Math Review Warm-Up with Cones, Lines, and Functions

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In this math review warm-up activity, you will work on finding lateral and total surface areas of shapes, determining the radius of a cone-shaped hole, converting numbers to scientific notation, calculating slopes of lines, and identifying functions from relations. Challenge yourself with these math problems to strengthen your skills.

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Semester Review Warm Up Day 2 Jan. 8, 2016 1st Semester

1. Find the lateral surface area and then find the total surface area. 2. The volume of a cone-shaped hole is 49 ft3 . If the hole is 3 feet deep, what is the radius of the hole?

3. Write the number in scientific notation or standard form. a. 6.93 x 106 c. 1.22 x 109 b. 8,930,000,000 d. 287,600,000 4. Line one passes through the points ( 2, 2) and (1, 3). Line 2 passes through the points (3, 10) and (7, 22). Find the slope of each line. The slope of Line 1 is ___________ The slope of Line 2 is ___________ Which line has the greater slope? ________________ 5. Determine whether the following relation represents a function. Yes ______ (7, 5), ( 2, 1), (6, 4), (4, 3) No ______

1. Find the lateral surface area and then find the total surface area. Lateral Surface Area S = Ph S = (1.5+2.5+2)(3.5) S = 6(3.5) S = 21 cm2 Total Surface Area S = Ph+2B 1 2bh S = Ph+2 1 2 (2)(1.5) S = (1.5+2.5+2)(3.5)+2 S = 21+ 3 S = 24 cm2

2. The volume of a cone-shaped hole is 49 ft3 . If the hole is 3 feet deep, what is the radius of the hole? V =1 3Bh 49p =1 3pr23 49 = r2 radius = 7 ft 49 = 7 = r r2

3. Write the number in scientific notation or standard form. a. 6.93 x 106 6,930,000 1,220,000,000 c. 1.22 x 109 b. 8,930,000,000 8.93 x 109 2.876 x 108 d. 287,600,000 4. Line one passes through the points ( 2, 2) and (1,3). Line 2 passes through the points (3, 10) and (7, 22). Find the slope of each line. Which line has the greater slope? 1 3 1 ( 2) 3 2 1 3 = The slope of Line 1 is ___________ 22 10 7 3 12 4 = = 3 3 The slope of Line 2 is _____________ Line 2 Which line has the greater slope? ________________

5. Determine whether the following relation represents a function. X Yes ______ (7, 5), ( 2, 1), (6, 4), (4, 3) No ______ Each input has exactly one output.

a2+b2= c2 152+272= c2 954 = c2 954 = 30.886...= c 30.9 cm c 1. What is the slant height? c2 30 2 =15

7. What is the surface area? S = Ph+2B 1 2i4.5i6 S = (7.5+ 4.5+6)(12)+2 S = 216+27 S = 243 in.2

8. What is the surface area of the CUP? (NO top) S = 2prh+pr2 S = 2(3.14)(8)(13)+ 3.14(82) S = 653.12+200.96 S = 854.08 S 854.1 cm2

10. V =1 3Bh V =1 3pr2h 16p =1 3pr23 ( ) 16 = r2 4 = r

18. Identify a pair of corresponding angles.

xPy 19. Find a congruence statement that justifies .

mQ 20. Find the value of the variable and . x = _____ m Q = _____ x+(x+72)+(x-12)=180 (x+ x+ x)+(72-12)=180 3x+60=180 -60 -60 3x =120 x = 40 m Q = 40+72 =112