TCAP MATH PLAYBOOK 7th Grade

Notes about TCAP TCAP is the state mandated test. It will cover all subjects and will be multiple choice. It will be given April TCAP will count 25% of your second semester average. The grades will be shown on your final report card.

Helpful Tips Get a good night sleep and eat a healthy breakfast. Your brain works better when it is well rested. Take your time and completely read each question. Make sure you know exactly what the question is asking *don’t just assume! Highlight/ underline important parts in the question. Work out the problems. You can write in the book- so do it! DO YOUR BEST AND ROCK THE TEST!

Day 1: Bell Work 1) A jar contains 7 green, 19 black, and 13 pink marbles. A marble is drawn at random.P(not pink). 2) You flip a coin and toss a 1-6 number cube.P(heads and 2)

Day 2: Bell Work The heights, in inches, of the five starting players on a baseketball team are listed below. 73, 79, 76, 74, 73 What is the mean of this data set? F 73 inchesG 74 inches H 75 inchesJ 76 inches

Day 3: Bell Work Hector’s art teacher is giving prizes to the 10 students who worked on a mural for the school. The teacher will write the name of one prize on each of 10 slips of paper, as shown below. - She will write “set of markers” on 4 slips of paper - She will write “set of colored pencils” on 3 slips of paper - She will write “drawing paper” on 2 slips of paper - She will write “set of watercolor paints” on 1 slip of paper The teacher will then randomly select one of the slips of paper, and Hector will win the prize that is written on the slip of paper. What is the probability that Hector will win a set of markers or a set of colored pencils? A 1/5B 3/7 C 1/2 D 7/10

Day 4: Bell Work A small rectangular prism is 4 inches long. A large rectangular prism is 24 inches long. These two prisms are similar. Which statement is true? a. The volume of the large rectangular prism is 6 times the volume of the small one. b. The volume of the large rectangular prism is 20 times the volume of the small one. c. The volume of the large rectangular prism is 36 times the volume of the small one. d. The volume of the large rectangular prism is 216 times the volume of the small one.

Day 5: Bell Work Jamie has two cartons. The dimensions of the smaller carton are one-third the size of the larger carton. If the volume of the smaller carton is 120 cm3, find the volume of the larger carton. a. 40 cm3 b. 3,240 cm3 c. 1,080 cm3 d. 360 cm3

Day 1: Data Analysis, Statistics and Probability Part 1: Calculate and interpret mean, median, mode, upper-quartile, lower- quartile, and interquartile range of a data set

Vocabulary Mean- average of the numbers (divide the sum by the amount of numbers added) Median- number in the middle *****list least to greatest! Mode- number used most often ****there can be more than one or none at all Range- difference of the whole data set (largest # - smallest #= range) Upper-Quartile- median of the upper set of numbers Lower-Quartile- median of the lower set of numbers Interquartile range- difference of the quartiles (upper- quartile – lower-quartile = interquartile range)

1) The test scores of several students are listed below. 2, 27, 6, 29, 22, 6, 11, 8, 30, 6, 25, 19 Which box-and-whisker plot accurately represents this data? **What steps do we need to follow to make the plot! ** List the 5 parts –Lower extreme –Lower quartile –Median –Upper quartile –Upper Extreme

2) What is the upper quartile of the numbers listed below? 6, 47, 54, 15, 42, 41, 7, 39, 36, 41, 43 F 28G 41H 43J 48 3) What is the mean of the numbers listed below? 18, 2, 29, 33, 67, 89, 5, 13, 56, 44 F 31G 35.6H 38.2J 42 4) What is the inter-quartile range of the numbers listed below? 21, 10, 96, 74, 32, 8, 47, 59, 83, 65, 16 F 96G 88H 58J 47 5) What is the median of the numbers listed below? 1, 24, 7, 12, 38, 58, 19, 75 F 22.5G 19H 24J ) What is the lower quartile of the numbers listed below? 3, 88, 17, 11, 39, 62, 43, 22, 76 F 17G 14H 15J 11

Part 2: Use theoretical probability to make predictions Theoretical Probability: It is the likeliness of an event happening based on all the possible outcomes. C A L I F O R N I A One card is randomly selected from the bag. 1 ) What is the probability that the selected card shows the letter A? A 1/10B 2/5C 3/10 D 1/5

TCAP Practice Book Questions: # 11, 16, 24, 42, 45, 50

Day 2 and 3: Geometry and Measurement Part 1: Solve contextual problems involving similar triangles. Similar triangles: same shape but sizes are different (each side forms a ratio) *You can create a proportion to see if two triangles are similar. If you know that 2 triangles are similar then you can, create a proportion to solve for a missing side length.

1) The two similar triangles shown are patterns used to create a design on a jacket. What is the value of x, the height of the smaller triangle, in inches? A) 5 ½ in B) 2 1/5 in C) 5 in D) 2 in 11 in 5 in X 2 ½ in

2) The diagram below represents a triangular section of a park. Triangle WST is similar to Triangle WXY. If the length of WS is 234 feet, what is the length of XY ? A 39 feetB 58.5 feet C 117 feetD feet W X Y ST 117 ft

*Use this same methods when given a shadow. *indirect measurement

3) A triangle has side lengths of 28 inches, 32 inches, and 36 inches. Which list shows the side lengths of a similar triangle? F 6 inches, 8 inches, 9 inches G 14 inches, 16 inches, 18 inches H 21 inches, 26 inches, 27 inches J 54 inches, 64 inches, 72 inches 4) A triangle has side lengths of 3 inches, 5 inches, and 10 inches. Which list shows the side lengths of a similar triangle? F 9 inches, 12 inches, 30 inches G 12 inches, 20 inches, 45 inches H 16 inches, 30 inches, 60 inches J 24 inches, 40 inches, 80 inches

TCAP Practice Book Questions: # 4, 19, 54

Part 2: Apply scale factor to solve problems involving area and volume. Notes about Scale Factor Area uses an exponent of 2. You will always square the scale factor. Volume uses an exponent of 3. You will always cube the scale factor. There are 3 ways you will be asked these types of problems. #1 Given the area/volume of 1 figure and the scale factor- find the area/volume of the similar figure. #2 Given the area/volume find the side length ratio **Remember to “undo an area” you will square root it (√) and to “undo a volume” you will cube root it (exponent 1/3) #3 Given the 2 side lengths- find the difference in the figures (how many times larger/smaller one is)

#1 A rectangular painting has an area of 720 square inches. Jasmine reduced the length and width of this painting by a scale factor of 1/6to create a miniature copy. What is the area of the miniature copy? A 12 square inchesB 20 square inches C 60 square inches D 120 square inches Change 16 to 1/6 (fraction) on your packet

#2 Two squares are similar. The area of the smaller square is 256 square inches. The are of the larger square is 324 square inches. What is the ratio of the side length of the smaller square to the side length of the larger square? A 256/324B 64/81 C 1/4D 8/9

#3 Keziah built a scale model of the Gateway Arch in St. Louis, Missouri. A picture of the arch is shown below. The base at each end of the actual arch is shaped like an equilateral triangle with side lengths of 54 feet. Keziah built her model using equilateral triangles for each base that were foot long on each side. Which statement about the areas of these triangles is true? A) The area of the triangle at the base of the actual arch is 27 times the area of the triangle Keziah used for the base of her model. B) The area of the triangle at the base of the actual arch is 108 times the area of the triangle Keziah used for the base of her model. C) The area of the triangle at the base of the actual arch is 729 times the area of the triangle Keziah used for the base of her model. D) The area of the triangle at the base of the actual arch is 11,664 times the area of the triangle Keziah used for the base of her model.

TCAP Practice Book Questions: # 7, 25, 32

Day 4 and 5: Mathematical Processes Part 1: Use proportional reasoning to solve mixture/concentration problems.

1) A recipe for making 8 cups of soup requires 4 cups of water. At this rate, how many cups of water are required to make 16 cups of soup? A 8 cups B 12 cups C 16 cups D 32 cups 2) To make a certain concentration of a chemical, a scientist mixes 81 milliliters of the chemical with 180 milliliters of distilled water. To make more of this chemical concentration, exactly how many milliliters of the chemical should the scientist mix with 260 milliliters of distilled water? A36 millilitersB65 milliliters C117 millilitersD161 milliliters

Part 2: Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.

1) The graph shows five points of a relation. Which equation best represents this relation? F y = x + 2G y = 2x + 3 H J

2) The table shows values of x and y. Which equation represents the pattern shown by the data in the table? A) inversely proportional B) directly proportional C) linear D) Exponential X Y

Part 4: Use scales to read maps.

The map below shows three towns on the same highway. The scale shown on the map relates centimeters (cm) to kilometers (km). - The distance between Oaktown and Crestview is 2 cm on the map. - The distance between Crestview and Maple Grove is 5 cm on the map. According to the scale, what is the actual distance between Oaktown and Maple Grove along the highway? F 98 kmG 70 km H 49 kmJ 28 km

According to the scale drawing, which city is approximately 400 miles from Washington, D.C.? A Richmond B Charleston C Columbia D Raleigh

TCAP Practice Book Questions: # 2, 10, 14, 21, 26, 29, 36, 44, 48, 51