Free Printable FINAL EXAM, Algebra 2 2025, Sem 1

1.

What are the dimensions of this matrix?

a)

4x3

b)

3x4

c)

3

d)

4

2.

Value of element a₂₃

a)

-2

b)

-1

c)

7

d)

15

3.

Add.

a)

No Sum Exists

b)

c)

d)

4.

Subtract

a)

3 -8
0 -1

b)

3 -4
8 -13

c)

-3 8
0 1

d)

3 -8
-8 1

5.

Multiply.

a)

20 15 -10

30 -5 0

b)

-20 15 -10

30 -5 0

c)

1 8 3

11 4 5

d)

20 -15 10

-30 5 0

6.

Is the sequence arithmetic: 37, 31, 25, 19, ...

a)

Yes

b)

No

7.

Find the common difference: -34, -29, -24, -19, ...

a)

d = -5

b)

d = 5

c)

d = -6

d)

d = 6

8.

Find the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...

a)

-1, 7, 15

b)

-5, 2, 9

c)

3, 12, 21

d)

-65, -73, -81

9.

Identify f(1) and d for the sequence
-5, -2, 1, 4, ...

a)

a₁ = 3 and d = -5

b)

a₁= -8 and d = 3

c)

a₁ = -5 and d = 3

d)

a₁ = -5 and d = -3

10.

Find the 22nd term of the following sequence:
5, 8, 11, ...

a)

14

b)

68

c)

63

d)

71

11.

Find the 32nd term of this sequence.
34, 37, 40, 43, ...

a)

32

b)

64

c)

127

d)

356

12.

State if the following is geometric.

a)

A

b)

B

13.

Find the common ratio

a)

A

b)

B

c)

C

d)

D

14.

Find the next three terms.

a)

A

b)

B

c)

C

d)

D

15.

Which sequence is a geometric sequence with a common ratio of 2?

a)

5, 3, 1, -1, ...

b)

5, 7, 9, 11, ...

c)

5, 10, 20, 40, ...

d)

5, 15, 45, 135, ...

16.

Given $f\left(x\right)=\frac{x}{2}-x$ , find $f\left(-6\right)$ .

(a)

17.

Given the graph,

find:

$f\left(2\right)$

a)

$f\left(2\right)=5$

b)

$f\left(2\right)=4$

c)

$f\left(2\right)=3$

d)

$f\left(2\right)=0$

e)

$f\left(5\right)=2$

18.

If f(x) = 2x + 1, find f(1).

a)

f(1) = 1

b)

f(1) = 4

c)

f(1) = 0

d)

f(1) = 3

19.

f(x) is the same thing as ______.

a)

y

b)

x

c)

input

d)

an equation

20.

$If\ g\left(x\right)=-4x+7\ and\ h\left(x\right)=2x^2-3x+4$

$find\ g\left(-7\right)$

(a)

21.

-5x⁶(3x² - 12x + 30)

a)

-15x⁸+ 60x⁷- 150x⁶

b)

15x⁸- 60x⁷- 150x⁶

c)

8x⁶- 17x + 35

d)

-8x⁶+ 17x - 35x²

22.

Find the product:
(3x + 2)(2x + 4)

a)

6x² + 16x + 8

b)

5x² +11x + 6

c)

5x² + 16x + 6

d)

6x² + 11x + 8

23.

Simplify:
(x - 9)(x - 7)

a)

x² - 2x - 63

b)

x² - 16x - 63

c)

x² - 2x + 63

d)

x² - 16x + 63

24.

Simplify: $3x\left(x+7\right)$

a)

$3x^2+21x$

b)

$3x+21$

c)

$3x^2+7$

25.

The length of a rectangle is x - 5. The width is x + 1. What is the area?

a)

$x^2\ -\ 4x\ -\ 5$

b)

$2x\ -\ 4$

c)

$x^2\ +\ 6x\ -\ 5$

d)

none of these

26.

Find the product:

(2x + y)²

a)

4x²+ y²

b)

4x²y²

c)

4x²+ 4xy + y²

d)

4x²+ 4x²y²+ y²

27.

$\left(k-8\right)\left(6k^2-4k+2\right)$

a)

$21k^3-53k^2+16k-64$

b)

$12k^3+52k^2+68k+28$

c)

$15k^3+49k^2+19k-3$

d)

$6k^3-52k^2+34k-16$

28.

$\left(a+2\right)\left(4a^2+4a+3\right)$

a)

$30a^3-22a^2-a+2$

b)

$28a^3-37a^2+24a-9$

c)

$4a^3+12a^2+11a+6$

d)

$10a^3-48a^2+20a+48$

29.

Given the following sequence and f(n) = 12, what is f(n - 1) ?

2, 7, 12, 17,...

a)

2

b)

12

c)

7

d)

22

30.

Find the first four terms of the sequence.

f(n) = 6n - 1

a)

6, 12, 18, 24

b)

5, 11, 17, 23

c)

0, 6, 12, 18

d)

6, 7, 8, 9

31.

Find the first four terms of the sequence.

f(n) = f(n-1)- 18 where f(1) =10

a)

18, 8, -2, -12

b)

28, 46, 64, 82

c)

-8, -26, -44, -60

d)

10, -8, -26, -44

32.

Which of the following recursive formulas represents the given sequence.

7, 49, 343, 2401, ...

a)

$f\left(1\right)=7$ , $f\left(n\right)=f\left(n-1\right)+7$

b)

$f\left(1\right)=7$ , $f\left(n\right)=f\left(n-1\right)\cdot7$

c)

$f\left(1\right)=7$ , $f\left(n\right)=f\left(n-1\right)\cdot2$

d)

$f\left(1\right)=7$ , $f\left(n\right)=f\left(n-1\right)+14$

33.

Write an explicit formula for the sequence 45, 40, 35, 30, ...

$f\left(n\right)=f\left(n\right)+d\left(n-1\right)\ or\ f\left(n\right)=f\left(1\right)\cdot r^{\left(n-1\right)}$ .

a)

$f\left(n\right)=45+5\left(n-1\right)$

b)

$f\left(n\right)=45+\ -5\left(n-1\right)$

c)

$f\left(n\right)=45\cdot\left(\frac{8}{5}\right)^n$

d)

$f\left(n\right)=5-45\left(n-1\right)$

34.

Which graph is an example of a geometric sequence?

a)

b)

c)

35.

Which explicit formula represents the sequence: 8, 16, 24, 32, ...?

a)

$f\left(n\right)=8\cdot2^{n-1}$

b)

$f\left(n\right)=8+8\left(n-1\right)$

c)

$f\left(n\right)=8n$

d)

$f\left(n\right)=16n$

36.

Given the polynomials:

$c\left(x\right)=x^3-15x^2+72x-112$

$a\left(x\right)=x^2+5$

$k\left(x\right)=x^3+21x^2+144x+324$

$e\left(x\right)=2x^2+28x+96$

match each polynomial function to its graph.

a)

1.

$c\left(x\right)=\left(x-4\right)^2\left(x-7\right)$

b)

2.

$a\left(x\right)=x^2+5$

c)

3.

$k\left(x\right)=\left(x+9\right)\left(x+6\right)^2$

d)

4.

$e\left(x\right)=2\left(x+8\right)\left(x+6\right)$

37.

Match the graph to the function

a)

f(x) = -x⁴-x³+5x²-6

b)

f(x) = x⁴+3x²-3x+1

c)

f(x) = -x³+2x²-x-6

d)

f(x) = x⁴+x³+5x²-6

38.

Describe the end behavior of the graph.

a)

x → ∞, y→ ∞ and
x→ ∞, y→⁻∞

b)

x → ∞, y→ ∞ and
x→⁻∞, y→∞

c)

None of these

d)

x →∞,y→⁻∞ and
x→∞, y→⁻∞

39.

Describe the end behavior of the graph.

a)

x →∞, y→∞ and x→∞, y→⁻∞

b)

x →∞, y→∞ and x→⁻∞, y→∞

c)

x →∞, y→∞ and x→⁻∞, y→0

d)

x →∞,y→0 and x→∞, y→⁻∞

40.

What is the quotient when (10n²- 37n - 12) is divided by (n - 4)?

a)

(10n - 3)

b)

(3n - 10)

c)

(10n + 3)

d)

(3n + 10)

41.

Identify the missing term to complete the solution.

a)

4

b)

-4

c)

5

d)

-5

42.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

43.

What x value can this graph not reach because of a vertical asymptote?

a)

1

b)

-15

c)

3

d)

15

44.

What are the zeros of the function graphed above?

a)

x = {-2, -4, 5, 6}

b)

x = {2, 4, 5, 6}

c)

x = {-6, -5, -4, -2}

d)

None

45.

Find all zeros.

a)

A

b)

B

c)

C

d)

D

46.

If the zeros of a polynomial are -1, 3, and 7 then what does the polynomial look like in factored form?

a)

(x-1)(x+3)(x+7)

b)

(x+1)(x-3)(x-7)

c)

(x-1)(x-3)(x-7)

d)

(x+1)(3x-1)(7x-1)

FINAL EXAM, Algebra 2 2025, Sem 1

Total questions: 46

Worksheet time: 4hrs 9mins

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