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1st quarter review Test is Friday!!! Number Patterns • arithmetic patterns: – have a common difference between all terms • geometric patterns: – common ratio between all terms • think of it as: – arithmetic: we add or subtract to get the next term – geometric: we multiply or divide to get the next term Example • Give the next 5 terms in the patterns: • 2, 4, 6, 8,… • 2, 6, 18,… Another sequence… • What is the pattern? • 1, 2, 9, 16, 25, 36, … Primes & Composites • prime number: – has only two different factors, one and the number itself • composite number: – has more than two factors • the number one (1) is neither prime nor composite! Greatest Common Factor • using two or more numbers • find the prime factorization of both numbers • find what they have in common, and that is the GCF • example: 190 360 Least Common Multiple • find the GCF • then, multiply in the leftover numbers • example: 32 100 Fractions Vocabulary Review • fraction: • improper fraction: • mixed fraction: Least Common Denominator • uses the least common multiple of the denominators • Example: 5 11 15 • What is the LCD for: , , 12 24 16 Adding/Subtracting Fractions • must have common denominators • adding mixed numbers: – add fractions first – add whole numbers – reduce the fraction, if needed • subtracting mixed numbers: – subtract fractions first, borrowing if needed – subtract whole numbers – reduce the fraction, if needed Examples • Find the sum or difference: 7 5 3 2 9 9 1 3 6 4 2 10 Examples • Find the sum or difference: 1 3 9 2 5 4 Multiplying/Dividing Fractions • multiplying fractions: – multiply numerators – multiply denominators – reduce, if needed • dividing fractions: – flip the second fraction – multiply the fractions – reduce, if needed • mixed numbers: – change into improper fractions Examples • Find the product or quotient: 2 6 3 7 5 3 12 4 Vocabulary Review • Mean: • Median: • Mode: Percents • means per hundred or divided by 100 • you can change percents to a reduced fraction or a decimal • use multiplication to find the percent of a number Example • Find 5% sales tax on a CD selling for $12.95. Example • Estimate 74% of 840. Example • A sale sign says 20% off, save $30! What is the original cost of the item? Example • Margo knows that the tax on the new coat she bought was $12.60 and that the sales tax rate was 7%. What was the cost of her new coat? Multiplication Properties of Exponents • When two powers have the same base, add the exponents and keep the base x x • When finding a power of a power, multiply the exponents x • When finding the power of a product, “distribute” the power to each part of the product 3 2 3 4 x y 3 2 4 Negative & Zero Exponents • Negative exponents make the number or variable a reciprocal • Anything raised to a zero exponent is 1 b m 2 0 Division Properties of Exponents 8 • When dividing two powers with the same base, subtract the exponents x 3 x • When finding a power of a quotient, “distribute” the power to top and bottom a 2 b 3 4 Scientific Notation • Uses powers of 10 to write decimal numbers • Contains a number between 1 and 10 that is multiplied by a power of 10 Example 1 • Write expressions for the perimeter and the area of the rectangle: 3x+5 x Example 2 • Evaluate each expression if m = 4, n = -3, and t = 0: • 2m + 3(4n)3 • (5n3 – 2s7)t • 9m – 4m2 – m2 + m + 5n2 Example 3 • Write an expression for the perimeter of: n 3n n n Example 1 • Solve each equation: 1 3 x 2 3 4 5x 85 Example 3 • Solve: 3x + 5 = 6 Example 5 • Solve: x 13 4x 3 3 Perimeter • The distance around a polygon, shape, object, etc. • When you have a flat figure, add up all the sides • Circles: use the formula C = 2πr = πd Area • Area of square = (side)2 • Area of rectangle/parallelogram = base x height • Area of triangle = ½ x base x height • Area of trapezoid = ½ x height x (base + base) • Area of circle = πr2 Surface Area • Surface area is the sum of the areas of all its bases and faces • i.e. like wrapping a present Formulas • Surface Area of a Rectangular Prism SA 2lw lh wh • Surface Area of a Cylinder SA 2r 2rh 2 • Surface Area of a Cone SA rs r 2 Volume of a Prism V Bh Height Area of the base Volume of a Pyramid Height 1 V Bh 3 Area of the Base Volume of a Cylinder V r h 2 Volume of a Cone 1 2 V r h 3 Volume of a Sphere 4 3 V r 3