G9 Extension Semester 2 Review
Topic 1: Sequences
For questions 13 and 14 above: is 2000 a term in the sequence? Why or why not?
G9 Math Ext
Exponentials and Radicals Practice Test
Criterion A/D
Level 1 – 2
Topic 2: Exponentials and Radical Equations
Simplify Radicals
√75
Useful formulas
√3
!
√32
√2
3√98
2√2
√50
2√2
!
"
Half-Life
!(#) = & ∗ (") , & is the initial amount, * is the half-life
Rationalize Radicals
6
Compound Interest
9 value, 0 is the interest rate as a percent,
1
35 is the future value, -, is the present
+, = -, (1 + !$$%) , +,
2 is the
√3
#
number of compounds per
√7 year, 3 is the time in years
√3
3√5
!(#) = 2' + 3
!(#) = 2' − 1
!(#) = 2'
Identify the Asymptote
!(#) = 2' + 2
Identify the domain and range
Graph Exponential Functions
Graph Radical Functions
%&
Level 5-6
Solve Radical Equations
√3# = √4# − 1
√3# + 12 = √# + 8
√# − 9 − √# = −1
√2# − 5 = 1 − √# − 3
Solve Growth and Decay Problems
The population of ants A weeks
The population of ants A weeks
after it is established is given by
after it is established is given by
- = 500 ∗ (1.12)+ . How many
- = 500 ∗ (1.02)+ . How many
ants were there initially? How
ants were there initially? How
many ants will there be after 10
many ants will there be after 5
weeks?
weeks?
Sketch a graph of the function.
Use the graph to estimate when
the population will double.
Sketch a graph of the function.
Use the graph to estimate when
the population will double.
#
@ = √3# − 58
10
√11 − # = √# − 7
@6 − √# = √#
@6 + √# = √#
When a liquid in a container is
placed in a refrigerator, its
temperature in ℃ is given by D =
100 ∗ (0.933)& where t is the
number of minutes that has
passed. What was the initial
temperature of the liquid? What
is the temperature of the liquid
after 3 minutes?
When a liquid in a container is
placed in a refrigerator, its
temperature in ℃ is given by D =
150 ∗ (0.997)& where t is the
number of minutes that has
passed. What was the initial
temperature of the liquid? What
is the temperature of the liquid
after 10 minutes?
Sketch a graph of the function.
Use the graph to estimate when
the temperature will be 90 ℃
Sketch a graph of the function.
Use the graph to estimate when
the temperature will be 120 ℃
Solve Half-Life Problems
The half-life of iodine-131 is 8.14
days. How much of a 200 mg
sample will be left after 72 days?
What is the half-life of a 100 gram
sample of nitrogen-16 that decays
to 12.5 g in 21.6 seconds?
The half-life of carbon-14 is 5730
years. How much of a 24 mg
sample will be left after 3,000
years?
The half-life of HG-197 is 64.128
hours. How much of a 12 mg
sample will be left after 72 hours?
The half-life of SR-85 is 64.9 days.
How much of a 8 mg sample will
be left after 100 days?
A 208 gram sample of sodium-24
decays to 13 grams in 60 hours.
What is the half-life of this
radioactive isotope?
If the half-life of iodine-131 is 8.1
days, how long will it take a 50
gram sample to decay to 6.25
grams?
Chromium-48 has a half-life of
21.6 hours. How long will it take a
360 gram sample to decay to
11.25 grams?
Fifi invested $500 at 10% interest
compounded weekly. How much
will she have after 10 years?
Joe has $2,000 to invest at 4.2%
interest compounded daily. How
much will he have after 3 years?
Solve Compound Interest Problems
$10,000 is invested for 4 years at
Bob wants $15,000 for a trip to
7% compounded monthly. What
Fiji in 5 years. How much should
is the value after 4 years?
he invest at 7.25% interest
compounded weekly to reach his
goal?
Topic 3: Rational Equations, Graphs, and Inequalities
Precalculus
Name___________________________________
©g k2e0N1u5N bKlu]tBac AS_oRfHt\w\a]rLeg mLoLrCL.z c nAPl\l` qraidgmhZtAsm mrwexsOeFrUvre]di.
Rational Functions: Holes and Asymptotes
Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, horizontal asymptote,
and domain of each. Then sketch the graph.
1) f ( x ) =
x+1
x-2
2) f ( x ) =
x2 + 2 x - 8
- x2 + 6 x - 8
y
-8
-6
3) f ( x ) =
-4
y
8
8
6
6
4
4
2
2
-2
2
4
6
8 x
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
x 2 - 7 x + 12
- 2 x 2 - 2 x + 24
4) f ( x ) =
-6
-4
8 x
4
6
8 x
y
8
8
6
6
4
4
2
2
-2
6
3 x 2 - 3 x - 18
x2 - 4
y
-8
4
2
4
6
8 x
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
Worksheet by Kuta Software LLC
-1-
©i _2Y0b1b5t ^KWubtjaJ lSQoBfHt\wdaDrTeJ \L^LqCJ.h n YAtlVly rrHiqgThStKsr frveCs`earCvpeedw.R i cMsatdUev TwGintehh GIknofRiinPiWtBec HALl\gIeJbTrDal [2_.
Kuta Software - Infinite Algebra 2
Name___________________________________
Graphing Simple Rational Functions
Date________________ Period____
Identify the vertical asymptotes, horizontal asymptote, domain, and range of each.
1) f ( x) = −
4
x
2) f ( x) =
4
+1
x−1
3) f ( x) = −
3
−1
x−1
4) f ( x) = −
3
x
Identify the vertical asymptotes, horizontal asymptote, domain, and range of each. Then sketch the
graph.
5) f ( x) =
3
−2
x+1
6) f ( x) =
3
+2
x+1
y
−8
−6
−4
y
8
8
6
6
4
4
2
2
−2
2
4
6
8 x
−8
−6
−4
−2
2
−2
−2
−4
−4
−6
−6
−8
−8
©Y t2j0G1i2c NKfugtgaa aSoojfEtHwLafrfeY 4LBL6Cq.O d 7A9lRlm srpirghhztNsN broeVsCe6r2vZerdT.R 5 DMuaOdSeH GwsiEt6hK AIRnnf8iRnHiutPek IAbl6gkeEbcrRat P2u.j
-1-
4
6
8 x
Worksheet by Kuta Software LLC
Topic 4: Trigonometry and Geometry
Trig Geometry Review
Use sine/cosine/tangent to find missing length and missing angles
12C.2 #2
12C.3 #1
Use sine rule to find missing lengths and angles
25D.1 #2 and 25D.2 #1
Use cosine rule to find missing length and angles
25E #1(a-c) and #2(a-c)
Solve problems that include bearings
12E #9-10 and 25F #2,3,7,8
Use the area rule to find area
Solve multi-step problems using trig
Remember properties about the unit circle
-radius is 1
Coordinates are (cos %, sin %)
Topic 5: Trigonometric Functions