ALGEBRA I AND GEOMETRY SUMMER ASSIGNMENT

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1 NAME: This packet has been designed to help you review various mathematical topics that are necessary for your success in Algebra I and/or Geometry next year, as well as PSAT/SAT/ACT. Complete all problems and show your work! It will be collected for a grade by your Algebra I/Geometry teacher the first week of school, August 20 24, There are examples within most of the sections. TOPIC 1: Evaluating Expressions and Equations Example 1 Example 2 Example 3 Find the value of the expression Find the value of the expression Find the area of a circle whose 4xy + 2y 2 when x = 3 and y = 5 94x radius is 4 inches. when x = 2 and y = 3 2x:5y A = πr 2 4(3)( 5) + 2( 5) 4 = (25) 4( 2) 2( 2) + 5(3) A = π(4) 4 = A = π(16) = 16π = = A = in 2 = 8 11 Evaluate each expression when x = 5 and y = 4. Show your work! Note: you should use the π button on your calculator to get the most accurate answer 1. 8xy 2. x 4 y x 4 2xy 4. 9x 4 IJ y 4y 5. KL:MJL 6. J9L NJL Evaluate the following formulas given the variable values. 7. P = 2w + 2l; w = 15, l = A = πr 2 ; r = 6 9. S = 2πrh; r = 3, h = V = πr 2 h; r = 5, h = V = 1 3 πr2 h; r = 3, h = A = 1 2 h(b 1 + b 2 ); h = 4.5, b^ = 7, b 4 = 8

2 TOPIC 2: Solving Linear Equations ALGEBRA I AND GEOMETRY SUMMER ASSIGNMENT Example 1 Example 2 Example 3 Solve for the variable: Solve for the variable: Solve for the variable: 7x 9 = add 9 to both sides 7x = divide by 7 on both sides x = 4 8g + 11 = 6g g -6g move lower variable 2g + 11 = subtract 11 from both sides 2g = 20 g = 10 divide by 2 on both sides 2(5 + 3x) = 4( 10 x) x = 40 4x distribute + 4x + 4x move lower variable x = subtract 10 from both sides 10x = 50 x = 5 divide by 5 on both sides Solve the following equations for the variable. 1. 5x + 1 = x 4 = x = x 4. 6x + 7 = 8x g + 20 = 7g b 6.5 = 2.3 b (x 3) = 4 8. K y 1 = ^ y (a + 2) 4 = (4 + 9x) = 7( 2 11x) 11. 4(2c 8) = ^ (49c + 70) e 12. If the length of a rectangle is three times its width and its perimeter is 24cm, what is its area?

3 TOPIC 3: Pythagorean Theorem: If the lengths of the legs of a right triangle are a and b, and the length of the hypotenuse (side opposite from the right angle) is c, then a 2 + b 2 = c 2. a 2 + b 2 = c 2 Note: Legs a and b are interchangeable, but c MUST be the hypotenuse x Example 1 Example 2 Example 3 A 13-foot ladder leans against a wall, with its base 5 feet away from the wall. How high up on the wall does the ladder reach? a 4 + b 4 = c 4 Pythagorean Theorem = x 4 Substitute = x 4 Multiply 113 = x 4 Add x = Take the square root a 4 + b 4 = c 4 x = 12 4 x = 144 x 4 = 63 x = Pythagorean Theorem Substitute Multiply Subtract 81 from both Take the square root a 4 + b 4 = c 4 x = 13 4 x = 169 x 4 = 144 x = 12 feet Solve for the missing side. Round all decimals to the nearest hundredth *.

4 For #7-8, draw a diagram modeling the scenario and solve. Round all decimals to the nearest tenth. 7. A 15-foot ladder is leaning against a tree. If the ladder reaches 10 feet high on the tree, how far is the base of the ladder from the tree? 8. Maria leaves her house and walks north for 6 blocks. She then turns and walks directly east for 8 more blocks until she reaches Natalie s house. What is the shortest distance between Maria s house and Natalie s house? 9. A skateboard ramp covers a horizontal distance of 17 feet and raises to 4 feet above the ground. What is the length of the skateboard ramp? TOPIC 4: Distance Formula: The distance formula is derived from the Pythagorean Theorem. To find the distance between two points (x^, y^)and (x 4, y 4 ), use the coordinates of the ordered pairs and apply the formula: d = l(x 2 x 1 ) 2 + (y 2 y 1 ) 2 Example 1 Example 2 Determine if the triangle below is isosceles (two sides with the same length). This triangle is not isosceles since all three sides are different lengths Find the distance between the given points. Round all decimals to the nearest hundredth. 1. (4, 8) and (6, 12) 2. (10, 7) and ( 3, 1) 3. (3, 8) and ( 5, 0)

5 4. (4, 5) and ( 6, 1) 5. (2, 4) and (6, 7) 6. (0, 12) and ( 4, 9) 7. Use the distance formula in order to classify the triangle below as equilateral (all sides the same length), isosceles (two sides the same length) or scalene (all sides different lengths). 8. Use the map below to find the flying distance in blocks between the two landmarks. For #9-12, determine if the quantity in Column A or Column B is larger, or if they are the same

6 TOPIC 5: SAT PREP (It is never too early to practice for the SAT!) SHOW YOUR WORK FOR EACH PROBLEM Questions 5 and 6 refer to the following information 5. 6.