Unit 1 Review Part 1 3 combined Handout KEY.notebook. September 26, 2013


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1 Math 10c Unit 1 Factors, Powers and Radicals Key Concepts 1.1 Determine the prime factors of a whole number 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) 1.3 Determine, using a variety of strategies, the greatest common factor or least common multiple of a set of whole numbers, and explain the process. Find the GCF (answer is a smaller # than your original #s) Find the LCM (answer is a bigger # than your original #s)
2 1.1 Determine, concretely, whether a given whole number is a perfect square, a perfect cube or neither. 1.2 Determine, using a variety of strategies, the square root of a perfect square, and explain the process. (Hint: USE PRIME FACTORIZATION) 1.3 Determine, using a variety of strategies, the cube root of a perfect cube, and explain the process. (Hint: USE PRIME FACTORIZATION) Solve problems that involve prime factors, greatest common factors, least common multiples, square roots or cube roots 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? 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 =2x3 2 =2 3 x3 LCM = 2 3 x3 2 = 72 The smallest square that could be tiled would have a side length of 72 cm. 2
3 2.1 Sort a set of numbers into rational and irrational numbers. Identify as Relational or Irrational a) b) c) d) a) Rational b) Rational c) Rational d) Irrational (nonrepeating and nonterminating) 2.2 Determine an approximate value of a given irrational number. (Estimate without calculator) a) b) c) = 4.1 =4.45 = 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) b) c) d) e) f) 2.5 Express a radical as a mixed radical in simplest form (limited to numerical radicands). = a) b) c) 4 d) 3
4 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. 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). 4
5 3.1 Explain, using patterns, why a n = 1/a n, a 0 / 3.2 Explain, using patterns, why a 1/n = n, n> = 10 2 = 10 1 = 10 0 = 10 1 = 10 2 = /10 1/100 a 3 = a 3 a 2 = a 2 a 1 = a a 0 = 1 a 1 = 1/a 1 a 2 = 1/a 2 a 3 = 1/a Apply the exponent laws to expressions with rational and variable bases and integral and rational exponents, and explain the reasoning: (a m )(a n ) = a m+n x 8 2 x 8 4 x 8 7 = 12x 9 = y 4 = 8 2 = 64 a m a n = a m n, a = 8y 9 = x 4 z 6 (a m ) n = a mn 1. = 4 15 (ab) m = a m b m = c 4 d 4 = 3 4 c 4 d 8 = 81d 8 c 4 (a/b) n = a n /b n, b 0 1. = y 6 z 9 5
6 3.4 Express powers with rational exponents as radicals and vice versa. = or = 3.5 Solve a problem that involves exponent laws or radicals. A square has an area of 1134 m 2. 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 = s = s 2 s = simplify 1134 s = = 9 14 P = 4(9 14) = The perimeter is m. 3.6 Identify and correct errors in a simplification of an expression that involves powers did not flip the equation to the reciprocal and incorrectly put a negative base forgot index 3 6
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