math 1310 final review where/when: casa testing center
TRANSCRIPT
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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