Download Ch. 1 Review Study Guide

Name _________________________________ Period ___________ Date _________________
Ch. 1 Review Guide
Reteaching 1-­‐‑1 Rational Numbers A fraction is in simplest form when the greatest common factor (GCF) of the numerator and
denominator is 1.
24
Example 1: Write
in simplest form.
36
Use prime factorization and circle the common factors.
24 = 2 · ·2
36 = 2 · ·2
So,
· 32·
· 33·
24 2
=
36 3
To write a fraction as a decimal:
(1) Divide numerator by decimal:
(2) Divide until the remainder is 0 or until the remainder repeats.
(3) Use a bar to show digits repeating.
Example 2: Write
5
as a decimal
6
0.833
6 5.000
−48
20
−18
è So
5
= 0.833..., or 0.833.
6
20
−18
2 ← Remainder repeats.
To write a decimal as a fraction:
Example 3: Write 0.375 as a fraction.
0.375
(1) Write as a fraction 0.375 =
with the denominator 1.
1
375
(2) Since there are 3 digits =
to the right of the decimal point, multiply the numerator
1000
and the denominator by 1,000.
375÷125
(3) Divide the numerator =
and denominator by the GCF
1000 ÷125
3
3
(4) Simplify. =
è So 0.375 = .
8
8
Name _________________________________ Period ___________ Date _________________
Ch. 1 Review Guide
Reteaching 1-­‐‑2 Irrational Numbers and Square Roots • The square of 5 is 25. 5 · 5 = 52 = 25
• The square root of 25 is 5 because 52 = 25.
25 = 5
12 = 1 !
#
22 = 4 #
#
32 = 9 " perfect squares
#
42 = 16#
52 = 25#$
62 = 36 !
#
72 = 49 #
#
82 = 64 " perfect squares
#
92 = 81 #
102 = 100#$
Example: You can use a calculator to find square roots. Find
tenth.
36
=6
21
36 and
21 to the nearest
≈ 4.5825757 ≈ 4.6
You can estimate square roots like
49 = 7
52 ≈ 7
64 = 8
112 = 121 !
#
122 = 144#
#
132 = 169 " perfect squares
#
142 = 196#
152 = 225#$
52 and
61 .
49 = 7
Estimate
61 ≈ 8
64 = 8
Remember to look and see what two perfect squares the square must fall between. Which
number is it closer to? Multiply a number by itself and repeat until you find something that
gets close to the number you want.
Name _________________________________ Period ___________ Date _________________
Ch. 1 Review Guide
Reteaching 1-­‐‑3 The cube of 1 is 1.
1×1×1 = 13 = 1
The cube of 3 is 27.
3× 3× 3 = 33 = 27
perfect cubes
!#####
#"######
$
3
3
3
3
1 = 1 2 = 8 3 = 27 4 = 64
x3 =
3
=
3
3
27
216
x=
Cube Roots The cube of 5 is 125.
5× 5× 5 = 53 = 125
perfect cubes
!########"########
$
3
3
3
3
5 = 125
6 = 216 7 = 343 8 = 512
Example: You can solve cube root equations x3 =
3
27
.
216
27
← Find the cube root of each side.
216
←
Find the cube root of the numerator and denominator.
3 1
= ← Simplify.
6 2
Name _________________________________ Period ___________ Date _________________
Ch. 1 Review Guide
Reteaching 1-­‐‑4 The Pythagorean Theorem
The sum of the squares of the lengths of the
legs of a right triangle is equal to the square of
the length of the hypotenuse.
Example 1: Find the length of the
hypotenuse.
a 2 + b2 = c 2
32 + 42 = c 2
9 +16 = c 2
25 = c 2
25 = c 2
5= c
The length, c, of the hypotenuse is 5 cm.
The Pythagorean Theorem Name _________________________________ Period ___________ Date _________________
Ch. 1 Review Guide
Reteaching 1-­‐‑5 Using the Pythagorean Theorem You can use the Pythagorean Theorem to find the length of a leg in a right triangle.
Example: Find the length of the unknown
side.
a 2 + b2 = c 2
62 + b2 = 102
36 + b2 = 100
b2 = 100 − 36
b2 = 64
b=8
The length b of the unknown leg is 8 cm.
Name _________________________________ Period ___________ Date _________________
Ch. 1 Review Guide
Reteaching 1-­‐‑6 Converse of the Pythagorean Theorem You can use the Pythagorean Theorem to determine whether a triangle is a right triangle.
?
a 2 + b2 = c 2 ←
Use the Pythagorean Theorem.
?
32 + 42 = 52 ← Substitute 3 for a, 4 for b, and 5 for c.
?
9 +16= 25 ←
Simplify.
25 = 25 ✓
The equation is true, so the triangle is a right triangle.
You can use the Triangle Inequality to determine whether given lengths can make a
triangle.
Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater
than the length of the third side.
Name _________________________________ Period ___________ Date _________________
Ch. 1 Review Guide
Reteaching 1-­‐‑7 Distance in the Coordinate Plane You can graph a point on a coordinate plane. Use an ordered pair (x, y) to record the
coordinates. The first number in the pair is the x-coordinate (left/right on the x – axis). The
second number is the y-coordinate (up/down on the y – axis).
To graph a point, start at the origin, O. Move horizontally according to the value of x. Move
vertically according to the value of y.
Example 1: (4, – 2)
Example 2: (– 3,2)
Start at O, move right 4, then down 2.
Start at O, move left 3, then up 2.
**To find the distance between two coordinates you have to find the horizontal distance
and the vertical distance. To find the horizontal distance, subtract the two x – coordinates
from the ordered pairs. Next, in order to find the vertical distance, subtract the two y –
coordinates from the ordered pairs.
Once you have the vertical & horizontal distances, you can make a right triangle between
the coordinates; of which the hypotenuse is the shortest, straight-line distance between the
two coordinates. You can then use the Pythagorean theorem to find the distance between
the two points.