Jefferson Township Public Schools Mathematics Department Dear Student of Math Investigations, Your first assignment as a Math Investigations student will be the summer assignment. This packet is a review of previously taught concepts. Each topic includes a study guide and practice. Additional help could be found at http://www.khanacademy.org. Khan Academy is a free website for learning academic and real-world knowledge from tutorial videos. It is a great resource where you could find conceptual videos and worked examples from basic algebra through calculus. Follow the directions in the packet and do all of the exercises, neatly showing all of your work in the packet or on additional paper. Do your work without a calculator. Follow directions to get the best possible grade on this packet!!!! The packet will be due the second day of school. Your Math Investigations teacher will provide opportunities the first few days of class for you to ask questions. Please be aware that your work will be collected, graded and counted as a homework grade. Once the summer packet has been corrected and reviewed in class, you will be tested on the topics. The assessment will count as part of your first marking period grade. You could download/print the Math Investigations summer assignment from the school district web page at http://www.jefftwp.org/district/hssummerassignments2.shtml. Copies of the assessment can be found throughout the summer in the high school front office. If you need any further assistance, please contact Dr. Marius Petric, Supervisor of Mathematics at mpetric@jefftwp.org Have a great summer and we will see you in September!
Formulas Circle Rectangle Triangle Area = πr 2 Area = lw Area = bh 2 Circumference = 2πr Perimeter = 2(l + w) Pythagorean Theorem a 2 + b 2 = c 2 Sphere Rectangular Prism Cylinder Volume = 3 4 πr 3 Volume = lwh Volume = πr 2 h Surface Area = 4πr 2 SA = 2lw + 2wh + 2lh SA = 2πrh + 2πr 2 In any triangle, the sum of the measures of all the angles must equal 80. If the measure of each angle of the triangle ABC is expressed as an algebraic expression, where the measure of angle A is 2x + 0, the measure of angle B is 5x 30, and the measure of angle C is x + 40, what is the measure of angle B? a. 20 b. 50 c. 60 d. 70 2. Which of these equations is satisfied by the pairs of numbers in the table? x y 0 6 2 2 6 24 0 36 a. y = x + 6 b. y = 3x 6 c. y = 6 x d. y = 3x + 6 3. Spies at McGoohan Agency use code names. Each code consists of a single letter of the alphabet from A to Z, followed by a single digit from to 9. How many different code names are possible at the agency? a. 260 b. 234 c. 36 d. 35 4. What is the next term in this sequence? 2, 3.25, 4.50, 5.75,. a. 6.25 b. 6.50 c. 6.75 d. 7 5. The general partners in a small company, Miranda, Cohen, and Brown, share its profits in the ratio of: 3:2:5, respectively. If that company s profits amount to $24,300 this year, what is Mr. Miranda s hare? a. $2,430 b. $7,290 c. $8,00 d. $4,580
6. Lisa bought a skirt that rang up at $2.28. She noticed that this was a discount of 20% from the original price on the tag. What was the original price on the tag? a. $4.74 b. $5.35 c. $9.82 d. $0.28 7. A club has 25 members, 20 boys and 5 girls. Two members are selected at random to serve as president and vice president. What is the probability that both will be girls? a. 5 b. 25 c. 30 d. 4 8. Find the equation of the line containing the points (, 3) and (0, 5) a. y = 8x b. y = 8x + 5 c. y = 8x + 5 d. y = 8 x + 5 9. Mrs. Anderson had her 30 students vote for their favorite lunch as shown: Lunch Item Number of Votes Tacos 7 Pizza 9 Hot Dogs 3 Hamburgers 6 Spaghetti 5 She then told them to show the data in a circle graph. How many degrees in the central angle of the sector of that circle would represent the number of votes for pizza? a. 72 b. 84 c. 96 d. 08 0. A block of wood measures (in centimeters) 5 x 5 x 5 and weighs 24 grams. What would be the weight of a block of the same material that measures (in centimeters) 0 x 0 x 0? a. 24 grams b. 48 grams c. 72 grams d. 92 grams. Circle O is inscribed in square EFGH. The circumference of circle O is 20 centimeters. Which of the following is closest to the perimeter of square EFGH? a. 24 cm b. 25.5 cm c. 27cm d. 28.5 cm 2. Which of the following is a correct representation for the ratio of 2 ounces to 2 pounds? a. 6: b. 3:8 c. :2 d. 8:3
3. What is the probability of drawing 2 blue marbles from a bag containing 5 blue and 7 green marbles? a. 5 2 b. 2 5 c. 5 7 d. 5 33 4. What is the first term in the exponential sequence below?,,, 8, 243, 729, a. b. 3 c. 9 d. 27 5. At what point do the lines representing the equations y = x 3 and y = 2x + intersect? a. ( 4, 7) b. ( 7, 4) c. (4, 7) d. (7, 4) 6. On a 4 hour trip, Susan traveled at an average speed of 25 mph for the first hour and an average speed of 55 mph for the next three hours. What was her average speed in miles per hour for those four hours? a. 47.5 mph b. 46.5 mph c. 45.5 mph d. 42.5 mph 7. A steel rod is 4.25 feet long. If you cut the rod into 0 equal pieces, how many inches long will each piece be? a. 0.425 inches b. 4.2 inches c. 4.8 inches d. 5. inches 8. Which of the following is not a correct application of the distributive property? a a. (6 + a) = 2 + 3 3 2 3t c. (2 + 3t)( ) = + b b b b. 4(5 + x) = 20 + 4x d. (3 + 2p)(3 + 2p) = 9 + 4p 2 9. Which of the following is an irrational number? a. 3.0 b. 3.000000 c. 3.0000000. d. 3 00
20. The table indicates a linear relationship between x and y. Based on the indicated relationship, which of the numbers below is the missing number in the table? x y 6 2 8 3 0 4 2 0? a. 4 b. 20 c. 24 d. 26 2. The rectangular garden shown contains a rectangular, brick walkway. What is the probability that a seed tossed randomly into the garden will land on the walkway? a. 6 b 5 c. 4 d. 3 22. A sphere has a surface area of 256 square meters. What is the radius of the sphere? a. 0 m b. 20 m c. 00 m d. 200 m 23. During a baseball season, the National League home run champion had the following home run statistics by month: April May June July August September October 5 3 7 6 8 6 Which month contains the median for the player s home run statistics? a. June b. July c. August d. September
24. Rainbow Rent-A-Car rents cars for $2 per day plus 7 per mile. When Ed rented a car for 3 days, his cost was $46.92. Which expression could be used to find the number of miles he drove? a. 3($2.00 + $0.07m) = $46.92 b. $36.00m + $0.07 = $46.92 c. $36.00 + $0.07m = $46.92 d. $36.00 = $46.92 $0.07m 25. A rectangle has a perimeter of 34 inches and an area of 72 square inches. What are the lengths of the sides of the rectangle? a. 2 in and 36 in b. 4 in and 8 in c. 8 in and 9 in d. 0 in and 7 in 26. Lira rolls two number cubes, each with sides numbered through 6. What is the probability that the sum of the two upward faces is 5? a. 6 b. 9 c. 8 d. 36 27. In 945 a tube of toothpaste costs 37 cents. In 2000 a similar tube of toothpaste cost $2.89. What is the approximate percent of increase in the cost of the tube of toothpaste? a. 78% b. 68% c. 87% d. 5% 28. If ABC with vertices A( 2, 0), B( 2, 2), C( 4, 2) is reflected over the x-axis and then the image is reflected over the y-axis, which coordinates would represent the final image of point A? a. ( 2, 0) b. (2, 0) c. (0, 2) d. (0, 2) 29. A basketball player makes 3 out of every 5 of her foul shots. At this rate, if she attempts 55 foul shots, how many will she miss? a. 50 b. 40 c. 33 d. 22 30. A rectangle has dimensions 5 cm by 2 cm. How many centimeters long is a diagonal of the rectangle? a. 2 b. 3 c. 7 d. 30 3. The price of a pair of sneakers was reduced 20%. The amount by which the price was reduced was $2. What was the original price of the sneakers? a. $36 b. $48 c. $60 d. $72
32. Suppose this pattern was continued: A BA BBA BBBA AB BAB BBAB ABB BABB ABBB How many B s will be in the 20 th diagram? a. 20 b. 60 c. 360 d. 380 33. Arrange the three figures in increasing order of area. I. a rectangle with dimensions of 6 inches by 8 inches II. a square with a side of 7 inches III. a right triangle with sides of 5 inches, 2 inches, and 3 inches a. rectangle, square, triangle b. rectangle, triangle, square c. triangle, rectangle, square d. square, rectangle, triangle 34. A catalog advertises a sweater available in the following styles, sizes and colors: Style Size Color Long Sleeve S Black Sleeveless M Navy L XL How many variations of this sweater are there? Red White Green a. b. 20 c. 40 d. 60 35. Which of the following equals 0.0503? a. 5.03 x 0 2 b. 5.03 x0 c. 5.03 x 0-2 d. 5.03 x 0-3 36. Which of the following would represent the area of a rectangle with length = 5p + 8 and width =? a. 55p + 8. b. 5p + 98 c. 55p + 98 d. 0p + 58
. Jacy, a busy college student who has two part-time jobs, wants to buy a cell phone. She considers the following two plans: Plan A Plan B $20 per month + $26 per month + 2 cents per minute 8 cents per minute Based on this information, what is the cost of 30 minutes of phone calls under each plan? Write an expression to represent the monthly cost for Plan A. Write an expression to represent the monthly cost for plan B. What length phone call will cost the same under plan A and Plan B? What is that cost? Show your work.
2. A carpenter cuts a solid block of wood in the form of rectangular prism with dimensions 2 inches by 4 inches by 8 inches. What is the volume, in cubic inches, of the block of wood? Show your work. If the carpenter reduced each dimension of the block by 50%, what would the volume of the resulting block be? State your answer in cubic inches. Show your work. Calculate the ratio of the volume of the original block to the volume of the block created by reducing each dimension by 50%. Show your work
3. A baseball players batting average is the ratio of the number of times he gets a hit to the total number of times he gets a hit to the total number of times at bat. If the baseball player has a.220 batting average after 500 at bats, how many hits did the player have? After the next 40 at bats, the players average increased to.225. How many more hits did the player get? How many consecutive hits would the player then need to get to increase his average from.225 to.228?
4. On this semester s math quizzes, Jeff earned scores of 79, 82, 52, 83, 85, 89, 82, 88. Which score is an outlier of Jeff s quiz performance? Why? Find the mean and the median of Jeff s quiz scores. Show your work and label your answers. Remove the outlier and find the mean and median of his remaining quiz scores. Show your work and label your answers. Is the mean or median more affected by the outlier score? Explain.