Intermediate Algebra Summer School Credit Recovery.

Intermediate Algebra Summer School Credit Recovery

Welcome! Expectations Earning Credit Passes Supplies (student packet, folders, paper)

Day 1: Solving Equations Goal: To solve equations in one variable that contain more than one operation Standard: Prior Standard Guiding Question: How do I solve an equation for a variable? Materials: Pencil, Folder, Student Packet

Adding and Subtracting Fractions When you add or subtract fractions, you need a common denominator Adding and Subtracting Decimals 13.34 + 12 When you add or subtract decimals, make sure you line the decimals up. Dividing Fractions To give dividing fractions a try, flip the second and multiply. Reflection Starters: I know or I need to work on Menta l Math Math Review Day 1

Access: Apply the correct order of operations: A)7 x 4 + 3 = B) (1 + 3) 2 9 3 + 6 = C)12 6 x 2 + 7 = D) 24 12 2 x 3 + 7 =

One-Step Equations: A)3 + x = 7B) -10 = x 4 Try: C) X 9 = 11 D) -5 x = 10 E) -13 = x 4F) 17 = 6 - x

One-Step Equations: G) 5x = -30H) 6x - 42 Try: I) 16 = -2xJ) 24 =5x K) L)

Two-Step Equations: A) 2x 9 = 18B) 3x + 6 = -8 Try: C) 4 3x = 10D) E) 13 + 2x = 9F) 2(5x + 3) = 20

Word Problems: Josie bought 4 cases of sports drinks for an upcoming meet. After talking to her coach she bought three more cases spending an additional $6.95 on additional items. Her receipts totaled $74.15. Write and solve an equation to find out how much each case of sports drink costs.

Work Time: Work through pages 3 and 4 in your packet Multiplication test at: ______ Exit Slip at: _________

Multiplication Timed Test: -Page 5 of your packet tear in half and remove one from the packet You have five minutes to fill in as much as you can Go = Start, Stop = hands up! Highlight the ones you did not know

Exit Slip: (on a half-sheet of scratch paper) A)5x 9 = 17 B) Make sure it has your name and turn it in!

Day 2: Solving Equations Goal: To solve equations that have variables on both sides Standard: Prior Standard Guiding Question: How do I solve an equation for a variable? Materials: Pencil, Folder, Student Packet

Adding and Subtracting Fractions When you add or subtract fractions, you need a common denominator Adding and Subtracting Decimals 45 9.867 When you add or subtract decimals, make sure you line the decimals up. Dividing Fractions To give dividing fractions a try, flip the second and multiply. Reflection Starters: I know or I need to work on Menta l Math Math Review Day 2

Access: Solve the equation: A)3x 9 = 11B) C)

Solve the equation: A)3d + 8 = 2d 17B) t + 5 = t 19 C) 5 (t 3) = -1 + (2 3) D) x + 4 6x = 6 - 5xE)-8x + 6 + 9x = -17 + x

Try: F) 2y + 3 = 3(y + 7) G) 10 - y + 5 + 6y = 1 + 5y + 3

Try: H) 4(x 3) = 2x + 3x 9 I) 3(2x 5) = 2(3x 2)

Multiplication Timed Test: -Page 5 of your packet tear out of packet You have five minutes to fill in as much as you can Go = Start, Stop = hands up! Highlight the ones you did not know

Exit Slip: (on a half-sheet of scratch paper) Previous Material (PM): A)5y 9 = 16 New Material (NM): B) 3x 8 = 6 2xC) 6x = 5x 10 Make sure your name is on it, and turn it in!

Day 3: Solving Inequalities Goal: To solve multi-step inequalities AND to solve inequalities that contain variables on both sides. Standard: Prior Standard Guiding Question: How do I solve an inequality for a variable? Materials: Pencil, Folder, Student Packet

Adding and Subtracting Fractions When you add or subtract fractions, you need a common denominator Adding and Subtracting Decimals 15.87+ 1.9 When you add or subtract decimals, make sure you line the decimals up. Dividing Fractions To give dividing fractions a try, flip the second and multiply. Reflection Starters: I know or I need to work on Menta l Math Math Review Day 3

Access: Solve the equation: A)3x + 9 = x 8 B) 7 4x = 6x + 2 C) 7x = 10x - 1

Solve: - 3x > 9 Check a Number. What is the rule when solving inequalities?

Solve the inequality and graph the solution: A)2m + 1 > 13B) 2d + 21 11 C) D) 4 X > 3(4 2)

Solve the inequality and graph the solution: E) 4r 9 > 7F) 3 5 2x G)-4x 8 > 16H) I) 12 (x 3) + 2x 6

Solve the inequality and graph the solution: J) 2x > 4x 6K) 5(4 x) 3(2 + x)

Solve and graph the solution: L) 27x + 33 > 58x 29M) 5c 4> 8c + 2 N) 2(6 x) < 4xO) 4(y+1)< 4y +2 P) -3(n + 4) 6( 1 n)

Exit Slip: (on a half-sheet of scratch paper) Previous Material (PM): A)2r + 20 = 200B) 3(2x 5) = 2(3x 2) New Material (NM): C) 2 + (-6) > -8p D) 3(1-x) 3(x + 2) Make sure your name is on it, and turn it in!

Day 4: Graphing Linear Functions Goal: To solve for a variable AND To graph linear functions using tables or equations Standard: 9.2.1.8 Make Qualitative statements about the rate of change of a function based on its graph or table of values 9.2.2.3 Sketch graphs of linear, quadratic and exponential functions and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions. Guiding Question: What and how are the many ways I can graph a line? Materials: Pencil, Folder, Student Packet

Adding and Subtracting Fractions When you add or subtract fractions, you need a common denominator Adding and Subtracting Decimals 1.309+ 134.8 When you add or subtract decimals, make sure you line the decimals up. Dividing Fractions To give dividing fractions a try, flip the second and multiply. Reflection Starters: I know or I need to work on Menta l Math Math Review Day 4

Access: Graph the points on a coordinate plane: A (5, 6) B (-1, -3) C (4, -9) D (-1.5, 0)

Solve for a variable: A)2x - 3y = 12 B) 2x + y = 8 Try: C) 5y = 5x - 10 D) 2y - 6y = -8

What is a function? What makes a function linear? How can I graph a line? Table, Slope and Intercept, x-and y- intercepts, and slope-intercept form

Graph: A)Slope = y-intercept = 4 B) Slope = 4, y-intercept =

Try: C) Slope = y-intercept = 4 D) slope = 3, y-intercept = 2

Graph A) B) C) y = x + 6

Try: D) E) y = 3x - 1 F) y = -2x + 4

Graph: A)6x + 3y = 12 B) 2x + y = 8

Try: C) 2x - 6y = 6 D) 2x + 3y = -12 E) 5x - 2y = 10

Exit Slip: (on a half-sheet of scratch paper) New Material (NM): Solve for y: A)7y + 14x = 28 B) -5y = 2x + 7 Graph: A)B) y = -3x C) y = 2 D) 3x - 2y = 6 Make sure your name is on it, and turn it in!

Day 5: Graphing Linear Inequalities Goal: To graph linear inequalities using tables or equations. AND To write equations to describe lines. Standard: 9.2.4.4 Represent relationships in various contexts using systems of linear inequalities; solve them graphically. Indicate which parts of the boundary are included in and excluded from the solution set using solid and dotted lines. Guiding Question: How do I graph a linear inequality? AND How can I write equations of lines? Materials: Pencil, Folder, Student Packet

Adding and Subtracting Fractions Adding and Subtracting Decimals A)67.8 + 5.23 B)71 8.09 Dividing Fractions Math Review Day 5 QUIZ

Access: Graph: A)y = 3x - 2 B) C) y = -2x + 5

Write an equation with the following information: A)Slope =, y-intercept = 4 B) Slope = 4, y-intercept = Try: C) Slope =, y-intercept = 4 D) slope = 3, y-intercept = 2

E) Slope: -4 and contains (-1, -2) F) Slope: and contains (5, 1) Try: G) Slope = -4, and contains (0, 3) H) Slope = 1 and contains (-1, -4)

I)Contains (1, -4) and (3, 2) J) contains (4, -7) and (0, 5) Try: K) contains (2, -3) and (4, 1) L) Contains (0, 1) and (-2, 9)

How are parallel lines related? How are perpendicular lines related? M) Parallel to y = -3x + 5, contains (6, -2) N) Perpendicular to y = -2x + 4, contains (-2, 5) Try: O) Parallel to y = x - 6, contains (-1, 2) P) Perpendicular to y = 5 - 3x, contains (2, -4)

Graph the inequality: A)y - 2x + 6 B) y < 3x -3 C) y > 4x + 7

Try: D) y 2 - 3x E) 3x - 2y > 6 F) y x + 5 G) y > 3x + 1 H) y > 2/3x - 1

Work Time: Work through pages 15 and 16 in your packet Exit Slip at: _________

Exit Slip: (on a half-sheet of scratch paper) Previous Material (PM): Solve for y: A)6x - y = 10 B) 4y = 4x - 8 New Material (NM): Write the equation: A)Contains (1, 2) and (-3, 4) B) slope: -2, contains (0, 3) Graph: A)Y x - 2 B) y < 2x + 3 Make sure your name is on it, and turn it in!

Solve the proportion: "Make sure x is in the numerator and solve" Find 10%, 20%, 50% and 100%: 80 "Find 10% by moving the decimal one place, and use it to find the others. Percent Problems: What is 15% of 40? "Write an equation, is =, of x, and solve for x." Reflection Starters: I know or I need to work on Menta l Math Math Review Day 6

Day 6: Exponents Goal: To simplify expressions containing exponents. AND to evaluate expressions Standard: Standard 9.2.3: Generate equivalent algebraic expressions involving polynomials and radicals; use algebraic properties to evaluate expressions. Guiding Question: How can I evaluate expressions? AND How do I use exponent properties to simplify expressions? Materials: Pencil, Folder, Student Packet

Access: What does 2 2 mean? 2 3 ? 2 4 ? (x + 2) 2 ?

Simplifying Exponential Expressions: -no negative exponents -same base does not appear more than once -no powers, products or quotients are raised to powers (ie no parenthesis) -numerical coefficients are relatively prime

Integer Exponents: Zero Exponent: x 0 = 1 Negative Exponent: x -n = Simplify: A)4 -3 B) 7 0 Try: C) (-5) -4 D) -2 -3 E)2r 0 m -3 F) G)

Product of Powers: a m a n = a m+n Power of a Power: (a m ) n = a mn Power of a Product: (xy) m = x m y m Simplify: A)(x 2 ) 5 B)n 6 n 2 C) (2t) 5 D) (a 2 b 2 ) 5 (a - 5 ) 2 Try: E) (2 3 ) 3 F) (3 6 ) 0 G) (p 4 q 2 ) 7 H) (-4x 3 ) 4 I)(ab) 3 (ab) -2

Quotient of Powers: Positive Power of a Quotient: Negative Power of a Quotient: Simplify: A) B) Try) C) D) E) F)

Evaluate each Expression for the given variable: A)2x + 3 for x = 7 B)4x+8; x=-2 C) p 0 for p = 9 D) x -3 y for x = 4 and y = -2 Try) E) 3n - 5 for n = 7 F)-5t - 15; t = 1 G) t -6 for t = 2 H) (5 d) -7 for d = 6 I)r 0 s -2 for r=8 and s = 10

Exit Slip: (on a half-sheet of scratch paper) NM: Simplify each expression: A)x^4/y^-6 B) 8f -4 g 0 C) (m 3 n 3 ) 5 D)(x^3y^4/xy^5)^-3 Make sure your name is on it, and turn it in!

Day 7: Polynomials Goal: To simplify polynomial expressions by adding or subtracting Standard: 9.2.3.2 Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree. Guiding Question: How do I simplify polynomials expressions? AND how do I add or subtract polynomials expressions? Materials: Pencil, Folder, Student Packet

Solve the proportion: "Make sure x is in the numerator and solve" Find 10%, 20%, 50% and 100%: 53 "Find 10% by moving the decimal one place, and use it to find the others. Percent Problems: 13 is what percent of 52? "Write an equation, is =, of x, and solve for x." Reflection Starters: I know or I need to work on Menta l Math Math Review Day 7

Access: Put a circle on those that are alike in each set: A) 2x, 4, -10x, 7x 2, 9x, 15 B) 8, -5x, 11, x 2, 12x 3, 14, -8 C) 14x 4, 9x, 9x 2, 14x 2, -13, 6x 2, x 5

What is a polynomial? Word Problems: A tourist accidentally drops her lip balm off the Golden Gate Bridge. The bridge is 220 feet from the water of the bay. The height of the lip balms is given by the polynomial -16t 2 +220, where t is the time in seconds. How far above the water will the lip balm be after 3 seconds?

Try: The surface area of a cone is approximated by the polynomial 3.14r 2 + 3.14rl, where r is the radius and l is the slant height. Find the approximate surface area of a cone that has radius of 6 cm and slant height 10cm.

Add or Subtract: A)12p 3 + 11p 2 + 8p 3 B) 5x 2 - 6 - 3x + 8 Try: C) t 2 + 2s 2 4t 2 s 2 D) 10m 2 n + 4m 2 n 8m 2 n

E)(6x 2 - 4y) + (3x 2 + 3y 8x 2 - 2y) F) ( a 2 + b + 2) + ( a 2 - 4b + 5) Try: G) (4m 2 + 5) + (m 2 - m + 6) H) (10xy + x) + (-3xy + y)

I) (x 3 + 4y) - (2x 3 ) J) (7m 4 2m 2 ) - (5m 4 5m 2 + 8) Try: K) (-10x 2 - 3x +7) - (x 2 - 9) L) (9q 2 - 3q) - (q 2 - 5)

Exit Slip: (on a half-sheet of scratch paper) NM: Add or Subtract: A) 7m 2 + 3m + 4m 2 B) (r 2 + s 2 ) - (5r 2 + 4s 2 ) C) (10pq + 3p) + (2pq - 5p + 6pq) D) (14d 2 - 8) +(6d 2 - 2d + 1) Make sure your name is on it, and turn it in!

Day 8: Polynomials Goal: To simplify polynomial expression by multiplying. Standard: 9.2.3.2 Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree. Guiding Question: How can I multiply polynomials? Materials: Pencil, Folder, Student Packet

Solve the proportion: "Make sure x is in the numerator and solve" Find 10%, 20%, 50% and 100%: 65 "Find 10% by moving the decimal one place, and use it to find the others. Percent Problems: 45 is 33% of what number? "Write an equation, is =, of x, and solve for x." Reflection Starters: I know or I need to work on Menta l Math Math Review Day 8

Access: Simplify using exponent properties: A) x 2 x 4 B) 3x(4x 3 ) C) 2x 2 - 9x + x 2 D) -7x 3 + 9x + 18x 3 - 10x

Multiply: A)(6y 3 )(3y 5 ) B) (3mn 2 )(9m 2 n) Try: C) (3x 3 )(6x 2 ) D) (2r 2 t)(5t 3 )

E) 6pq(2p-q) Try: F) 4(3x 2 + 4x - 8)

F O I L A)(s + 4)(s - 2) B)(x 4) 2 C)(8m 3 n)(m 3 - 3n) Try: C) ( a + 3)(a - 4) D) ( x 3) 2 E) (2a b 2 )(a + 4b 2 )

Multiply: A)(x - 5)(x 2 + 4x - 6) B) (2x 5)(-4x 2 - 10x + 3) C) (3x + 1)(x 3 + 4x 2 - 7) Try: D) (x + 3)(x 2 - 4x + 6) E) (3x + 2)(x 2 - 2x + 5)

Exit Slip: (on a half-sheet of scratch paper) NM: Multiply: A)(6s 2 t 2 )(3st) B)4xy 2 (x + y) C)(x + 2)(x - 8) D)(2x - 7)(x 2 + 3x - 4) E) 6mn (m 2 + 10mn -2) F) (2x - 5y)(3x + y) Make sure your name is on it, and turn it in!

Day 9: Factoring Goal: To factor polynomials by using the greatest common factor Standard: 9.2.3.3 Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares. Guiding Question: How do I find the greatest common factor of a polynomial? Materials: Pencil, Folder, Student Packet

Solve the proportion: "Make sure x is in the numerator and solve" Find 10%, 20%, 50% and 100%: 90 "Find 10% by moving the decimal one place, and use it to find the others. Percent Problems: What is 22% of 31? "Write an equation, is =, of x, and solve for x." Reflection Starters: I know or I need to work on Menta l Math Math Review Day 9

Access: Simplify: A)2(w + 1) B) 3x(x 2 - 4) C) (x + 3)(x + 8) Write the prime factorization (factor tree) A) 20 B) 50 C) 17 D) 38

What is the greatest common factor: A)100 and 60 B) 26 and 52 C) 18 and 27 Try) D) 12 and 16 E) 15 and 25 F)55 and 121

Find the GCF of the pair of monomials: A) 15x 3 and 9x 2 B) 8x 2 and 7y 3 C)3x 3 and 6x 2 Try: D) 18g 2 and 27g 3 E) 16a 6 and 9b F) 8x and 7x 2

Word Problems: A cafeteria has 18 chocolate milk cartons and 24 regular milk cartons. The cook wants to arrange the cartons with the same number of cartons in each row. Chocolate and regular milk will not be in the same row. How many rows will there be if the cook puts the greatest possible number of cartons in each row?

Try: Samantha is making beaded necklaces using 54 glass beads and 18 clay beads. She wants each necklace to have the same number of beads, but each necklace will have only one type of bead. If she puts the greatest number of beads on each necklace, how many necklaces can she make?

Factor each polynomial: A)2x 2 - 4 B) 8x 3 4x 2 - 16x C) -14x 12x 2 D) 3x 3 + 2x 2 10 Try: E) 5b + 9b 3 F) 9d 2 8 2 G) -18y 3 7y 2 H) 8x 4 + 4x 3 2x 2

Factor each expression A)5(x + 2) + 3x(x + 2) B) -2b(b 2 + 1) + (b 2 + 1) Try: C) 4s(s+ 6) - 5(s+6) D) 3x(y + 4) - 2y(y+4)

Exit Slip: (on a half-sheet of scratch paper) PM: Multiply A) 2x(3x 2 + 9x - 8) B) (x - 6)(x+6) NM: Find the GCF: A)18 and 75 B) 12x and 28x 3 Factor: A)16x + 20x 3 B) 4m 4 12m 3 + 8m C) 7k(k-3) + 4(k-3) Make sure your name is on it, and turn it in!

Day 10: Factoring Goal: To factor quadratic trinomials of the form x 2 + bx + c Standard: 9.2.3.3 Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares. Guiding Question: How does FOIL help me factor trinomials? Materials: Pencil, Folder, Student Packet

Solve the proportion: Find 10%, 20%, 50% and 100%: A) 30 B) 41 Percent Problems: A)15 is what percent of 80? B)What is 9% of 72? Reflection Starters: I know or I need to work on Math Review Day 10 QUIZ

Access: A)What two numbers add or subtract to 6 and multiply to 8? B) What two numbers add or subtract to -1 and multiply to 42? C) What two numbers add or subtract to 5 and multiply to -6? D) What two numbers add or subtract to 14 and multiply to 24?

Factor: A)x 2 + 6x + 5 B) x 2 + 6x + 9 C)x 2 - 8x + 15 Try: D) x 2 + 8x + 12 E) x 2 - 5x + 6 F) x 2 + 13x + 42

G) x 2 + x -20 H) x 2 - 3x - 18 I) x 2 + 7x - 18 Try: J) x 2 + 2x - 15 K) x 2 - 6x + 8 L) x 2 - 8x - 20 How would you know if the trinomial is not factored correctly?

Work Time: Work through page 27 in your packet Exit Slip at: _________

Exit Slip: (on a half-sheet of scratch paper) NM: Explain in your own words how to factor x 2 + 9x + 14. Show how to check your answer. Factor: A)x 2 - 11x + 30 B) x 2 + 10x + 9 C) x 2 - 6x -27 D) x 2 + 14x 32 Make sure your name is on it, and turn it in!

Day 11: Factoring Goal: To factor quadratic trinomials of the form ax 2 + bx + c Standard: 9.2.3.3 Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares. Guiding Question: How does FOIL help me factor trinomials? Materials: Pencil, Folder, Student Packet

Order the Fractions from least to greatest: "To order fractions, they must have a common denominator." Order the Decimals from least to greatest: 0.88, 0.8, 8, 0.81 "When ordering decimals compare each place value" Prime Factorization: 24 "What prime numbers multiply to make the number?" Reflection Starters: I know or I need to work on Menta l Math Math Review Day 11

Access: Find the product: A)(x-2)(2x+7) B) (3y +4)(2y+9) Factor: A) x 2 + 4x - 32 B)z 2 + 15z + 36

Factor: A)2x 2 + 17x + 21 B) 3x 2 - 16x + 16 C) 6x 2 + 17x + 5 D) 9x 2 - 15x + 4 Try: E) 5x 2 + 11x + 2 F) 2x 2 + 11x +5 G) 4x 2 - 9x + 5 H) 2y 2 - 11y + 14

I)3n 2 + 11n - 4 J) 2x 2 + 9x - 18 K) 4x 2 - 15x - 4 L) 6x 2 + 7x 3 Try: M) 4a 2 + 8a - 5 N) 15x 2 + 4x - 3 O) 2x 2 + x - 6 P) 6n 2 - 11n -10

Q) -2x 2 - 5x - 3 R) -6x 2 - 17x - 12 S) -3x 2 - 17x - 10 T) -2x 2 -15x 7 Try: U) -2x 2 + 5x + 12 V) -4n 2 - 16n + 9

Work Time: Work through page 28 in your packet Exit Slip at: _________

Exit Slip: (on a half-sheet of scratch paper) NM: Factor each trinomial: A)5x 2 + 17x + 6 B) 2x 2 + 5x - 12 C) 6x 2 - 23x + 7 D) -4x 2 + 11x + 20 E) -2x 2 + 7x - 3 F) 8x 2 + 27x + 9 Make sure your name is on it, and turn it in!

Day 12: Quadratics Goal: To identify and graph a quadratic function. Standard: 9.2.1.8 Make qualitative statements about the rate of change of a function, based on its graph or table of values. Guiding Question: How can I graph a quadratic using a table? Materials: Pencil, Folder, Student Packet

Order the Fractions from least to greatest: "To order fractions, they must have a common denominator." Order the Decimals from least to greatest: 13.876, 13.901, 11.875, 13.87 "When ordering decimals compare each place value" Prime Factorization: 30 "What prime numbers multiply to make the number?" Reflection Starters: I know or I need to work on Menta l Math Math Review Day 12

Access: Evaluate x 2 + 5x for x = 4 and x = -3 What is Domain? What is range?

Tell whether each function is a quadratic. Explain: A){(-2, -9), (-1, -2), (0, -1), (1, 0), (2, 7)} B) y = 7x + 3 C) y 10x 2 = 9 Try: D) {(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)} E) y + x = 2x 2

Use a table of values to graph each quadratic function A)y = x 2 B) y = -4x 2 Try: C) y = x 2 + 2 D) y = -3x 2 + 1

Tell whether the graph of each quadratic function opens up or down. Explain: A)y x 2 = x - 3 B) y = 5x 3x 2 Try: C) f(x) = -4x 2 - x + 1 D) y 5x 2 = 2x - 6

Identify the vertex of each parabola. The give the maximum or minimum value of the function. Find the domain and Range.

Exit Slip: (on a half-sheet of scratch paper) NM: A)Is y = -x - 1 quadratic? Explain. B) Graph using a table of values y = 1.5x 2 C)Identify the vertex D) Does the function have a minimum or maximum? What is it? E) Find the domain and range Make sure your name is on it, and turn it in!

Day 13: Quadratics Goal: To find the axis of symmetry, vertex and zeroes of a quadratic function. Standard: 9.2.1.5 Identify the vertex, line of symmetry and intercepts of the parabola corresponding to a quadratic function, using symbolic and graphical methods, when the function is expressed in the form f (x) = ax 2 + bx + c, in the form f (x) = a(x h) 2 + k, or in factored form. Guiding Question: How can I find the axis of symmetry, zeroes and vertex of a quadratic function? Materials: Pencil, Folder, Student Packet

Access: Find the x-intercept of each linear function: (hint y = 0) A)y = 2x - 3 B) y = 3x + 6 Evaluate each quadratic function for the given input values A)y = -3x 2 + x - 2, when x = 2 B) y = x 2 + 2x + 3, when x = -1

Find the zeros of each quadratic function from its graph. Check your answer. Try:

Find the axis of symmetry of each parabola: Try: C) y = -3x 2 + 10x + 9 D) y = x 2 + x + 3 Try: E) y = x 2 + 4x - 7 F) y = 3x 2 - 18x + 1

Find the vertex: B)y = -3x 2 + 6x - 7 C) y = 5x 2 - 10x +3 Try: D)y = -5x 2 + 10x + 3 E) y = x 2 + 4x - 7 F) y = -x 2 + 6x - 1

Word Problems: The graph of f(x) = -0.6x 2 + 0.6x + 10.26 can be used to model the height in meters of an arch support for a bridge, where the x-axis represents the water level and x represents the distance in meters from where the arch support enters the water. Can a sailboat that is 14 meters tall pass under the bridge? Explain.

Try: The height of a small rise in a roller coaster track is modeled by f(x) = -0.07x 2 + 0.42x + 6.37, where x is the distance in feet from a support pole at ground level. Find the height from the rise.

Exit Slip: (on a half-sheet of scratch paper) NM: A)Find the zeros and axis of symmetry of the parabola. Find the axis of symmetry and vertex: A)y = 3x 2 + 12x + 8 B) y = -x 2 + 8x + 16 C) y = x 2 + 7x Make sure your name is on it, and turn it in!

Day 14: Quadratics Goal: To graph a quadratic function using the axis of symmetry, vertex and zeroes. Standard: 9.2.2.3 Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions. Guiding Question: How can I graph a quadratic function? Materials: Pencil, Folder, Student Packet

Access: Find the axis of symmetry: A)y = 4x 2 - 7 B) y = x 2 - 3x + 1 Find the vertex: A) y = x 2 + 4x + 5 B) y = 3x 2 + 2

Graph the Quadratic Function: Step 1: Find the axis of symmetry Step 2: Find the vertex Step 3: Find the y-intercept Step 4: Find two points on the same side of the axis of symmetry as the point containing the y-intercept.

Graph: A)y = 3x 2 - 6x + 1 B)y = 2x 2 + 6x + 2 C) y + 6x = x 2 +9

Try: D) y = x 2 - 2x - 3 E) y = 2x 2 + 2x - 4 F) y = x 2 + 4x - 8 G) y + x 2 + 5x + 2 = 0

Word Problems: The height in feet of a basketball can be modeled by f(x) = -16x 2 + 32x, where x is the time in seconds after its thrown. Find the basketball's maximum height and the time it takes the basketball to reach this height. Then find how long the basketball is in the air.

Try: The height in feet of a golf ball that is hit from the ground can be modeled by the function f(x) = -16x 2 + 96x, where x is the time in seconds after the ball is hit. Find the ball's maximum height and the time it takes the ball to reach this height. Then find how long the ball is in the air.

Exit Slip: (on a half-sheet of scratch paper) NM: Graph: A)y = -2x 2 - 8x + 4 B) y = x 2 - 8x C) y = 3x 2 + 12x + 9 D) The height in feet of a fireworks shell can be modeled by h(t) = -16t 2 + 224t, where t is the time in seconds after it is fired. Find the maximum height of the shell, the time it takes to reach its maximum height, and the length of time the shell is in the air. Make sure your name is on it, and turn it in!

Day 15: Data Goal: To organize data in various graphs. AND To describe the central tendency of data. Standard: 9.4.1.1 Describe a data set using data displays, including box-and-whisker plots; describe and compare data sets using summary statistics, including measures of center, location and spread. Measures of center and location include mean, median, quartile and percentile. Measures of spread include standard deviation, range and inter-quartile range. Know how to use calculators, spreadsheets or other technology to display data and calculate summary statistics. Guiding Question: How can I organize data? AND What can the measures of central tendency tell me about a set of data? Materials: Pencil, Folder, Student Packet

Order the Fractions from least to greatest: Order the Decimals from least to greatest: A)0.01, 0.1, 0.11, 0.101 B) 16.7, 16.07, 15.7, 16.32 Prime Factorization: A) 18 B)72 Reflection Starters: I know or I need to work on Math Review Day 15 QUIZ

Access: Write the percent: A) B) Put the data set in order from least to greatest: A) 2.4, 5.1, 3.7, 2.1, 3.6, 4.0, 2.9, B) 5, 5, 6, 8, 7, 4, 6, 5, 9, 3, 6, 6, 9

Read and Interpret the graph: A)What casserole was ordered the most? B) About how many orders were placed? C) About how many more tuna noodle casseroles were ordered than king ranch casserole? D) About what percent of the total orders were baked ziti?

A)Which feature received the same satisfaction rating for each SUV? B)B) Which SUV received a better rating for mileage?

A)At what time was the humidity the lowest? B) During which 4-hour time period did the humidity increase the most?

A)In which months did station A charge more than station B B) During which month(s) did the stations charge the same for gasoline?

A) Which ingredients are present in equal amounts?

Stem and Leaf plots: The number of defective widgets in batches of 1000 are given below. Use the data to make a stem-and-leaf plot. 14, 12, 8, 9, 13, 20, 15, 9, 21, 8, 13, 19

Try) The temperatures in degrees Celsius for two weeks are given below. Use the data to make a stem-and-leaf plot. 7, 32, 34, 31, 26, 27, 23, 19, 22, 29, 30, 36, 35, 31

Frequency Tables and Histograms: The numbers of students enrolled in Western Civilization classes at a university are given below. Use the data to make a frequency table with intervals and then a histogram: 12, 22, 18, 9, 25, 31, 28, 19, 22, 32, 14

Try: The number of days Maria's last 15 vacations are listed below. Use the data to make a frequency table and then a histogram: 4, 8, 6, 7, 5, 4, 10, 6, 7, 14, 12, 8, 10, 15, 12

Measures of Central Tendency: Mean: Median: Mode: Rico scored 74, 73, 80, 75, 67 and 55 on six history tests. Find the mean, median and mode. Which value best describes Rico's scores?

Try: Josh scored 75, 75, 81, 84 and 85 on five tests. Find the mean, median and mode. Which value best describes the score Josh received most often? Which value best describes Josh's scores?

Box-and-Whisker Plot: Quartiles: Interquartile Range (IQR): The numbers of runs scored by a softball team at 19 games are given. Use the data to make a box-and-whisker plot: 3, 8, 10, 12, 4, 9, 13, 20, 15, 10, 5, 11, 5, 10, 6, 7, 6, 11

Try: Use the data to make a box-and-whisker plot: 13, 14, 18, 13, 12, 17, 15, 12, 13, 19, 11, 14, 14, 18, 22, 23

Misleading Graphs: Explain why this graph is misleading:

Try: Explain why this graph is misleading:

Exit Slip: (on a half-sheet of scratch paper) A) The number of people at a caterer's last 12 parties are given below. 16, 18, 17, 19, 15, 25, 18, 17, 18, 16, 17, 19 i)Use the data to make a frequency table with intervals. ii) Use your frequency table to make a histogram B) The daily high temperatures on 14 consecutive days in one city were: 59, 49, 48, 46, 47, 51, 49, 43, 35, 52, 51, 51, 51, and 38 i)Find the mean, median and mode of the temperature ii)Which value describes the average high temperature for the 14 days? iii) Which value best describes the high temperature? Explain. C) Use the data in B to make a box-and-whisker plot.

Day 16: Data and Probability Goal: To determine the experimental or theoretical probability of an event. Standard: 9.4.3.1 Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities. Guiding Question: How can I determine the probability of an event? Materials: Pencil, Folder, Student Packet

Conversions: How many inches are in 6 feet? "When converting make sure your labels cancel Time: "The short hand on the clock gives the hour, the long hand gives the minute" Find the perimeter: "Perimeter is the distance around an object" Reflection Starters: I know or I need to work on Math Review Day 16 Menta l Math

Access: Write the percent: A)3/10 B) 18/90 Write the fraction: A)40% B) 35% Write the decimal: A) 18% B) 1/5

Experiment: Trial: Outcome: Sample Space: Identify the sample space and the outcome of A)rolling a number cube. A)Flipping a coin

Event: Probability:

Write impossible, unlikely, as likely as not, likely, or certain to describe each event. A)A shoe selected from a pair of shoes fits the right foot B) Katrina correctly guesses the last digit of a phone number C) Max pulls a green marble from a bag of all green marbles D) A radomonly selected month contains the letter R

Try: Write impossible, unlikely, as likely as not, likely or certain to describe the event: A)Anthony rolls a number less than 7 on a standard number cube. B) A coin lands heads up C) There are 31 days in August D) You roll a 10 on a standard number cube.

Experimental Probability: An experiment consists of spinning a spinner. Use the results in the table to find the experimental probability of each event: A)the spinner lands on orange B) The spinner does not land on orange. Green15 Orange10 Purple8 Pink7

A manufacturer inspects 500 strollers and finds 498 have no defects A)what is the experimental probability that a stroller chosen at random has no defects? B) The manufacturer shipped 3500 strollers to a distribution center. Predict the number of strollers that are likely to have no defects.

Try: One game of bowling consists of ten frames. Elyse usually rolls 3 strikes in each game. A)What is the experimental probability that Elyse will roll a strike on any frame? B) Predict the number of strikes Elyse will throw in 18 games.

Theoretical Probability: An experiment consists of rolling a number cube. Find the theoretical probability of each outcome: A)rolling a 5 B)rolling an odd number C) rolling a number less than 3

Try: Find the Theoretical probability of each: A)flipping 2 coins and both landing on heads B) rolling a number divisible by 3 on a number cube You have a 1/50 chance of winning, what is the probability of not winning?

A box contains only red, black and white blocks. The probability of choosing a red block is 1/4, the probability of choosing a black block is 1/2. What is the probability of choosing a white block? Try: The probability of randomly choosing a blue marble from a bag of 5 blue marbles, 8 red marbles and 7 yellow marbles?

Exit Slip: (on a half-sheet of scratch paper) A) The neighbor's dog barked at Tana the last 4 out of 5 times she walked by the house. i) What is the experimental probability that the dog barks at Tana when she walks past the house? ii) Predict the number of times the dog will bark at Tana if she walks past the house 45 times. B) Find the theoretical probability of randomly choosing B from the letters in ALGEBRA. C) The probability that it will be sunny is 15%. What is the probability that it will not be sunny?

Day 17: Data and Probability Goal: To find the probability of independent or dependent events AND To solve problems involving permutations and combinations. Standard: 9.4.3.1 Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities. Guiding Question: How can I find the probability of an event? AND How can I determine the amount of times an event will occur? Materials: Pencil, Folder, Student Packet

Conversions: How many feet are in 3.5 yards? "When converting make sure your labels cancel Time: "The short hand on the clock gives the hour, the long hand gives the minute" Find the perimeter: "Perimeter is the distance around an object" Reflection Starters: I know or I need to work on Math Review Day 17 Menta l Math

Access: Find the theoretical probability of each outcome. A)rolling a 6 on a number cube B) rolling on an odd number on a number cube C) flipping a coin and it landing heads up

Independent Event: Dependent Event: Tell whether each set of events is independent or dependent. Explain your answer. : A)You select a card from a standard deck of cards and hold it. A friend selects another card from the same deck B)You flip a coin and it lands heads up. You flip the same coin and it lands heads up again.

Try: Tell whether each set of events is independent or dependent. Explain your answer, A)A number cube lands showing an odd number. It is rolled a second time and lands showing a 6. B) One students in your class is chosen for a project. Then another student in the class is chosen.

Probability of Independent Events: If A and B are independent events, then P(A and b) = P(A) P(B) A) An experiment consists of randomly selecting a marble from a bag, replacing it and selecting another marble. The bag contains 3 red marbles, and 12 green marbles. What is the probability of selecting a red marble, and then a green marble? B) A coin is flipped 4 times, what is the probability of flipping 4 heads in a row?

Try: An experiment consists of spinning the spinner twice. What is the probability of spinning two odd numbers?

Probability of Dependent Events: If A and B are dependent events, then P(A and B) = P(A) P(B after A) A) A snack cart has 6 bags of pretzels and 10 bags of chips. Grant selects a bag at random, and then Iris selects a bag at random. What is the probability that Grant will select a bag of chips?

Try: A bag has 10 red marbles, 12 white marbles and 8 blue marbles. Two marbles are randomly drawn from the bag. What is the probability of drawing a blue marble and then a red marble?

Fundamental Counting Principle: If there are m ways to choose a first item and n ways to choose a second item after the first item has been chosen, then there are mn ways to choose both items. A) A voicemail system password is 1 letter followed by a 3-digit number less than 600. How many different voicemail passwords are possible?

Try) A sandwich can be made with 3 different types of bread, 5 different meats and 2 types of cheese. How many types of sandwiches can be made if each sandwich consists of one bread, one meat, and one cheese?

Compound Event: Combination: Permutation:

Tell whether each situation involves combinations or permutations. Then give the number of possible outcomes. A)An English test contains 5 different essay questions labeled A, B, C, D and E. You are supposed to choose 2 to answer. How many different ways are there to do this? B) A family of 3 plans to sit in the theater. How many ways can the family be seated in 3 seats

Try: A)Ingrid is stringing three different types of beads on a bracelet. How many ways can she use one bead of each type to string the next three beads? B) Nathan wants to order a sandwich with two of the following ingredients: mushroom, eggplant, tomato and avocado. How many different sandwiches can Nathan choose?

Factorial: A) Four people need to be selected from a class of 15 to help clean up campus. How many different ways can the 4 people be chosen?

Try: A basketball team has 12 members who can play any position. How many different ways can the coach choose 5 starting players?

Exit Slip: (on a half-sheet of scratch paper) A)Tell whether the set of events is independent or dependent and explain your answer: flipping two different coins and each coin landing showing heads B)Eight cards are numbered from 1 to 8 and placed in a box. ne card is selected at random and not replaced. Another card is randomly selected. What is the probability that both cards are greater than 5? C) You are ordering a triple-scoop ice-cream cone. There are 18 flavors to choose from and you dont care which flavor is on the top, middle, or bottom. How many different ways can you selected a triple-scoop ice-cream cone?

Day 18: Exponential Functions Goal: To evaluate, identify and graph exponential functions. Standard: 9.2.4.2 Represent relationships in various contexts using equations involving exponential functions; solve these equations graphically or numerically. Know how to use calculators, graphing utilities or other technology to solve these equations. Guiding Question: How can I graph, evaluate and identify exponential functions? Materials: Pencil, Folder, Student Packet

Conversions: How many feet are in 1.2 miles? "When converting make sure your labels cancel Time: "The short hand on the clock gives the hour, the long hand gives the minute" Find the perimeter: "Perimeter is the distance around an object" Reflection Starters: I know or I need to work on Math Review Day 18 Menta l Math

Access: Simplify each expression: A) 3 -2 B) 5 4 C) 2(3) 3 D) 2/3(3) 4

Exponential Function: A)The function f(x) = 500(1.035) x models the amount of money in a certificate of deposit after x years. How much money will there be in 6 years? B) The function f(x) = 200,000(0.98) x, where x is the time in years, models the population of a city. What will the population be in 7 years?

Try: The function f(x)= 1500 (0.995) x, where x is the time to years, models a prairie dog population. How many prairie dogs will there be in 8 years?

Tell whether each set of ordered pairs satisfies and exponential function. Explain your answer. A) {(-1, 1.5), (0, 3), (1, 6), (2, 12)} B) {(-1, -9), (1, 9), (3, 27), (5, 45)}

Try: Tell whether the set of ordered pairs satisfies an exponential function. Explain your answer: {(- 1, 1), (0, 0), (1, 1), (2, 4)}

Graph: A)y = -1/4 (2) x B)-1(1/4) x C) y = 4(0.6) x

Try: Graph A)y = -6 x B) y = 4(1/4) x

Exponential Growth: Exponential Decay: Compound Interest:

A)A sculpture is increasing in value at a rate of 8% per year, and its value in 2000 was $1200. Write an exponential growth function to model this situation. The find the sculpture's value in2006. B) Write a compound interest function to model the situation, then find the balance after the given number of years. $1200 invested at a rate of 3.5% compound quarterly; 4 years

Try: A)The original value of a painting is $9000 and the value increases by 7% each year. Write an exponential growth function to model this situation. Then find the painting's value in 15 years. B) The population of a town is decreasing at a rate of 3% per year. In 2000, there were 1700 people. Write an exponential decay function to model the situation. Then find the population in 2012.

General Forms of Functions: Linear: Quadratic: Exponential:

Look for a pattern in the data set to determine which model best describes the data:

Try:Look for a pattern in the data set to determine which model best describes the data:

Exit Slip (on a half-sheet of scratch paper) A)The function y = 11.6(1.009) x models residential energy consumption in quadrillion Btu where x is the number of years after 2003. What will residential energy consumption be in 2013? B) Graph y = -0.5(3) x C) What kind of model best describes the data set?

Day 19: Review Goal: To review the last 18 days in preparation for the Final! Standard: See Days 1 to 18. Guiding Question: How can I study for the Final? Materials: Pencil, Folder, Student Packet

Conversions: How many inches are in 5.5 feet? "When converting make sure your labels cancel Time: "The short hand on the clock gives the hour, the long hand gives the minute" Find the perimeter: "Perimeter is the distance around an object" Reflection Starters: I know or I need to work on Math Review Day 19 Menta l Math

Access: Look over your packet, exit slips, and notes. Create three questions you have still in this class?

Ask questions. - Teacher answer - Student answer - work in pairs to answer Do you need some work time to complete the packet? How can I study for the final?

Sample Problem for Final (this question is NOT on the final) Part I: Short Answer 1)Simplify the expression: 6 (8 + 1) x 9 3 Part II: Multiple Choice 1)Simplify the expression: 6 (8 + 1) x 9 3 A) -9 B) -21 C) -25 D) -3

Make 5 to 15 practice problems for a friend. Include the short answer and multiple choice. Trade to take home and study!

Exit Slip: (on a half-sheet of paper) Quick Write: How can I study for the test? How will I know I am prepared?

Day 20: Final Goal: To show what you have learned at summer school! Standard: See Days 1 to 18. Guiding Question: Will I pass this class? Materials: Pencil! GOOD LUCK!

Intermediate Algebra Summer School Credit Recovery.

Documents

Transcript of Intermediate Algebra Summer School Credit Recovery.