Final Review Math 1314

Matrices

100

Solve by substitution/ addition- elimination

2𝑥 − 3𝑦 = −4             

2𝑥 + 𝑦 = 4 

x = 1

y = 2

200

Solve for x and y

 5𝑥 − 4𝑦 = 9 

𝑥 − 2𝑦 = −3

y = 4

x = 5

300

Perform the operation:

 3   6             0  -1

-1  -3      +    6   0

-5  -1            2   3

 3   5

 5  -3

-3   2

400

Perform the operation:

-5  -5          -2  -3

-1   2    x     3    5

-5   -10

 8    13

500

Perform the operation:

 0   5         -4   4

-3   1    x   -2  -4

-5   1

-10  -20

 10  -16

 18  -24

Quadratic Functions and Transformations

100

Solve for x

x² - 4x + 24

2 +/- 2 root 5 i

200

Solve for x

x^1/2 = 4 

x = 16

300

Identify if the following is a function and give domain and range:

(-3, -1) , (2, 1) , (6, -5)

Yes, it is a function

domain: -3, 2, 6

range: -1, 1, -5

400

Is y a function of x?

x² + y² = 49

no, two outputs

500

determine the inverse function:

f(x) = 2x + 7

1/2 x - 7/2 = f^-1(x)

Polynomials and Rational Inequalities

100

Y = (x - 2)² - 1

Opens:

Vertex: 

Y-int:

X-int:

Up, (2,-1), (0,3), (3,0)(1,0)

200

-2(x - 7)(x + 3)³

Find the zeros:

Find the multiplicity for each zero and its behavior:

End behavior:

(-3,0)(7,0), 3,1 rises left rises right

300

Solve by synthetic division:

X²  + 14x + 45 / (x + 9)

(x+9) and (x+5)

400

Find the horizontal asymptote:

x / x - 2 

x = 2

500

X² - x - 20 > 0

1. Find the x- intercepts

2. Write solutions that satisfy the given equation (positive or negative values)

x = 5, x = -4

(-infintiy, -4) U (5, infinity)

Exponents and Logs

100

Write in its equivalent exponential/log form:

8 = log₅M

5⁸ = M

200

Solve without a calculator:

ln e⁷

7

300

Solve by using like bases:

5 ^{2x - 3} = 125

x = 3

400

Solve:

log₆ (x + 5) + log₆ x = 2

x = 4

500

Solve:

5^x = 134

X = ln 134/ ln5

Sequences and Summations

100

Find the next four terms:

a_n = 3a_(n-1)      a1= 5

5, 15, 45, 135, 405

200

Give the first three terms:

a_n  = 20 / (n+1)!

10, 10/3, 5/6

300

Find the 9th term if a₁ = 6 and d = -5

-34

400

Give the 10th term for the following sequence: 12, 9, 6, 3

-15

500

Find the sum of the infinite series:

0.54545454...

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