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1
Math 1310 Final Review
Where/When: CASA Testing Center / May 4 β May 10
Number of Questions: 30 multiple choice questions.
Time: 110 minutes.
What is covered: All chapters.
Chapter 1 β 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 3π₯ β 10π¦ + 6 = 0.
4) Find the x- and y-intercepts of the line 0542 yx .
2
Chapter 2 β Solving Equations and Inequalities
5) Solve the following equations:
a) π₯2 + 17π₯ + 72 = 0.
b) 2π₯2 β 5π₯ + 4 = 0
c) β3
5π₯+
3
15π₯= 2
d) π₯4 β 5π₯2 β 36 = 0
e) π₯ β 11βπ₯ + 28 = 0
f) 10412 x
3
6) Simplify the following expressions.
Write the complex numbers in the standard form π + ππ.
a. 3 + ββ25(4 β ββ36)
b. 1+ββ25
ββ81ββ16
c. 5β2π
3+5π
7) Solve the following inequalities:
a. π₯β7
(π₯+3)(π₯β9)β€ 0
4
b. (π₯+3)(π₯β4)
π₯+6β₯ 0
c. |8β7π₯
4| > 3
d. β2|3π₯ + 2| + 9 β₯ 1
e. |4 + 5π₯| β₯ β2
f. |6π₯ β 1| + 5 < 3
5
Chapter 6 β Systems of Equations
8) Solve the following system of equations:
a. 4π₯ + π¦ = 47
6π₯ β 2π¦ = β10 for π₯.
b. 3π₯ + 2π¦ = 15π₯ β 4π¦ = 9
for π¦.
6
Chapter 3 β Introduction to Functions
9) Given the function π(π₯) = β8π₯ + 5, evaluate:
a) π(2)
b) π(π)
c) π (1
π+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 .
7
11) Find the domain of the following functions:
a) 72)( 23 xxxg
b) 405
2)(
x
xxf
c) xxf 211)(
d) π(π₯) =βπ₯+3
π₯β5
8
12) Find the vertex of the following function. Find the maximum/minimum value.
a) 212)( 2 xxxf
b) π(π₯) = 3π₯2 β 12π₯ + 7
13) Let 3)( xxf and 125)( xxg . Find )(xgf and (πππ)(π₯).
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14) Find the inverses of the following functions, if possible.
a) π(π₯) =3
π₯β7
b) π(π₯) = βπ₯ β 43
+ 2
15) Describe the transformations needed to:
a) Go from xxf )( to 24)( xxf .
b) Go from xxg )( to 5)( xxg + 4.
10
Chapter 4 β Polynomial and Rational Functions.
16) Given π₯ β 3 is a factor of the polynomial π(π₯) = π₯3 β 10π₯2 + 31π₯ β 30,
find all the zeros of the polynomial.
17) Find a polynomial of 5th degree with integer coefficients that has zeros β2, π, β3π
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) π(π₯) =π₯2+23π₯+132
π₯2+3π₯β88
b) π(π₯) =π₯2+7π₯+10
π₯2β4π₯β12
12
19) Write the equations for the functions graphed below:
a)
b)
c)
13
Chapter 5 β Exponentials and Logarithms
20) Find the domain, range and the asymptote for the following functions.
a) π(π₯) = 3 β 2π₯β5 β 7
b) π(π₯) = β4 β 3π₯+1 + 5
c) π(π₯) = πππ2(3π₯ β 7) + 2
d) π(π₯) = πππ5(β2π₯ + 5) β 3
14
21) Simplify the following expressions:
a) πππ3(5) β πππ3(405)
b) πππ6(24) + πππ6(54)
22) Solve the following equations:
a) 3π₯+5 = 18
b) πππ3(2π₯ β 5) = 3
c) β4 β ππ₯+2 + 5 = β19
d) πππ2(π₯ β 3) + πππ2(π₯ + 11) = 5
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