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SUMMER REVIEW PACKET FOR STUDENTS ENTERING
PRECALCULUS HONORS or PRECALCULUS ACCELERATED
This packet contains material you have learned in Algebra 2 and
Geometry.
Since you may have forgotten some of that material, this packet
gives you the
opportunity to review and in some cases relearn much of the
Geometry and
Algebra that you will once again need starting in the fall. This
packet should be
done during August so the material is still fresh when you
return to school.
Due: This packet will be collected on DAY 1 and play a role in
your first quarter
effort grade. SHOW ALL WORK.
Use the ANSWER KEY to help with any problems that you don’t
remember.
Also, use the ANSWER KEY to CORRECT your work.
The purpose of this packet is to refresh your Algebra and
Geometry skills.
This will not be graded but IT WILL BE COLLECTED DAY 1.
Give this a good effort and the first quarter will go much
smoother for you.
NAME:_______________________________________________
Approximate time : 2 Hours 15 Mins
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SUMMER PREP FOR PRECALCULUS
A) Factor all of the following completely, if possible:
1) N2 – N – 6 2) 81y4 – 16x8 3) 9x2 – 15x + 6
4) (2x – 3)2 – 6(2x – 3) + 8 5) 6x2 + 3xy + 10x + 5y 6) 8A3 –
27B3
7) 36N4 + 44N3 + 24N2 8) 4x2y – 36y 9) 9x4 + 16
10) m(n – 2) – 3( 2 – n) 11) x6n – 2x3n + 1 12) ( a + b)4 – ( a
– b)4
B) Solve each equation. Find ALL solutions
1) x = ( x – 6)2 2) y2 ( y –3) ( y2 – 9 ) = 0 3) x6 + 9x2 =
10x4
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4) ( x – 4)3 – 4(x – 4) = 0 5) (x + 1) ( x – 5) = 7 6) y4 – 5y2
+ 4 = 0
C) Write and solve an equation for the each of the following
problems.
1) The product of three consecutive integers is 21 more than the
cube of the smallest integer. Find the three integers
2) A rectangular garden has a perimeter of 66 ft and an area of
216 ft2 Find the dimensions of the rectangle.
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3) A farmer plans to use 21 ft of fencing to enclose a
rectangular corral having an area of 55 ft2. Since the Corral
is
attached to the back of the barn, the farmer only needs to build
3 sides with fencing using the barn as the fourth side.
Find the dimensions of the rectangular corral.
D) Graph each solution set on a number line
1) x2 – 7x + 12 > 0 2) (x2 – 4x) ( x2 – 4) < 0
E) Given f(x) = 2x – 5 g(x) = x2 + 3 and h(x) = ½ x + 5 Evaluate
each of the following, if possible
1) f( -2) 2) f(g(2)) 3) h(g(0)) 4) f( x + 2)
5) f-1(x) { Find the inverse of f(x) } 6) f(h(x)) 7) Does g-1(x)
exist ? Explain
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F) Evaluate WITHOUT A CALCULATOR
2 8 5
2 3
11) (2 ) _______ 2) 32 _______ 3) ______ 4) ln( ) ______ 5) Log
100 _____
81Log Log e
2 15 2 3
13 2
5 1 6
3 96) ______ 7) 27 ______ 8) 25 ______ 9) 4 8 ______ 10)
______
33
x x
Simplify #11-14 making sure to leave NO Radicals in the
denominator of your answer.( Rationalize the denominator)
3
5 4 6 311) ______ 12) ______ 13) ______ 14) ______
2 2 6 2 3
Simplify:
215) ( 3 5) _________________ 16) (5 2 10)(3 2 2 10)
____________________
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Solve for x :
17) 2 5 4 18) 10 15 4x x x
G) CALCULATOR ALLOWED
1) State the QUADRATIC FORMULA :
Solve by any method : ( Answers should be exact and MAY contain
Radicals)
222) (5 3) 16 3) (3 1)( 3) 1 4) 4 (4 5) 5 0x x x x x
5) 22 5 8 0x x 6) 2 81x 7)
22 3 5 7x
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8) An express train travels 150 km in the same time that a
freight train travels 100 km. The average speed of the freight
train is 20 km/hr less than the express train. Find the speed of
each train.
9) Solve by COMPLETING the square. ( SHOW ALL WORK…RELEARN
COMPLETING THE SQUARE, if necessary)
a) 2 8 3 0 x x b) 22 5 1 0x x
Simplify:
10) 4 6 3 2 11) ( 3 5)( 3 5) 23)12) (5
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Trigonometry and Right Triangles.
Use your knowledge of right Triangles to find ALL sides and ALL
angles
13)
A = _____ a = ____ b = ____ A = ____ B = _____ b = _____
Use the Pythagorean Theorem to find missing side of the given
right triangles.
14) 15)
16) A rectangle has length 12 and width of 5. Find the
diagonal.
30o
4
A
B C
A
B C
5
5
13b
)
4 2
8
14
12
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17) A boy is 50 ft from a tall tree. The angle from his feet to
the top of the tree is 60 . How tall is the tree?
K) Polynomial and Rational Expressions
1) The graph of f(x) is given to the right.
Use the Graph to estimate the following:
a) domain of f
b) range of f
c) f(6)
d) estimate the value(s) of x if f(x)=-4
Perform the indicated operation and simplify. Leave you answer
in factored form if necessary.
2)
2 2
3 2
2 1 4 4
2
x x x
x x x x
3)
2
2 3
3 12
4 8
x x x
x x
f(x)
x
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4) 2
2
1
4
x
x x
5)
2 2
2 3
3 2 1
x x
x x x
6)
1 3
23
4
xx
7)
2
24
2 21
x
xx
x
8) Solve for x. 5 3
44 2x x
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L)
1) Find a third degree polynomial given the Zeros are : 5, -5,
and 2
2) Find all of the Zeros of the polynomial 3 2( ) 2 5 6f x x x x
given that x = -3 is one of the Zeros
3) Is ( x – 4) a factor of x3 – 3x2 – 16x + 48 ? EXPLAIN/ Show
how you know
4) Use your polynomial long division skills to divide : ( 5x5 -
x3 - 4x2 - 233x + 28) ( x2 - 7)
Hint : Remember to use “place fillers.”
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5) Solve each system of equations, if possible
) 3 9
2 4
a x y
x y
) 2 4
3 6 12
b x y
x y