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VILLA VICTORIA ACADEMY (2016)
PREPARATION AND STUDY GUIDE
ENTRANCE TO ADVANCED ALGEBRA 1
FROM PRE-ALGEBRA
1) Write an expression for the following:
Sean has a dollars which is $8 more than Tina. Write an expression which gives
the amount of money that Tina has in dollars?
2) Complete the following:
a)  12   17 
b)  12   17 
c)  3  15
3) If there are 12 eggs in a dozen, write an expression for the number of dozens in e
eggs.
4) Simplify: 7  3  4   3  2   1 .
5) Insert grouping symbols to make the number sentence true.
2  6  5  4  2 14
h4
6) Evaluate
, for h  14 and j  3.
j
7) If you earn d dollars working 40 hours. Write an expression which describes how
much you earn per hour.
8) Evaluate 4  a  b  , for a 11; b  4.
9) Which symbol,
 , , ,  , makes
15   7  ?  2 11 a true statement?
10) Use the distributive property to simplify this expression: 4  98
11) Simplify the expression: 5  2  m  3  m.
12) Solve each equation. Display all steps.
a ) h  6  27
b) 16  m  36
a
6
8
d )  4a  56
a
 4
11
d )  5a   50
c)
13) Solve each inequality. Display all steps.
a) 19  y  7
b) a  12   23
14) Simplify the following:
a) 36   2  4  3
c)
b) 12   3  4 3  1
15) Determine the number of hours it would take to drive 168 mi at an average rate of
48
mi
. Use the formula d  rt .
h
2
16) Solve the following:
a ) a  5.07  7.23
b)  3t  0.174
c) a  5.04   12.43 d )
a
 1.6
3.2
17) Using the data: 94; 85; 86; 92; 86; determine the following.
a) mean
b) median
c) mode
18) Simplify:
m 4 n5
a )  2 y   3k  2 y   3k
b)  6  m  m  n  3  m c ) 6 2
mn
2
w10 y12 z
6
2
3
2
7
d) x  y x  y
e)
f
)
5
g
)
x
h ) 53  50
6 5
wz
 
19) Determine all the factors of 56.
3
20) Determine the GCF of 12 x and 32 xy .
21) Is this number divisible by both 2 and 3? 58, 404
3 5
1
, , and .
4 8
6
22) Determine the sum in simplest form for:
23) Determine the prime factorization of 72 in exponential form.
24) Determine the following in simplest form:
a)
7
5

12
8
b)
5 5

9 6
c)
7
7
 2
10
12
25) Complete the following:
1
a) 3 ft
2
 ? in
b) 9 qt .  ? gal .
26) Write each decimal as a fraction in simplest form.
a ) 0.55
b ) 0.13
27) Simplify the following:
4
5 2 1
3
a )  6  11 b )    
5
7 3 6
c )  6k 
4
2
 x 
 2m 
d )   e)  2 
 3 
n 
3
28) Solve the following:
a )  6n   31.26
29)
30)
31)
32)
b) n% of 50 is 20.7 c) Find 70% of 60
1
d )  4 x  25
6
Write in standard notation: 6.11  10 .
Write 360 mi in 8 hours as a unit rate.
Which is a better deal: $9.52 for 8 gal or 11 gal for $11.99?
Determine the sale price of an item with a regular price of $29.99 marked 30% off.
5
3
33) Write each number as a percent, round to the nearest tenth of a percent if necessary.
a ) 0.039
b)
14
25
c)
8
33
34) Determine the probability for one spin of a spinner numbered 1 to 9.
a) P 1 or 2
b) P less than 7 
35) The scale on a map is 1inch : 8 miles . Determine the actual distance for the
following.
a ) 4.5 in.
b ) 10.75 in.
36) Solve the proportions:
a)
6 9

10 x
b)
n
5

14 3
37) Write each ratio as a fraction in simplest form.
a ) 24 : 56
b) 40 : 75
38) Simplify the following: 5z  3 y   z  y  .
39) Use the formula t 
mi
d
for t  3.5 h and r  60
, to determine the
h
r
distance.
3 2
4
40) Determine the GCF: 5a b and 15ab .
41) Twenty-one of the 25 members of the Science club had an entry in the science fair.
What percent of the club had an entry?
42) Graph on a number line the solution to the following: 9  4 x  1
43) A car costs $29 a day plus $ 0. 25 a mile to rent. The rental company uses the
formula C  29  0.25m to find the daily cost (c) for (m) miles. Solve the
formula for m.
44) Use the formula that you found in #43, to find the number of miles driven in a day
for a total cost of $60.25.
45) Convert 0.25% to a fraction.
46) Solve the following equations:
a) 3 y  9  6
b) 3 x  7   2  x  5   x  5
d ) 0.2n  13  1.3n  14.5
e)
c)
2
1
p  12  p  10
3
3
1
1
 e  6    e  8
2
4
47) Use >, <, or = to complete the statement.
18 4   5 ?  40   311
48) The rate of interest on a savings account is 7%. What is the simple interest for three
years of $352?
49) Parth deposits $600 into a savings account that earns 4% interest compounded
yearly. What is Parth’s balance after three years?
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50) How much interest did Parth earn in #49?
51) Tracie is 59 inches tall. How tall is she in feet and inches?
52) The probability that Steven gets a hit playing baseball is 1 in 4 times at bat. About
how many hits would you expect him to get in 29 times at bat?
53) When a number is multiplied by
1
, the result is the same as when 5 is subtracted
2
from 3 times the number. Write an equation which expresses this situation. Then
solve the equation.
54) Determine the slope for the points A 3,  2; B 1, 4  .
55) Solve 3n  1   8 .
56) Express the equation in slope- intercept form. 3 x  2 y  8
57) Determine the slope of the line with the equation: 3 x  4 y  24.
58) Write a function rule to describe the amount of sales tax t  p  as a function of the
price p of an item purchased if sales tax is 6%.
59) Graph the equation and label the points. 4 x  2 y  8
60) Simplify the following:
1
b) x  x  y  2    y   x  5
 x  12  2
3
2
61) Convert
yd to inches.
3

62) If an angle is 18 , determine the following:
a)
c)
8  4  2  4
4
a) its complement
b) its supplement

63) In  PQR, mP  38 and mQ  52 . Classify  PQR .
64) Given:  JKL   PQR . Determine the following.

a ) K  ?
b) LJ  ?
65) STU with vertices S 1, 4 , T 1, 1 , U  3, 0  . Graph STU and determine
the following:
a) Graph the image of its translation 4 units left and 3 units down (Label the
points.)

b) Graph the image of its rotation of 90 .
66) Determine the circumference of a circle with a radius of 18 cm.
67) If a rectangle is 8 in long and 6.5 in wide, and if a triangle has a base of 8 inches and
a height of 6.5 inches, which figure has the larger Area and by how much?
68) If a rectangle has a perimeter of 110 feet and a length of 23 ft. Determine its area.
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69) Determine the area of the following:
a) Triangle: base 26 in, slant height of 15 inches and a perpendicular height 7 in.
b) Circle: diameter of 30 ft.
c) Trapezoid: bases are 8 and 11 cm., a slant height of 8 cm. and perpendicular
height of 7 cm.
70) Determine the Lateral Surface Area, Total Surface Area and the Volume for the
following:
a) Right Circular Cylinder: diameter 10 cm, height 6 cm
b) Square Pyramid:
square base is 12 m on an edge, slant height is 15 m
c) Sphere:
radius is 19 in.
71) Determine the Volume of a Triangular Pyramid whose triangular base is an
equilateral triangle which measures 18 m on an edge and the pyramid is 27 m
high.
72) Determine the hypotenuse of a triangle whose legs are 5 in and 12 in.
73) A 25 foot ladder is placed against a wall. The base of the ladder is 12 ft from the
wall. Determine how high up the wall the ladder reaches.
74) If  ABC   XYZ , write three congruence statements and 3 ratios for these
triangles.
75) Determine the area of a trapezoid with bases 8 in and 2 in and height 4 in.
76) Determine the volume of a cone with diameter of 9 cm and a height of 6 cm.
77) Could the following numbers be the measures of the sides of a right triangle?
a) 16, 30, 35
b) 5, 12, 14
c) 9, 12, 15
d) 6, 8, 9
78) Determine the distance between the following points: A 3,  2; B 1, 3 .
79) Determine the midpoint of the points: A 3,  2; B 1, 3 .
80) Determine the Surface Area and the Volume of a Rectangular Prism which measures
8 ft by 6 ft. by 4 ft.



81) If the hypotenuse of a 30  60  90 triangle is 8 cm. What is the length of the
shorter leg and the length of the longer leg?
82) Marisa has seven pairs of shoes. Three are white and four are black. She randomly
chooses a pair to wear each day. Determine the probability that Marissa chooses
a white pair two days in a row under the following conditions:
a) Marissa may wear the same pair two days in a row.
b) Marissa will not wear the same pair two days in a row.