Math 3 Review Second Semester
WHS May 2014
1. Locate the following SAT Math Scores on the z-score normal distribution seen below.
Assume the μ = 500 and σ = 100.
SAT Math Scores: x = 650, x = 400
2. Refer to #1, find
a) P(x < 650). ___________ c) P (x < 400). ___________ e) P (400 < x < 650). __________
b) P(x > 650). ___________ d) P (x > 400). ___________ f) P (x > 3). ________
3. Refer to #1.
a) P(z < 1) = ________
b) P(z < -1) = ________
c) P( -1 < z < 1) = _________
d) P(z < 2) = ________
e) P (z < -2) = ________
f) P( -2 < z < 2) = _________
g) P(z < 3) = ________
h) P(z < -3) = ________
i) P(-3 < z < 3) = _________
4. The Empirical Rule was taught in Math 2 (See graph below).
a) The Empirical Rule states that
approximately 68% of the data (from a
normal distribution) can be found
within 1 standard deviation of the
mean. Refer to the calculations in #3.
The actual percentage is _________ %
(rounded to hundredths of a percent).
b) The bars show the actual data. You
can see that this is not a perfectly
normal distribution, but it is close. If
the data set represents 2200
participants, how many of them would
you expect to find within 1 standard
deviation of the mean? ____________
5. Use your z-score table to do an analysis of this ACT Math score data. Assume the μ = 18 and σ = 6.
a) P (z < 2.23) = __________ b) P (z > - 1.6) = _________ c) P (-1.57 < z < 3.03) = ________
d) P (x < 23) = __________
e) P (x > 23) = _________
f) P (23 < x < 25) = ________
g) If the Nerd-R-US Scholarship requires an ACT math score of at least 26, what percent of a
normal population would be eligible for the scholarship? ____________ (nearest
hundredth of a percent)
h) If you examined 750 randomly selected ACT test takers, how many would you expect to
score above 30? __________ test takers
i) What percentage would you expect to score between 20 and 30 on the ACT math portion?
______%
j) Of the 750 randomly selected test takers, how many would you expect to score between
20 and 30 on the math portion of the ACT? __________
6. You score a 540 on the SAT Math test (μ = 500 and σ = 100) and score a 22 on the ACT math test
(μ = 18 and σ = 6). Which score should you submit to your favorite University admissions office?
___________ Why? ________________________________________________________________
_________________________________________________________________________________
7. In Georgia, the SAT combined math/verbal score was 994 with a standard deviation of 196 (not
real data, but probably close to real data). Jacinta scored in the 87 th percentile. Assuming a
normal distribution, what was her raw combined math/verbal SAT score? ____________
8. In the United States, men have an average height of 69.1 inches with a standard deviation of 2.8
inches and women have an average height of 64.0 inches with a standard deviation of 2.5 inches.
Assume normal distributions.
a)
b)
c)
d)
Mr. Shook is 74.5 inches tall. What percentage of the U.S. men population would you expect
to be shorter than Mr. Shook? ______________
Mrs. Shook is 63 inches tall. What percentage of the U.S. women population would you
expect to be shorter than Mrs. Shook? ______________
How tall are you? _______ inches
What percent of the U.S. population would you expect to be taller that you? ___________
9. Which of the following scenarios describes an experiment?
a. Scientists monitor the growth of pet fish to determine if their color affects their size.
b. Scientists separate pet fish into different groups to determine if the water
temperature affects their size.
c. Scientists count the number of people passing a certain point during an hour wearing
a red shirt.
d. Scientists monitor the long-term health conditions of patients who smoke and those
who do not smoke to measure the effects of smoking.
10. Every possible sample of the same size has the same chance of being selected. This can be
accomplished by assigning every member of the population a distinct number and then using a
random number generator or table to select members of the sample.
a) Simple Random Sample
c) Stratified Random Sample
b) Systematic Sample
d) Cluster Sample
11. It is the state finals and WHS’s own Larry the Legend is at the free throw line. His free throw %
for the season is 80%. It turns out that we win the championship by 1 point if he makes all 8 of
his free throws.
a) Find the probability that he makes all 8 of his free throws. _____%
b) Find the probability that he makes exactly 7 of his free throws and we play overtime.
______%
c) Find the probability that he makes less that 7 of his free throws and we lose!
______%
12. Wolfpackster completes 60% of his passes in football. If he throws 6 passes, find the probability
that he has a horrible night and completes 0 passes. ________%
13. Write an equation for a circle with radius r = 4 and center (6,1). ________________________
14. A circle is given by x2 + y2 +6x – 8y – 24 = 0. The center is at ( __ , __ ) and r = ____
15. A circle is given by x2 + y2 = 16. The units of the radius are in cm.
a) Area = _____________(include units)
b) Circumference = __________(include units)
16. A circle is given by (x-3)2 + (y+2)2 = 169. The center is at (___ , ___).
17. Is the point (8,10) on the circle (x-3)2 + (y+2)2 = 169? ______ How can you tell?____________
18. The following points are on the circle (x-3)2 + (y+2)2 = 169.
Find an equation for the tangent to the circle at each point.
a) At (15,3).
________________________
b) At (16, -2)
____________________________
c) At (3, 11)
____________________________
d) At (-2, 10)
____________________________
19. Identify the conic section: (circle, ellipse, hyperbola, parabola)
a)
C)
20.
(𝑥+3)2
64
(𝑥+3)2
64
(𝑥−8)2
41
+
−
+
(𝑦−8)2
49
(𝑦−8)
49
(𝑦+3)2
9
= 1 _______________ b)
=1
(𝑥+3)2
36
−
_______________ d)
(𝑦−8)2
36
(𝑥+3)2
64
= 1 _________________
+
(𝑦−8)2
64
= 1 _________________
=1
A) Name of graph/conic. _________________
B) Center? __________
C) Vertices of major axis? ________ or ________
D) Vertices of Minor Axis? ________ or ________
E) Sum of Focal radii? ______
G) Range? __________
F) Domain? ___________
H) Foci? ________ or ________
I) Sketch the graph.
21.
(𝑦−8)2
144
−
(𝑥+3)2
25
=1
A) Name of graph/conic. _________________
B) Center? __________
C) Vertices? ________ or ________
D) Equations of asymptotes? y = _______________ or
y = __________________
E) Difference between lengths of Focal radii? ______
F) Domain? ___________ G) Range? __________
I) Sketch the graph.
H) Foci? ________ or ________
22.
(𝑥−3)2
4
−
𝑦+1
16
=1
A) Name of graph/conic. _________________
B) Focus? ___________
B) Vertex?___________
C) Equation of Directrix? ____________________
D) Domain? ___________ E) Range? __________
F) Sketch the graph.
23. Write an equation for a sphere with center (-2, 5, 4) and diameter 8 cm.
__________________________________________________
24. Find an equation of the sphere with a diameter whose endpoints are at (0,4,-3) and (-6, 12, 9).
__________________________________________________
𝟏
25. The vertex of y = - 𝟖 (x -4)2 +3 is at ______ and the focus is at _______.
𝟏
26. The vertex of x = - 𝟖 (y -4)2 +3 is at ______ and the focus is at _______.
27. Expand completely.
𝒙𝟑
log(𝟑𝒚) = ______________________________
28. Simplify. 2log(x) - 3log(y) -
𝟏
𝟑
log (z) = _____________________
28. Solve for x.
ln (12) – ln(x-2) = ln (4)
_____________________
29. Solve for x.
9(x+3) = 27(x)
______________________
30. Solve for x.
log3(x-4) = 2
______________________
31. Solve for x.
2(7)x-3 - 5 = 17
32. Compound Interest Formulas:
_______________
𝑟 𝑛𝑡
𝑛
𝐴 = 𝑃 (1 + )
𝐴 = 𝑃𝑒 𝑟𝑡
a) How much is in the account if Mrs. Hajduk places $2500 in the bank at 4% interest
compounded monthly for 10 years? $ _____________________
b) How much is in the account if Mr. Fuqua places $2500 in the bank at 4% interest compounded
continuously for 10 years? $ _____________________
c) Mr. Shook is considering the 4% interest compounded quarterly option. How long will it take
for his invested money to double in value? __________ years
33. Find the half-life of Brooksonium if 14 grams of a 48 gram sample remains after 200 years.
_________________________
34. The half-life of Packisium is 28 days. If you start with a 32 Kg sample, how much Packisium will
remain after 62 days? ____________ Kg
35. Graph y = f(x) = 2 log3(x +4) +5.
36. Refer to #35.
a) Domain? ______________
b) Range?_________________
c) y-intercept? ___________
d) x-intercept? _____________
e) f-1(x) = ___________________________
f) Solve for x. 2 log3(x +4) +5 < 9
____________________
g) Solve for x. 2 log3(x +4) + 5 > 9
____________________
Free Response:
#36. It is the state finals and WHS’s own Larry the Legend is at the free throw line. His free throw %
for the season is 80%. It turns out that we win the championship by 1 point if he makes all 8 of
his free throws.
a) Create a probability Distribution for the Number of free throws made.
b) Create a histogram for this distribution.
c) Find P(Larry makes exactly 3 of 7 free throws). ______%
d) ) Find P(Larry makes at least 3 of 7 free throws). ______%
#37. Write
(𝒚−𝟖)𝟐
𝟏𝟒𝟒
−
(𝒙+𝟑)𝟐
𝟐𝟓
= 𝟏 in General Form.
___________________________________________________________________
#38. If Pt is the Population of ants after “t” years and Pt = P0 (2)0.06 x then find the ant population
after 5 years if the initial population is 1.5 million ants (1,500,000).
#39. If Pt is the Population of ants after “t” years and Pt = P0 (2)0.06 x then how long will take an
initial population of 1,500,000 ants to reach a colony size of 100,000,000? ______________ yrs
(assume ants do not die).
#40. The population of the dreaded mathelaticia bacteria grows as shown (where “t” is in hours).
𝟏
A = 40,000 ( )0.05t
𝟐
a) Find the initial population. ________________
b) Find the population after 24 hours. _________________
c) How long did it take for population to double? _______ hours