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Math 9A: Quick Reminders Rational Numbers Adding and Subtracting fractions Example 2 1 + 5 2 2 2 5 1 = ( )( ) + ( )( ) 2 5 5 2 4 5 = + 10 10 9 = 10 Multiplying fractions You need a common denominator. Your Turn a) 4 2 (− ) + 7 3 b) 5 2 − (− ) 4 11 Multiply numerators and multiply denominators. 5 Example 3 × (− ) 7 12 15 =− 84 5 =− 28 Your Turn a) 3 1 ( ) (− ) 8 6 b) 1 1 2 × (−3 ) 3 4 Dividing fractions Keep the first fraction the same, change the division to multiplication, and take the reciprocal of the second fraction. Example 4 5 ) ÷ (− ) 11 3 4 3 = (− ) × (− ) 11 5 12 = 55 (− Your Turn a) 3 1 ÷ (− ) 10 4 b) 1 1 5 ÷( ) 2 3 Order of Operations Brackets, Exponents, Division/Multiplication (working left to right), Addition/Subtraction (again, working left to right). BEDMAS. 2 Example 1 4 − × (− ) 3 7 3 7 1 8 = ( )( ) − 7 3 21 7 8 = − 21 21 1 =− 21 Your Turn a) b) c) 3 1 3 − (− ) ÷ 4 2 7 3 4 1 ( − ) 5 9 6 1 5 1 2 +4 − 3 6 2 Math 9A: Quick Reminders Square Roots Perfect Squares You need to memorize this! Practice by writing them all down on a piece of paper to see how many you remember. You must know all perfect squares from 1 to 400. Estimating Perfect Squares squares. Identify perfect square benchmarks, estimate non-perfect Your Turn Estimate. Example Estimate the value of √0.3. 0.3 = 0.30 Benchmarks are 0.25 and 0.36 √0.25 = 0.5 and √0.36 = 0.6 √0.30 ≅ 0.55 a) √0.75 b) √1.2 c) √80 d) √2 e) √17 Pythagorean Theorem In a right triangle, 𝑎2 + 𝑏 2 = 𝑐 2 , where 𝑐 is the hypothenuse. Example Determine the missing value. 𝑏 2 + 122 = 152 𝑏 2 = 152 − 122 𝑏 2 = 225 − 144 𝑏 2 = 81 𝑏 = √81 𝑏 = 9 cm Your Turn Calculate the missing value. a) « b) Math 9A: Quick Reminders Composite Shapes Example Surface Area Remember to subtract the overlap. Don’t forget units. Calculate total surface area. Your Turn Calculate total surface area. The prism 2(𝑏ℎ + 𝑏𝑤 + ℎ𝑤) = 2(8 × 5 + 8 × 5 + 5 × 5) = 2(40 + 40 + 25) = 2(105) = 210 cm2 a) The cylinder 2𝜋𝑟ℎ = 2𝜋(2)(4) = 50.27 𝑐𝑚2 Total surface area 210 + 50.27 = 260.27 cm2 b) Math 9A: Quick Reminders Statistics Definitions Make sure you can define the vocabulary terms in this unit. (See textbook page 423 for a list). Bias Make sure you can identify the different forms of bias in a survey question (See textbook page 432 for a helpful chart). Histograms Make sure you can create and interpret a histogram. Math 9A: Quick Reminders Symmetry Lines of Reflection Make sure you can identify lines of reflection in an image. Rotational Symmetry Make sure you can identify the order of rotation and the angle of rotation in an image. Math 9A: Quick Reminders Scale Factor Similarity When calculating scale factor, the original is the denominator. Your Turn Determine the scale factor of the reduction. Example Calculating scale factor. A 4- inch-by-6-inch picture is enlarged to measure 24 inches by 36 inches. What is the scale factor of the enlargement? The smaller picture is the original. 24 =6 4 The scale factor is 6. Example Calculating a missing side. Your Turn Determine what is asked. A couch is 6 feet long. If John created a replica for his dollhouse using a scale factor of 0.02, what is the length of the scale couch? a) One car of a train is 85 feet long. A model train is created, using a scale of 1:22. What is the length of the model train? (Original Measurement) x (Scale factor) = Scale measurement b) Barbie is 11.5 inches tall. If the scale factor used is 1/12, calculate Barbie’s height if she were a real person. (6)(0.02) = 0.12 The length of the couch in the dollhouse is 0.12 feet. Similar Triangles Calculate the missing side with similar triangles. Example Determine the value of x. Your Turn Determine the missing side. a) 𝑥 16 = 21 24 𝑥= 16 × 21 24 𝑥 = 14 b) Math 9A: Quick Reminders Circle Geometry Vocabulary Things you need to know: In the diagram to the right: - The radius is OB - (Diameter is twice the radius) - A point of tangency is B - A tangent line is AC - A chord is DE Notes In the following diagram: Your Turn Calculate the size of angle POQ. Angle A is an inscribed angle. Angle B is a central angle. Angle B is twice Angle A. Notes Using the following diagram: The angle between a radius and a tangent is always 90°. Your Turn Use the Pythagorean Theorem to find the missing side.