1. CAPT Practice Jan 2013

2. Pythagorean Theorem Holding an electronic measurement tool 5.5 feet above the ground, the rock climber measures her horizontal distance from the cliff to be 32.25 feet and the distance to the top of the cliff to be 54.5 feet. How high, in feet, is the cliff from the ground?

3. Pythagorean Theorem How high, in feet, is the cliff from the ground? Horizontal distance from the cliff: 32.25 ft Distance to the top of the cliff: 54.5 ft.

4. Pythagorean Theorem How high, in feet, is the cliff from the ground? Pythagorean Theorem: a 2 +b 2 = c 2 where c = hypotenuse. Hypotenuse : 32.25 2 +b 2 = 54.5 2 1040.1+b 2 = 2970.25 b 2 = 1930.15 b = 43.93 43.93

5. Pythagorean Theorem How high, in feet, is the cliff from the ground? Hypotenuse : b = 43.93 is the side of the triangle 43.93 Starts 5.5 ft above the ground Height of cliff is 43.93 + 5.5 49.43ft

6. Pythagorean Theorem How high, in feet, is the cliff from the ground? Height of cliff is 43.93 + 5.5 49.43ft 4 9 4 3

7. Transformation Nailah’s graphics software allows her to draw and rotate images by a specified angle. Nailah begins by drawing hexagon E and sqaure D. She plans to rotate square D to produce square F. By how many degrees must Nailah instruct the software to rotate square D to produce square F?

8. Transformation By how many degrees must Nailah instruct the software to rotate square D to produce square F? 60 ◦ A Regular Hexagon has 60-degree Rotational Symmetry. So Rotating 120-degrees will move square D to square F.

9. Data/Statistics Lorna swam 30 laps per day for the first 6 days of swim practice. She swam 40 laps per day for the next 4 days of practice. What was the mean number of laps that Lorna swam per day for these 10 days? 6(30) + 4(40) = 180 + 160 = 340 total laps Average = 340 / 10 = 34 laps per day

10. Number Properties On the real number line between what two consecutive integers is ? 2 2 = 4 3 2 = 9 so, it is between 2 and 3.

11. Prom Candles Chloe is responsible for making 32 centerpieces for the tables at this years’ school prom. She will place 8-inch tall candles into prism vases of the same height. Then she will fill the vases with blue sand.

12. Prom Candles Sand is sold in 240 cubic inch Bags at $4.79 per bag. How much will Chloe spend on sand to create 32 centerpieces?

13. Prom Candles Plan: 1.Find volume of the Prism. 2.Find volume of Cylinder. 3.Find the difference in volumes. 4.Divide by 2 (only half filled). 5.Times 32 Centerpieces 6.Determine number of bags. 7.Find Cost of sand.

14. Prom Candles 1.Find volume of the Prism. V = lwh 2. Find volume of Cylinder. V= Πr 2 h V = 5 x 5 x 8 V = 200 in 3 r = 4.5/2 = 2.25 V = 3.14(2.25) 2 (8) V = 127.17in 3

15. Prom Candles 1.Find volume of the Prism. V = lwh = 200 in 3 2. Find volume of Cylinder. V= Πr 2 h = 127.17in 3 3. Find the difference in volumes. 4. Divide by 2 (only half filled). 5. Times 32 Centerpieces 200 in 3 - 127.17in 3 = 72.83 72.83 / 2 = 36.415in 3 32(36.415) = 1165.28in 3

16. Prom Candles How much will Chloe spend on sand to create 32 centerpieces? She needs 1165.28in 3 of sand Sand is sold in 240 cubic inch Bags at $4.79 per bag. 6. Determine number of bags. 7. Find Cost of sand. 1165.28 / 240 = 4.86bags 5 bags x 4.79 = $23.95

17. Prom Candles How much will Chloe spend on sand to create 32 centerpieces? Chloe will spend $23.95 on sand for the centerpieces.

18. Data Displays A car manufacturer is testing a new car on a test track. The graph below represents the relationship between The number of miles driven and amount of gas left.

19. Data Displays Write an equation that relates gas in the tank (y) to miles driven (x). Equation of a line can be written in slope intercept form y = mx + b Where m is the slope And b is the y-intercept

20. Data Displays Write an equation that relates gas in the tank (y) to miles driven (x). y = mx + b m is the slope = And b is the y-intercept Rise = -2 Run = 75 slope = -2/75 The y-intercept = 12

21. Data Displays Write an equation that relates gas in the tank (y) to miles driven (x). y = mx + b Rise = -2 Run = 75 slope = -2/75 The y-intercept = 12

22. Percents Martin correctly answered 90% of the questions on a math test that contained exactly 40 questions. How many of the questions did he answer incorrectly? 90% correct means 10% incorrect 10% of 40 = 100x = 400 X = 4 4 Martin answered 4 questions incorrectly.

23. Percent The graph shows a family’s annual expenses. If the family’s annual income is $40,000, what is the family’s annual expense for housing? 30% of $40,000 100x = 1,200,000 X = 12,000

24. Probability To win a game, Yepa must get a sum of 8 on her next two spins. All the sections of the spinner are of equal size. What is the probability that the results of Yepa’s next two spins will have a sum of 8?

25. Probability What is the probability that the results of Yepa’s next two spins will have a sum of 8? Spin12345 123456 234567 345678 456789 5678910 Probability of getting a sum of 8 is 3/25 3/25 is 0.12 or 12%

26. Pythagorean Theorem What is the length, in units, of line segment AC? Pythagorean Theorem: a 2 +b 2 = c 2 where c = hypotenuse. 3 2 + 4 2 = c 2 4 3 9 + 16 = c 2 25 = c 2 C = 5 C

27. Area What is the area, in square units, of triangle ABC? 4 3 A = ½bh A = ½(3)(4) A = ½(12) = 6units

28. Area Draw a rectangle that has the same area in square units as triangle ABC. 4 3 A = 6units 2 Dimensions: 3 by 2 (same base by ½ the height)

29. Martin needs to estimate the cost of a lunch for himself and 12 of his friends at a Mystic restaurant. The highest priced menu item is $8.85 The lowest priced menu item is $4.35 Drinks are $0.90 each with free refills Everyone will have a $1.75 dessert A 6% sales tax will be added to the bill He will leave the serer a 15% tip based on the bill after the tax He will pay the bill in cash What is a reasonable estimate for the price of the lunch?