8x² + x + 5)

a)

4x⁴- 9x³- 10x²- 24

b)

4x⁴- 9x³ - 10x²- 2x - 24

c)

4x⁴ - 9x³ - 10x² + 2x - 24

d)

-4x⁴ - 9x³ - 10x² - 24

25.

What is the standard form of the polynomial,
7x - 125 - 6x⁴ + 14x²

a)

125 + 7x - 14x² +6x⁴

b)

6x⁴ -14x² - 7x +125

c)

125 + 14x² + 7x - 6x⁴

d)

-6x⁴+ 14x² + 7x - 125

26.

Which of the following are examples of like terms?

a)

2 and 2x

b)

y³and x³

c)

y and x

d)

-3x and 3x

27.

Combine Like Terms

3x²-x+2-5x²+8x-5

a)

8x²+9x+7

b)

-2x²+7x-3

c)

2x²+7x-3

d)

5x²-3

28.

Classify:
2x⁴+14x³−2x²

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

29.

Classify:
2n³

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

30.

What is the degree of the polynomial 17x + 4

a)

0

b)

1

c)

2

d)

3

31.

What is the above expression classified as?

a)

5th degree Monomial

b)

10th degree Monomial

c)

5th degree Trinomial

d)

10th degree Polynomial

32.

7) Degree of 10 is ______

a)

10

b)

1

c)

0

d)

Undefined

33.

What is the degree of P(x) = (x)(x - 4)

a)

0

b)

1

c)

2

34.

Given P(x) = (x - 2)(x+1)(x - 7), how many roots are there?

a)

2

b)

3

c)

4

35.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

36.

Use synthetic division:
(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

37.

What is the remainder when x⁴ - 5 is divided by x + 3?

a)

76

b)

81

c)

7

38.

Expand (x -1)⁴

a)

x⁴+ 4x³- 6x²+ 4x - 1

b)

x⁴+ 4x³+ 6x²+ 4x + 1

c)

x⁴- 4x³+ 6x²- 4x + 4

d)

x⁴- 4x³+ 6x²- 4x + 1

39.

What is the LAST term in the expansion of (x + 4)⁵?

a)

640

b)

160

c)

1024

d)

64

40.

How many terms would be in the expanded form of (x - 3)⁵ ?

a)

5

b)

6

c)

7

d)

8

41.

Which row of Pascal's Triangle would you use to expand (x+2)³?

a)

1

b)

1 1

c)

1 2 1

d)

1 3 3 1

42.

What row of Pascal's Triangle would you use for (x-2)⁷?

a)

1, 5, 10, 5, 1

b)

1, 5, 10, 10, 5, 1

c)

1, 7, 21, 35, 35, 21, 7, 1

d)

1, 7, 21, 35, 21, 7, 1

43.

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

a)

0

b)

1

c)

2

d)

3

44.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

45.

Is (x-7) a factor of (x²-5x+14)?

a)

Yes

b)

No

46.

Use synthetic division to determine f(-3), if

f(x)= (3x³ -5x² -4x +1).

(a)

47.

Simplify: $\left(729x^8y^4\right)^{\frac{1}{3}}$

a)

$9x^2y\ \ ^3\sqrt{x^2y}$

b)

$9x^2y$

c)

$^3\sqrt{729x^2y}$

d)

$x^2y\ \ \ ^3\sqrt{9x^2y}$

48.

Simplify the following expression:

a)

2

b)

4

c)

16

d)

64

49.

$\left(f^{-3}g^5h^8\right)^{-3}$

a)

$f^9g^5h^8$

b)

$f^{-6}g^2h^5$

c)

$\frac{g^2h^5}{f^6}$

d)

$\frac{g^9}{g^{15}h^{24}}$

50.

$3x^{-2}y^{-5}$

a)

$3x^{-2}y^{-5}$

b)

$\frac{3}{x^2y^5}$

c)

$\frac{1}{x^2y^5}$

d)

$3xy^{-7}$

51.

$\left(\frac{3x^7}{2y^{12}}\right)^0$

a)

$\frac{x^7}{y^{12}}$

b)

0

c)

$\frac{3x^7}{2y^{12}}$

d)

1

52.

$\left(\frac{3x^4}{y^6}\right)^5$

a)

$\frac{15x^{20}}{y^{30}}$

b)

$\frac{3x^{20}}{y^6}$

c)

$\frac{243x^{20}}{y^{30}}$

d)

$\frac{243x^9}{y^{11}}$

53.

$\left(\frac{a^3}{b^5}\right)^4$

a)

$\frac{a^{12}}{b^{20}}$

b)

$\frac{a^7}{b^5}$

c)

$\frac{a^7}{b^9}$

d)

$a^{12}b^{20}$

54.

$\left(\frac{6}{z^4}\right)^3$

a)

$\frac{18}{z^4}$

b)

$\frac{18}{z^{12}}$

c)

$\frac{216}{z^{12}}$

d)

$\frac{6}{z^{12}}$

55.

$\frac{5x^{-4}}{x^{-9}}$

a)

$5x^5$

b)

$5x^{-13}$

c)

$\frac{5}{x^5}$

d)

$\frac{1}{5x^5}$

56.

$p^2\cdot\left(p^5\right)^2$

a)

$p^{12}$

b)

$p^9$

c)

$p^8$

d)

$p^{10}$

57.

$\left(m^{-8}\right)^{-3}$

a)

$m^{-24}$

b)

$m^{24}$

c)

$m^{11}$

d)

$m^{-11}$

58.

$7x^3y^2\cdot5xy^9$

a)

$12x^4y^{11}$

b)

$35x^4y^{11}$

c)

$35x^3y^{11}$

d)

$12x^3y^{11}$

59.

(7uv²)^-5

a)

-35uv^-10

b)

-5/7uv²

c)

1/7⁵u⁵v¹⁰

d)

1/7uv¹⁰

60.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

Pre Calc End of Q2 Review Fall 2024

Total questions: 60

Worksheet time: 4hrs 4mins

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