Free Printable 1st Nine Weeks Review (Part 2)

1.

a)

A

b)

B

c)

C

d)

D

2.

2 sinθ+3=2

a)

π/6,2π/3

b)

7π/6

c)

7π/6, 11π/6

3.

Solve on the domain [0, 2π)
2sin x cos x = √2 cos x

a)

π/2, 3π/2

b)

0, π/4, 3π/4

c)

π/2, 3π/2, π/4, 3π/4

d)

No solution

4.

$\cos\theta=\frac{4}{5}\ \ and\ \ \frac{3\pi}{2}<\theta<2\pi$

Find the exact value of $\cos2\theta$ .

a)

$-\frac{1}{5}$

b)

$\frac{7}{25}$

c)

$-\frac{7}{25}$

d)

$-\frac{25}{7}$

5.

Find the exact value of sin $75\degree$

a)

$\frac{\sqrt{2}+\sqrt{6}}{4}$

b)

$\frac{\sqrt{8}}{4}$

c)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

d)

$\frac{\sqrt{7}}{4}$

6.

Simplify

$\cos\left(270+\theta\right)$

a)

$\sin\theta$

b)

$-\sin\theta$

c)

$\cos\theta$

d)

$-\cos\theta$

7.

Use the half-angle identities to find the exact value of $\cos112.5°$

a)

$1+\sqrt{2}$

b)

$\sqrt{2}-1$

c)

$-\frac{\sqrt{2-\sqrt{2}}}{2}$

d)

$\frac{\sqrt{2+\sqrt{2}}}{2}$

8.

Which sequence is NOT an arithmetic sequence?

a)

-7, -13, -19, -25,...

b)

-10, -6, -2, 2,..

c)

6, 8, 10, 12,...

d)

3, 15, 75, 375,...

9.

Find the 59th term of the arithmetic sequence 26, 17, 8, ...

(a)

10.

Insert five terms between 1.5 and 13.5

a)

3.5, 5.5, 7.5, 11.5

b)

2.5, 4.5, 6.5, 10.5

c)

1.5, 3.5, 5.5, 9.5

d)

0.5, 2.5, 4.5, 8.5

11.

Evaluate the arithmetic series described:
11 + 18 + 25 + 32..., S₇

(a)

12.

Write the explicit rule for the arithmetic sequence
-10, -3, 4, 11,...

a)

a_n= 10n + 17

b)

a_n = 7n - 17

c)

a_n = -7n + 17

d)

a_n = 7n + 3

13.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

14.

What is the 14th term of the geometric sequence?

(a)

15.

Evaluate $\sum_{k\ =\ 1}^7\left(-2\right)^{k\ -1\ }$ (geometric)

(a)

16.

Reduce, or simplify

the rational expression.

a)

( x + 5 )( x - 5 ) / ( x + 5 )( x - 2 )

b)

( x - 5 ) / ( x - 2 )

c)

( x + 5 ) / ( x - 2 )

d)

-25 / ( 3x - 10 )

17.

Simplify.

a)

A

b)

B

c)

C

d)

D

18.

Simplify and state the excluded values.

a)

A

b)

B

c)

C

d)

D

19.

Subtract the fractions

a)

a

b)

b

c)

c

d)

d

20.

a)

A

b)

B

c)

C

21.

Simplify the given complex fraction.

a)

(1-x)/(x+3)

b)

(3-x)/(x+1)

c)

1/(x+3)

d)

3-x

22.

Expand

a)

A

b)

B

c)

C

d)

D

23.

Find the 8th term in the expansion of (b+3)⁹

a)

78,732b²

b)

324b⁷

c)

78,732b⁷

d)

324b²

24.

Find the LCM: $\left(k^2+6k+9,\ 9k^4+27k^3\right)$

a)

$9k^3\left(k+3\right)^3$

b)

$9k^3\left(k+3\right)^2$

c)

$\left(k+3\right)^2$

d)

$3k^3\left(k+3\right)^2\left(3k+9\right)$

25.

Solve for x:
$\frac{6}{x-1}=\frac{4}{x-2}+\frac{2}{x+1}$

a)

1

b)

2

c)

-1

d)

No Solution

1st Nine Weeks Review (Part 2) - Algebra 3

Total questions: 25

Worksheet time: 6hrs 15mins

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