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Math 1310 Final Review

Where/When: CASA Testing Center / May 4 – May 10

Number of Questions: 30 multiple choice questions.

Time: 110 minutes.

What is covered: All chapters.

Chapter 1 – Background

1) Find the slope of the line that passes through the points (4, 12) and ( 1,6) .

2) Find the line that passes through the points (4, 12) and ( 1,6) .

3) Find the slope of the line 3𝑥 − 10𝑦 + 6 = 0.

4) Find the x- and y-intercepts of the line 0542 yx .

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Chapter 2 – Solving Equations and Inequalities

5) Solve the following equations:

a) 𝑥2 + 17𝑥 + 72 = 0.

b) 2𝑥2 − 5𝑥 + 4 = 0

c) −3

5𝑥+

3

15𝑥= 2

d) 𝑥4 − 5𝑥2 − 36 = 0

e) 𝑥 − 11√𝑥 + 28 = 0

f) 10412 x

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6) Simplify the following expressions.

Write the complex numbers in the standard form 𝑎 + 𝑏𝑖.

a. 3 + √−25(4 − √−36)

b. 1+√−25

√−81√−16

c. 5−2𝑖

3+5𝑖

7) Solve the following inequalities:

a. 𝑥−7

(𝑥+3)(𝑥−9)≤ 0

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b. (𝑥+3)(𝑥−4)

𝑥+6≥ 0

c. |8−7𝑥

4| > 3

d. −2|3𝑥 + 2| + 9 ≥ 1

e. |4 + 5𝑥| ≥ −2

f. |6𝑥 − 1| + 5 < 3

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Chapter 6 – Systems of Equations

8) Solve the following system of equations:

a. 4𝑥 + 𝑦 = 47

6𝑥 − 2𝑦 = −10 for 𝑥.

b. 3𝑥 + 2𝑦 = 15𝑥 − 4𝑦 = 9

for 𝑦.

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Chapter 3 – Introduction to Functions

9) Given the function 𝑓(𝑥) = −8𝑥 + 5, evaluate:

a) 𝑓(2)

b) 𝑓(𝑎)

c) 𝑓 (1

𝑎+1)

10) Given the function defined by

1 if ,4

1 if ,5

1 if ,12

)(

2 xx

x

xx

xf

Find (1)f , )2(f and )2(f .

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11) Find the domain of the following functions:

a) 72)( 23 xxxg

b) 405

2)(

x

xxf

c) xxf 211)(

d) 𝑓(𝑥) =√𝑥+3

𝑥−5

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12) Find the vertex of the following function. Find the maximum/minimum value.

a) 212)( 2 xxxf

b) 𝑓(𝑥) = 3𝑥2 − 12𝑥 + 7

13) Let 3)( xxf and 125)( xxg . Find )(xgf and (𝑔𝑜𝑓)(𝑥).

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14) Find the inverses of the following functions, if possible.

a) 𝑓(𝑥) =3

𝑥−7

b) 𝑓(𝑥) = √𝑥 − 43

+ 2

15) Describe the transformations needed to:

a) Go from xxf )( to 24)( xxf .

b) Go from xxg )( to 5)( xxg + 4.

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Chapter 4 – Polynomial and Rational Functions.

16) Given 𝑥 − 3 is a factor of the polynomial 𝑝(𝑥) = 𝑥3 − 10𝑥2 + 31𝑥 − 30,

find all the zeros of the polynomial.

17) Find a polynomial of 5th degree with integer coefficients that has zeros −2, 𝑖, √3𝑖

and y-intercept of 12.

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18) For the following rational functions, find the holes, vertical asymptotes,

horizontal asymptotes, if applicable.

a) 𝑓(𝑥) =𝑥2+23𝑥+132

𝑥2+3𝑥−88

b) 𝑓(𝑥) =𝑥2+7𝑥+10

𝑥2−4𝑥−12

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19) Write the equations for the functions graphed below:

a)

b)

c)

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Chapter 5 – Exponentials and Logarithms

20) Find the domain, range and the asymptote for the following functions.

a) 𝑓(𝑥) = 3 ∙ 2𝑥−5 − 7

b) 𝑓(𝑥) = −4 ∙ 3𝑥+1 + 5

c) 𝑓(𝑥) = 𝑙𝑜𝑔2(3𝑥 − 7) + 2

d) 𝑓(𝑥) = 𝑙𝑜𝑔5(−2𝑥 + 5) − 3

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21) Simplify the following expressions:

a) 𝑙𝑜𝑔3(5) − 𝑙𝑜𝑔3(405)

b) 𝑙𝑜𝑔6(24) + 𝑙𝑜𝑔6(54)

22) Solve the following equations:

a) 3𝑥+5 = 18

b) 𝑙𝑜𝑔3(2𝑥 − 5) = 3

c) −4 ∙ 𝑒𝑥+2 + 5 = −19

d) 𝑙𝑜𝑔2(𝑥 − 3) + 𝑙𝑜𝑔2(𝑥 + 11) = 5