42 This question requires the knowledge of 2 area formulas: ■ Area of rectangle = length width ■ Area of circle = πr2 This question also requires some reasoning.. Well, you might’ve not
Trang 1RATIO AND PROPORTION
7 If it takes 27 nails to build 3 boxes, how many
nails will it take to build 7 boxes?
a 64
b 72
c. 56
d 63
8 In Mrs Sam’s first grade class, the ratio of boys
to girls is 3 to 4 There are 28 students total How
many are girls?
a 12
b 20
c. 16
d 4
PERCENTS
9 Change 35% into a decimal.
a 3.5
b .35
c. 35.0
d .035
10 75 people were invited to the Frazzettas’wedding.
All but 9 were able to attend What percent
couldn’t come?
a 8.33%
b 7.5%
c. 12%
d 9%
ABSOLUTE VALUE
11 What is | 47 64 |?
a 17
b. 17
c. 111
d 47
12 Find | 23|.
a. 23
b. 32
c. 112
d. 23
EXPONENTS
13 Calculate 432 4
a 172
b 129
c. 7,396
d 1,849
14 Calculate (15)3
a. 1125
b. 15
c. –1125
d –135
SCIENTIFIC NOTATION
15 What is the correct way to write 3,600,000 in
sci-entific notation?
a 3,600 100
b 3.6 106
c. 3.6 106
d 36 106
16 7.359 multiplied by 106is equal to
a 0.0007359
b 0.00007359
c. 0.000007359
d 0.0000007359
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70
SQUARE ROOTS
17 Which of the following equations is correct?
a. 36 + 64 = 100
b. 25 + 16 = 41
c. 9 + 25 = 64
d There is no correct equation.
18 What is another way to write 512?
a 125
b 103
c. 63
d 12
CALCULATING MEAN, MEDIAN, AND
MODE
For questions 19 and 20, memorize these definitions:
Mean: When you are calculating the mean of a
series of numbers, you are simply finding the
average
Median: The median is the number in the
mid-dle of a series If there are two midmid-dle numbers
in a set, the median is the average of the two
Mode: The mode is the number that appears
most frequently in a series
19 Calculate the mean of the following test scores:
92, 89, 96, 93, 93, and 83
a 93
b 91
c. 92.5
d 91.5
20 Find the mode of the following series of
num-bers: 2 3 7 7 9 9 9 9 14
a 2
b 7
c. 9
d 14
GEOMETRY
Measurement
1 What is the area of the shaded region in the
fig-ure below?
a 42 4.5π
b 42 9π
c. 24
d 42
This question requires the knowledge of 2 area formulas:
■ Area of rectangle = length width
■ Area of circle = πr2
This question also requires some reasoning Exactly how much of the whole figure is shaded? How can you use these area formulas to help? Well, you might’ve noticed that the shaded region is just the area of the rectangle minus the area of12the circle You can write a formula for yourself:
Area shaded = Area of Rectangle 12Area of Circle Let’s get all the pieces we need by marking up the fig-ure a different way:
6
7
– BASIC SKILLS FOR COLLEGE –
Trang 3Notice that by drawing a new radius, we know that the
length of the rectangle is 7 We already knew that the
width was 6, so the area of the rectangle is just length
width 7 6 42
Now, we will figure out the area of the circle
using A πr2, which becomes π(3)2 9π If the area
of the whole circle is 9π, then the area of half the
cir-cle will be 12 9 π 4.5π
Thus, the area of the shaded region is
Area shaded = Area of Rectangle 12Area of Circle
Area shaded = 42 4.5π
The correct answer is a.
2 Using the formula V = 13πr2h, what is the
vol-ume of the cone below?
a. 435π
b 45π
c. 75π
d 125π
Looking at the figure, we see that the radius, r, is 5 and
the height, h, is 9 We plug the values r 5 and h 9
into the volume formula V 13πr2h The formula
becomes V13π(5)2(9) V 13π(25)(9) At this point,
you may be inclined to multiply 25 by 9 But
remem-ber what we told you in the beginning of the book about
questions working out nicely? Does it seem nice to
mul-tiply 25 by 9 and then take a third of that number? No
How about this: Take 13of the 9 instead
V13(9)π(25) 3π(25) 75π
Thus, the answer is c.
Quadrilaterals
1 What is the area of the trapezoid shown below?
a 260
b 210
c. 160
d 130
The area of a trapezoid is A12 (base1 base2)
height In this case, the formula becomes A12(10 16) 10 12(26) 10 13 10 130 Thus, choice
d is correct.
2 What is the area of the parallelogram shown
below?
a 64
b 32
c. 16
d It cannot be determined by the
informa-tion given
4 8
10
10
16
9
5
Trang 4CHAPTER 4 • LearningExpress Skill Builders
72
The area of a parallelogram is A base height
Look-ing at the diagram, we see that the base is 8 and the
height is 4 The area, A 8 4 32 Thus, choice b
is correct
Triangles
1 In the right triangle below, AB = 4 and AC = 5
What is the value of BC?
a 3
b between 6 and 7
c. 7
d between 7 and 8
To solve this question, we will use the Pythagorean
the-orem, a2 b2 c2, where a and b represent 2 legs of
the right triangle, and c represents the hypotenuse of the
right triangle The hypotenuse is the longest side of a
right triangle and it is always opposite the 90° angle (the
right angle) Let’s fill in the information that we know:
a2 b2 c2
(4)2 (5)2 c2
16 25 c2
41 c2
c 41 Because we know 62 36 and 72 49, we know that
41 will be between 6 and 7, choice b.
2 In the figure shown below, what is the value of
x ?
a 16
b 13
c. 9
d 6
The figure is comprised of 2 triangles These triangles
happen to be similar triangles Triangles are similar
when they have all three angles in common The sides
of similar triangles are in proportion
We know that these 2 triangles are similar because they both have right angles, and the angles marked below are equal as well
It follows that the third angles must also be equal because all triangles have 180° (90° marked angle 3rd angle 180° for both triangles.)
In order to figure out the proportion, you just look
at the sides opposite the equal angles
SAMPGEO_4
SAMPGEO_5
SAMPGEO_6
3
7 8
14
x
Equal angles
SAMPGEO_4
SAMPGEO_5
SAMPGEO_6
SAMPGEO_7
3
7 8
14
x
SAMPGEO_8
SAMPGEO_4
SAMPGEO_5
SAMPGEO_6
SAMPGEO_7
B
SAMPGEO_8
– BASIC SKILLS FOR COLLEGE –
Trang 5LearningExpress Skill Builders • CHAPTER 4 73
The top triangle has a side of 7, and the bottom triangle
has a side of 14, so we know that the sides of the bottom
triangle are double the sides of the top triangle.
Since x is opposite the 3rd angle, we look at the
top triangle to see that 3 is opposite the 3rd angle We
double the 3 to get x 6 Thus, the answer is d.
Parallel Lines
1 If A B is parallel to CD , what is the value of x ?
a 77°
b 87°
c. 103°
d 113°
We know that A B and CD are parallel, so any line that intersects them will create the same angles as it crosses each line Notice how we can write 103° in the figure below:
Also, we know that 103° x 180°, because there are
180° in a straight line:
We can solve for x by subtracting 103° from both sides
of the equation 103° x 180° Thus, x 77°, which
is choice a.
2 Given that l m and no are parallel, use the figure below to determine the value of a b c d.
a 120°
b 180°
c. 270°
d 360°
Just by knowing that straight lines are 180°, we can fill
in all the values for a, b, c, and d:
Now we just add up the values: a b c d 70°
110° 70° 110° 360°, choice d.SAMPGEO_4
SAMPGEO_5
SAMPGEO_6
70 110
70 110 110
110
70 70
o o
o o
SAMPGEO_1
SAMPGEO_2a
SAMPGEO_2b
SAMPGEO_3
a b
c d 110
110
70 70
SAMPGEO_1
SAMPGEO_2a
SAMPGEO_2b
SAMPGEO_3
103
o
o o
SAMPGEO_1
SAMPGEO_2a
SAMPGEO_2b
103
o
o o
SAMPGEO_1
SAMPGEO_2a
SAMPGEO_2b
SAMPGEO_3
103 x
o
o
SAMPGEO_5
SAMPGEO_6
SAMPGEO_7 SAMPGEO_8
3
7 8
14
x
– ESSENTIAL PRACTICE WITH MATH –
Trang 6CHAPTER 4 • LearningExpress Skill Builders
74
Coordinate Geometry
1 Which line below has no slope?
a Line A
b Line B
c. Line C
d Line D
Let’s review how to tell the slope of a line by looking at
each graph:
Thus, choice d is correct This line has no slope because
slope cchhaannggeeiinnx y
There is no change in x for Line D No change
zero, which means we would have a zero in the denom-inator of our slope formula Zeroes and denomdenom-inators
do not mix! (Actually dividing by zero is technically
termed undefined, as in you can’t do it!) Therefore, there
is no slope!
Line C is interesting to look at as well Here there
is a zero slope because there is a zero in the numerator
of the slope formula There is a zero in the numerator
of the slope formula because there is no change in y
2 Line AB below contains the points (2, 3) and (3, 2) What is the equation of line AB?
a y x 1
b y 3x 2
c. y x 1
d y 2x 3 The equation of a line is y mx b, where m is the
slope of the line (ΔΔx y ) and b is the y intercept We are
given 2 points to work with, so first we will determine the slope
m = ΔΔx y = x y2
2
y x
1 1
x
y
1 2 3 4 5 6 7 1
2 3 4 5 6 7
-1 -2 -3 -4 -5 -6 -7
-1 -2 -3 -4 -5 -6 -7
(-3,-2)
(2,3)
C
D
X
Y
X
Y zero
slope
no slope
A
B
X
Y
X
Y positive
slope
negative slope
C
D
X
Y
X
Y
A
B
X
Y
X
Y
– BASIC SKILLS FOR COLLEGE –