Download Unit 1 Review - Part 1-3 combined Handout

Unit 1 Review ­ Part 1­3 combined Handout KEY.notebook
September 26, 2013
Math 10c – Unit 1 Factors, Powers and Radicals – Key Concepts
1.1
Ex. 1.2
Determine the prime factors of a whole number. 650
Ex. 3910
Explain why the numbers 0 and 1 have no prime factors.
0 and 1 have no prime factors because there are no prime numbers small enough to fit
in them. Prime numbers have only two factors- 1 and itself. ZERO is not a prime
number because it has infinite factors (e.g. 0x1 = 0, 0x2 = 0, 0x3= 0, etc.). ONE is not
prime because it has only 1 factor: 1 (e.g. 1x1 = 1)
Determine, using a variety of strategies, the greatest common factor or least common multiple of a set of whole numbers, and 1.3
explain the process. Ex. Find the GCF (answer is a smaller # than your original #s)
204
48
Ex. Find the LCM (answer is a bigger # than your original #s)
27
4
32
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Unit 1 Review ­ Part 1­3 combined Handout KEY.notebook
September 26, 2013
Determine, concretely, whether a given whole number is a perfect square, a perfect cube or neither.
1.1
Determine, using a variety of strategies, the square root of a perfect square, and explain the process. (Hint: USE PRIME 1.2
FACTORIZATION)
Determine, using a variety of strategies, the cube root of a perfect cube, and explain the process. 1.3
(Hint: USE PRIME FACTORIZATION)
Ex. 625
Ex.
444
Ex. 64
1.7 Solve problems that involve prime factors, greatest common factors, least common multiples, square roots or cube roots
Ex. A farmer has a rectangular plot of land measuring 400 m by 640 m. He wants to subdivide this land into congruent square pieces. What is the side length of the largest possible square? Ex. What are the dimensions of the smallest square that could be tiled using 18‐cm by 24‐cm tile? Assume the tiles cannot be cut.
The largest possible
side length the square
could have is 80 m.
18
9 2
3 3 24
=2x32
6
3 2
4
2 2
=23x3
LCM = 23x32 = 72
The smallest square that could be tiled would have a side length of 72 cm.
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Unit 1 Review ­ Part 1­3 combined Handout KEY.notebook
September 26, 2013
2.1 Sort a set of numbers into rational and irrational numbers. Ex. Identify as Relational or Irrational
b) 0.234234234… c) a) 0.23223222322223222223…
a) Rational
c) Rational
b) Rational
d) d) Irrational (non-repeating and non-terminating)
2.2 Determine an approximate value of a given irrational number. (Estimate without calculator)
a)
b) c) = 10.2
=4.45
= 4.1
2.3 Approximate the locations of irrational numbers on a number line, using a variety of strategies, and explain the reasoning.
2.4 Order a set of irrational numbers on a number line. a) f) b) c) d) e) 2.5 Express a radical as a mixed radical in simplest form (limited to numerical radicands). a) b) c) 4
d) =
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Unit 1 Review ­ Part 1­3 combined Handout KEY.notebook
September 26, 2013
2.6 Express a mixed radical as an entire radical (limited to numerical radicands)
a) b) c) d) 2.7 Explain, using examples, the meaning of the index of a radical. Ex. In this example, 3 is the index.
This means it is a cubed root.
In other words, if this root was multiplied to itself
three times, you would get the radicand.
2.8 Represent, using a graphic organizer, the relationship among the subsets of the real numbers (natural, whole, integer, rational, irrational).
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Unit 1 Review ­ Part 1­3 combined Handout KEY.notebook
September 26, 2013
3.1 Explain, using patterns, why a‐n= 1/an, a≠0 / 3.2 Explain, using patterns, why a1/n = n
, n>0
Ex. Ex.
103 =
102 = 101 =
100 =
10­1 =
10­2 =
1000
100
10
1
1/10
1/100
a3 = a 3
a2 = a 2
a1 = a
a0 = 1
a-1 = 1/a1
a-2 = 1/a2
a-3 = 1/a3
3.3 Apply the exponent laws to expressions with rational and variable bases and integral and rational exponents, and explain the reasoning:
m+n
n
m
• (a )(a ) = a 1. 3. 8­3 x 82 x 8­4 x 87
2.
= 12x9
m
• a ÷ an = am­n, a≠0 1. = 82 = 64
= y4
2. = 8y9
= x4
z6
mn
m n
• (a ) = a 1. = 415
• (ab)m = ambm 1. 2. = c4d4
= 34c-4d8
= 81d8
c4
• (a/b)n = an/bn, b≠0 1. = y6
z9
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Unit 1 Review ­ Part 1­3 combined Handout KEY.notebook
September 26, 2013
3.4 Express powers with rational exponents as radicals and vice versa. Ex. = or Ex. =
3.5 Solve a problem that involves exponent laws or radicals. Ex. A square has an area of 1134 m2. Determine the perimeter of the square. Write the answer as a radical in simplest form.
P = s+s+s+s
or P = 4s
A = s * s
or A = s2
1134 = s2
simplify
s = √1134
s = √81√14 = 9√14
P = 4(9√14) = 36√14
The perimeter is 36√14 m.
3.6 Identify and correct errors in a simplification of an expression that involves powers
Ex.
did not flip the equation to the reciprocal and
incorrectly put a negative base
forgot index 3
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