Bell Ringer Below is a block with a hole in it. Find the volume of the shape below if the radius of the hole is 4 cm. Block V = 15•15•10 V = 2250 cm3 Circle V = π•42•10 V = 502.65 cm3 15 cm 15 cm 10 cm Final Volume = 2250 – 502.65 = 1747.35 cm3

Midterm Review

Graphing Linear Inequalities . . < or > = Open Circle < or > = Closed Circle < or < = Shade to the left. > or > = Shade to the right. .  Less Than Greater Than

Graphing Linear Inequalities x < 3 Open or Closed? Right or Left? x > -4 .

One-Step Linear Inequality x + 3 > 9 – 3 – 3 x > 6 Now graph it! .

Two-Step Linear Inequality 4x + 1 > -11 – 1 – 1 4x > -12 4 4 x > -3

– 1 – 1 -3x < 9 -3 -3 x > -3 Reverse the Sign -3x + 1 < 10 – 1 – 1 -3x < 9 -3 -3 x > -3 Reverse the Sign!

Key Words “At least” means greater than or equal to (>) “No more than” means less than or equal to (<) “More than” means greater than (>) “Less than” means less than (<)

Word Problems Tom calls a cab which charges $2.50 plus $0.50 a mile. If Tom has no more than $20.00 in his pocket, how far can he go? $2.50 + $0.50m < $20 -2.50 -2.50 0.50m < 17.50 0.50 0.50 m < 35 miles Tom in September. Tom now!

Two Independent Events To find the probability of two independent events occurring together, multiply their probabilities! Ex. Find the probability of flipping a head and rolling a die and getting a 1. Probability of rolling a 1 1 2 . 1 6 1 12 = Probability flipping a head.

Independent Events Ex. A coin is tossed and a card is drawn from a standard deck. a. What is the probability of tossing heads and drawing an ace? b. What is the probability of tossing tails and drawing a face card? 1 2 . 1 13 1 26 = 1 2 . 3 13 3 26 =

Working with Factorials 4! + 3! = 3! – 2! = 4! 2! = = (4•3•2•1) + (3•2•1) = 30 (3•2•1) – (2•1) = 4 (4•3•2•1) (2•1) = 48 6! 4! (6•5•4•3•2•1) (4•3•2•1) = 30

Combinations (Formula) (Order doesn’t matter! AB is the same as BA) nCr = Where: n = number of things you can choose from r = number you are choosing n! r! (n – r)!

Combinations The summer Olympic games had 16 countries qualify to compete in soccer. In how many different ways can teams of 2 be selected to play each other? 16C2 = = = 120 different ways! 16! 2! (16 – 2)! 16•15•14•13•12•11•10•9•8•7•6•5•4•3•2•1 2•1 (14•13•12•11•10•9•8•7•6•5•4•3•2•1)

Permutations (Formula) (Order does matter! AB is different from BA) nPr = Where: n = number of things you can choose from r = number you are choosing n! (n – r)!

15! Permutations 15•14•13•12•11•10•9•8•7•6•5•4•3•2•1 (15 – 8)! In the NBA, 8 teams from each conference make the playoffs. They are ranked by their records. If there are 15 teams in the Eastern Conference, how many different ways can they be ordered? 15P8 = = = 259,459,200 ways to order the teams! 15! (15 – 8)! 15•14•13•12•11•10•9•8•7•6•5•4•3•2•1 7•6•5•4•3•2•1

Fundamental Counting Principle For vacation, Ashley packed 5 shirts, 4 pants, and 2 pairs of shoes. How many possible outfits can Angela Create? 5 • 4 • 2 = 40 outcomes At Fake University there are 5 science, 6 social studies, 4 math, and 7 English classes to choose from. How many possible schedules could you create? 5 • 6 • 4 • 7 = 840 schedules

I get it. Add up the bottom sides to equal the top! Distance of Sides Find the missing value, x. 28 in x + 2x + x = 28 4x = 28 4 4 x = 7 inches x x 2x I get it. Add up the bottom sides to equal the top!

Perimeter Find the perimeter. Find x: x + 5 = 17 – 5 – 5 x + 5 x = 12 – 5 – 5 x = 12 x + 5 x – 1 If x = 12, then x – 1 is 11! 17 in Use x to find perimeter: 17 + 17 + 11 + 11 Perimeter = 56 inches

Area of Rectangles Find the area of the rectangle: Find x: 2x – 4 + 4 + 4 2x = 16 x = 8 2x – 4 x – 3 12 in If x = 8, then x – 3 is 5! Find the area: A = L • W A = 12 • 5 A = 60 in2

Area of Trapezoids (b1+ b2) 2 • h Area of a Trapezoid = (Find the average of the bases and multiply by the height!) b1 & b2 are the top and bottom bases. h is the height. b1 h b2 (b1+ b2) 2 • h

Area of Trapezoids (b1+ b2) A = • h 2 (12 + 16) = 126 ft2 = • 9 2 Find the area of the trapezoid below. 12 9 16 (b1+ b2) 2 A = • h (12 + 16) 2 = 126 ft2 = • 9

Word Problems It takes Sean 1 hour to paint 25 ft2. How long will it take Sean to paint the following wall? A = L • W A = 20 • 24 A = 480 ft2 Time = 480 ÷ 25 Time = 19.2 hours 20 ft 24 ft

See, I am smarter than Ke’Shila! Area Area of ‘A’ A = 6 • 18 A = 108 ft2 Area of ‘B’ A = 3 • 8 A = 24 ft2 A = 108 + 24 A = 132 ft2 Find the area. 18 6 A 2x B x 3 ft x + 5 8 ft Find x: 2x = 6 x = 3 See, I am smarter than Ke’Shila!

Perimeter Solve for x, if the perimeter is 34 ft. 2(2x – 1) + 2(x + 2) = 34 4x – 2 + 2x + 4 = 34 6x – 2 = 34 6x = 36 x = 6 x + 2 2x – 1

Area Solve for x, if the area is 40 ft2. 8 • (2x + 1) = 40

Area Solve for x, if the area is 30 ft2. A = ½ B H

Circumference of a Circle C = 2πr C = 2 π 5 C = 10π or 31.42 5

Circumference of a Circle What is the radius of a circle with a circumference of 28 inches? C = 2πr 28 = 2πr 2 2 14 = πr π π 4.46 = r Solve for r!

A = πr2 Area of a Circle A = π62 A = 36π A = 113.10 The area of a circle is equal to: A = πr2 . A = π62 A = 36π A = 113.10 6

Area of a Circle √ A = πr2 26 = πr2 π π 8.28 = r2 2.88 = r What is the radius of a circle with an area of 26 square inches? A = πr2 26 = πr2 π π 8.28 = r2 2.88 = r Solve for r! √