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Interactive Study Guide for Students: Pre-requisite Skills for Algebra II
Section 1: Comparing and Ordering Real Numbers
To determine which of two real numbers is greater, express each
number as a decimal. Then compare the numbers.
Examples
Replace each ( ) with <, >, or =
to make a true sentence.
1. 4/7 ( ) 0. 5
2. 1/8 ( )
1
18
Order from least to greatest:
3.
2. 5 4 ,  16 , 9/4,
22/-9
Section 2: Factoring
4. 4a2 + 8a
Factor using the distributive property or other tricks.
5. x2 + 5x + 6
6. x2 – 8x + 12
7. x2 + 14x – 15
8. 6x2 + 7x -3
9. 4x2 + 20x + 25
10. x2 – 4
Interactive Study Guide for Students: Pre-requisite Skills for Algebra II
Section 3: Congruent and Similar Figures
Two polygons are congruent if their corresponding sides are
congruent and their corresponding angles are congruent.
In similar figures, corresponding angles are congruent, and the
measures of the corresponding sides are proportional.
Examples
1. If ∆ABC  ∆DEF, name
the corresponding sides
and angles.
2.The triangles are similar.
Find the value of x & y.
X
4
4
3
y
8
Section 4: Pythagorean Theorem
The Pythagorean Theorem states that in a right triangle, the square of
the length of the hypotenuse is equal to the sum of the square of the
lengths of the legs.
3. In a right triangle, If
a=5 inches, b=12 inches,
what is c?
So, for any right triangle, a2 + b2 = c2
4. If the lengths of a
triangle are 5, 7, and 9
meters, is the triangle a
right triangle?
Section 5: Mean, Median and Mode
Mean: the sum of the data divided by the number of items in the data
Median: arrange the data in numerical order, the median is the
middle number, or the average of the two middle numbers
Mode: the number that appears most often, if no number appears
most often, then there is no mode
5. Find the mean,
median and most of
these numbers.
(6, 3, 7, 3, 5, 8, 2, 4, 1 )
Interactive Study Guide for Students: Pre-requisite Skills for Algebra II
Section 6: Bar and Line Graphs
Examples
Graphs are a way to display data with a picture. A bar
graph compares different categories of data by
showing each as a bar whose length is related to the
frequency. A double bar graph compares two sets of
data. A line graph usually shows how data changes
over time.
Section 7: Stem and Leaf Plots
In a stem and leaf plot, data are organized in two
columns. The greatest place value of the data is used
for the stems. The next greatest place value forms the
leaves. Stem and leaf plots are useful for organizing
long lists of numbers.
Step 1: Find the least and greatest number. Identify
place values. Draw a horizontal and vertical line, label
top left “stem” and top right “leaf”.
1. Make a double bar graph to display
the data
Average Age to Marry
Year
1990
1998
Men
26
27
Women 22
25
2. Make a line graph to display the
change of Mark’s height.
Age
2
4
6
8
10
12
14
16
Height
2.8
3.5
4.0
4.6
4.9
5.2
5.8
6
3. Make a stem and leaf plot for the
data:
Step 2: Write the stems on bottom left.
Step 3: Write the leaves to the left on the bottom,
with the corresponding stem.
4.0, 3.9, 3.1, 3.9, 3.8, 3.7, 1.8, 2.6, 4.0,
3.9, 3.5, 3.3, 2.9, 2.5, 1.1, 3.5
Step 4: Rearrange the leaves so they are ordered from
least to greatest.
Step 5: Include a key or an explanation.
Interactive Study Guide for Students: Pre-requisite Skills for Algebra II
Section 8: Box and Whisker Plots
Examples
In a set of data, quartiles are values that divide the
data into four equal parts.
23 24 29 30 31
33 34 35 39 43
The amount of money spent in the
cafeteria by 20 students is shown in the
table. Display the data in a box and
whisker plot.
The median of the lower half of a set of data is the
lower quartile.
The median of the upper half of a set of data is the
upper quartile.
To make a box and whisker plot, draw a box around
the quartile values, and lines or whiskers to represent
the values in the lower fourth of the data and the
upper fourth of the data.
The interquartile range (IQR) is the range of the
middle half of the data and contains 50% of the data in
the set.
The outlier is any element of a set that is at least 1.5
interquartile ranges less than the lower quartile or
greater than the upper quartile. The whisker
representing the data is drawn from the box to the
least or greatest value that is not an outlier.
Amount Spent
$2.00
$2.00
$1.00
$4.00
$1.00
$2.50
$2.50
$2.00
$2.50
$1.00
$4.00
$2.50
$3.50
$2.00
$3.00
$2.50
$4.00
$4.00
$5.50
$1.50