Scarsdale Middle School Popham House Mr. Weiss

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1 Scarsdale Middle School Popham House Mr. Weiss Final Exam Review Packet 1) Find the area of the triangle formed from the intersections of the lines: y = 3 2 x + 5, y x = 5 and y = 1. 2) ( 8, k) is on the line whose equation is y = 3 4 x + 5. Find k. 3) What is the slope of the line that passes through the points ( 5, 4) and (3, 2)? 5) Write the equation, in slope-intercept form, of the line that passes through the points ( 1, 9) and (7, 3) 6) Write the equation, in slope-intercept form, of the line parallel to the line whose equation is 6x 2y = 12 and passes through the point ( 1, 6).

2 8) 2 3 9) ) ( 4) 3 11) ) ) ( 3 4 )3 14) ( 2 5 ) 2 15) x 5 + x 5 + x 5 16) ( 5y 2 )(4y 3 ) 17) (5m)(4m 5 ) + (6m 2 )(2m 4 ) 18) (w 5 ) 4 19) ( 3q 3 ) 4 20) ( 5df 4 ) 3 21) " 1 3 a 3 b 7 % # $ & ' 3 22) 2 3 x 2 y 7 23) ( 4x) 2 + 4x 2 24) 15x 7 3x 9 25) 18mn5 p 12mn 2 p 26)! 2a 5 b $ # & 8 " 4a 2 b 5 % 3 27) (2x4 ) 3 (3x 2 ) (5x)(4x 7 ) 28) 8x0 y z 3 29) ( 5 3 ) 6 (5 4 )(5 24 ) 30) Write in scientific notation: Perform the indicated operation. Express your answer in scientific notation: 31) (6.7 x 10 8 )(4.5 x 10 3 ) 32) Solve for x:

3 59) What is the additive inverse of 3? 60) What is the additive inverse of x + 9? 61) What is the multiplicative inverse of 3? 62) What is the multiplicative inverse of 2.8? 63) Solve and graph: 3x + 6 > 12 or 5x ) Graph: 14 x 9 65) Solve: 2x + 7 = 9 67) Two sides of a triangle are 5 cm and 8 cm. Write as a double inequality, all possible third side lengths ) In each, find x. 68) 69) 70)

4 71-77) Given the 115º angle, find all other angles. 78) Angle A measures 36º less than three times the measure of angle B. The angles are supplementary. Find the measure of each angle. 79) The sum of an angle and four times its supplement is equal to 420º more than twice its complement. Find the angle. 80) What is the measure of each angle of a regular 20-sided polygon? Always, Sometimes or Never? 81) The diagonals of a parallelogram are congruent. 82) The diagonals of a parallelogram are perpendicular. True or False? 83) If a quadrilateral is a rectangle then it is a parallelogram. 84) If a quadrilateral is a parallelogram then it is a rhombus. (85-88) Find each numbered angle. 85) 86) 87) 88)

5 108) ) ) x 8 111) 25x ) ) ) ) The ratio of the sides of a triangle is 2:5:6. Its perimeter is 39 cm. What is the length of each side? 135) Two numbers are in a ratio of 5:3. If each of the numbers is reduced by 7, the numbers will be in a ratio of 2:1. What are the original numbers? 136) A 1.75-meter tall women has a height of 7 cm in a photograph. Her son is 5 cm tall in the photograph. What is his actual height? 137) How much money would have to be invested at a 5.5% annual rate to earn a one-year return of $220? 138) After receiving an 18% raise, Jim now earns $53,100. What was his salary before the raise? 139) An item is placed on sale. The price is reduced from $120 to $96. By what percent is the item reduced? 140) 42% of the 5000 students at a University are women. How many men attend the University? 141) How many ml of a 10% solution of acid should be mixed with a 60% solution to produce 150 ml of a 30% solution?

6 142) An investor purchased $10,000 in stock. He earned 5% for his ABC Corp. investment and 10% for his XYZ Corp. investment. He earned a total of $800. How much money did he invest at each rate? 143) James invested $12,000. Part of the investment earned 12% and the rest earned 6%. If the entire investment earned 9%, how much money was invested at each rate? 144) A family flew 2400 miles to California at an average rate of 400 mph. They returned by plane at an average speed of 600 miles per hour. What was their average rate for the entire trip? 145) Albany and NYC are 150 miles apart. One car left Albany for NYC averaging 40 mph. At the same time, another car left NYC for Albany, averaging 35 mph. How far from Albany did the cars pass each other? 146) Two planes started at the same time from the same airport and flew in opposite directions. One flew 60 miles per hour faster than the other. In 5 hours they were 2800 miles apart. Find the rate of each plane. 147) A salesman made a trip of 375 miles by bus and by train. He traveled 3 hours by bus and 4 hours by train. If the train averaged 15 mph more than the bus, find the rate of each. 148) A train traveled 240 miles. If it increased its average speed by 20 mph, it would have traveled 300 miles in the same amount of time. Find each speed. 149) How much simple interest would be earned on an investment of $4,000 at an annual rate of 5 1 8% for 66 months? 150) ΔABC ~ ΔDEF. Solve for x. 151) The scale of map reads 4 cm = 15 miles. What is the actual distance represented by 10 cm on the map?

7 152) The ratio of the corresponding sides of two polygons is 5:12. What is the ratio of their areas? 153) A 26-foot ladder is leaning against a building with the top of the ladder touching the exact top of the building. The bottom of the ladder is 10 feet from the base of the building. How tall is the building? 154) If a man hikes 9 miles west and then 40 miles north, how far will he be from his starting point? 155) Find the area of a square with diagonal equal to ) A man standing on the ground 70 feet away from a tree looks at the top of the tree at an angle of elevation of 55º. What is the height of the tree? 157) A man stands 403 feet away from The Washington Monument and views the top at an angle of elevation of 54º. What is the height of The Washington Monument? (round to the nearest whole number) 158) Use the triangle below. What is Cos A? 159) Use the triangle below. What is Sin A?

8 ( ) Find the area of each polygon: 160) 12 cm 161) 3 cm 12 cm 162) 18.5 cm 163) 2 cm 6 cm 8.5 cm 8 cm 3 cm 10 cm 164) Find the perimeter. Use π = 22/7 165) Find the area. Leave in terms of π. 28 cm 20 cm 14 cm 26 cm

9 68 cm ( ) Find the area of the shaded region: 166) Use π = ) Leave answer in terms of π. 40 cm 32 cm 30 cm30 cm 168) The circumference of a circle is 132 cm. What is the area of the circle? Use π = 22/7. 169) The cost of hardwood flooring is $3.75 per square foot. What is the cost of the hardwood flooring needed to cover a conference room 30 yards long and 24 yards wide? 170) The area of a trapezoid is 120 in 2. The height of the trapezoid is 12 inches and one of the bases is 7 inches. What is the length of the other base? 171) The circumference of a circle is 18π cm. What is the area of the circle? Leave your answer in terms of π. 172) When a wheel makes one revolution, it travels a distance equal to its circumference. A car has a tire diameter of 35 inches. How many feet will this car travel if its tires make 240 revolutions? Use π = 22/7 173) The area of a circle is 50π cm 2. What is the circumference of the circle? Leave your answer in simplest radical form and in terms of π

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