Standard:Number and Quantity
#1. Cassie is measuring the dimensions of her bedroom wall so that she will know how much paint to buy. Which of the choices shown is a reasonable measurement for a wall in her bedroom?
*Answer -10 feet by 22 feet
#2.Choose the situation in which the use of exact numbers is appropriate.
*Answer -paying your power bill
#3. The area of a city is commonly measured in
*Answer -square miles.
Video: http://mathispower4u.wordpress.com/
#1. Cassie is measuring the dimensions of her bedroom wall so that she will know how much paint to buy. Which of the choices shown is a reasonable measurement for a wall in her bedroom?
*Answer -10 feet by 22 feet
#2.Choose the situation in which the use of exact numbers is appropriate.
*Answer -paying your power bill
#3. The area of a city is commonly measured in
*Answer -square miles.
Video: http://mathispower4u.wordpress.com/
Standard:Algebra
#1. Solve for x:
−2x - 8 = −6x + 4
Answer- x=3
#2. Solve for d.
d - 2d - 3 = 1-m
Answer: d = 2m + 3m + 1
#3. Brandon is baking cookies for a school bake sale. If he can make 2 dozen cookies in 23 minutes which is a reasonable estimate of the amount of time it will take him to make 12 dozen cookies?
Answer- between 2 and 3 hours
Video: https://www.youtube.com/watch?v=ZGJU7aqE3mY
#1. Solve for x:
−2x - 8 = −6x + 4
Answer- x=3
#2. Solve for d.
d - 2d - 3 = 1-m
Answer: d = 2m + 3m + 1
#3. Brandon is baking cookies for a school bake sale. If he can make 2 dozen cookies in 23 minutes which is a reasonable estimate of the amount of time it will take him to make 12 dozen cookies?
Answer- between 2 and 3 hours
Video: https://www.youtube.com/watch?v=ZGJU7aqE3mY
standard: Functions
#1. Jeremy bought a new truck for $32,000. The value of the truck after t years can be represented by the formula V = 32,000(.8)t. When will the truck be worth approximately $6700?
Answer- in 7 years
#2. If there is 520 grams of radioactive material with a half-life of 12 hours, how much of the radioactive material will be left after 72 hours and is the radioactive decay modeled by a linear function or an exponential function?
Answer-8.125 grams exponential
#3. Anthony will be competing in a body building competition in 12 months. He initially weighs 160 pounds and by the end of 12 months weighs 232 pounds.
What is the approximate rate of change in Anthony's body weight?
Answer: 6 pounds per month
Video: https://www.youtube.com/watch?v=mDwN1SqnMRU
#1. Jeremy bought a new truck for $32,000. The value of the truck after t years can be represented by the formula V = 32,000(.8)t. When will the truck be worth approximately $6700?
Answer- in 7 years
#2. If there is 520 grams of radioactive material with a half-life of 12 hours, how much of the radioactive material will be left after 72 hours and is the radioactive decay modeled by a linear function or an exponential function?
Answer-8.125 grams exponential
#3. Anthony will be competing in a body building competition in 12 months. He initially weighs 160 pounds and by the end of 12 months weighs 232 pounds.
What is the approximate rate of change in Anthony's body weight?
Answer: 6 pounds per month
Video: https://www.youtube.com/watch?v=mDwN1SqnMRU
Algebra Connections to Geometry
#1. Defined by distinct lines which intersect at right angles and at exactly one point.
Answer-perpendicular lines
#2. Write an equation of the line that is perpendicular to 5x + 20y = 10 and passes through the point (8, 3).
Answer- y = 4x - 29
#3. Which transformation will be equivalent to rotating a figure 180° counterclockwise?
Answer-reflecting over the x-axis and the y-axis.
Videos: https://www.youtube.com/watch?v=aU6PFx72874
#1. Defined by distinct lines which intersect at right angles and at exactly one point.
Answer-perpendicular lines
#2. Write an equation of the line that is perpendicular to 5x + 20y = 10 and passes through the point (8, 3).
Answer- y = 4x - 29
#3. Which transformation will be equivalent to rotating a figure 180° counterclockwise?
Answer-reflecting over the x-axis and the y-axis.
Videos: https://www.youtube.com/watch?v=aU6PFx72874
Algebra Connections To Statistics And Probability
#1. Anna has decided to purchase a small car with a small gas tank. If x represents the number of miles driven, which linear function would best model the gas mileage that Anna can expect from her new car?
Answer- y = 10 - 0.05x
#2. Coach Woods made a comparison of Geometry quiz scores in his 2nd and 4th period classes:
2nd period 4th period
Mean..................... 13 13
Median................... 13 14
Mode................ 12 and 13 16
Range.................... 15 14
Standard deviation... 4.3 6.72
What can Coach Woods conclude about the comparison of quiz scores?
Answer: There was more variation in scores for 4th period.
#3. The population, in millions, of a city t years after 1990 is given by the equation P(t) = 2.9 + 0.08t. In this function,
Answer- 2.9 million is the population of the city in 1990 and 0.08 million is the increase per year in the population.
Videos: https://www.youtube.com/watch?v=AzM9rAhAaSc
#1. Anna has decided to purchase a small car with a small gas tank. If x represents the number of miles driven, which linear function would best model the gas mileage that Anna can expect from her new car?
Answer- y = 10 - 0.05x
#2. Coach Woods made a comparison of Geometry quiz scores in his 2nd and 4th period classes:
2nd period 4th period
Mean..................... 13 13
Median................... 13 14
Mode................ 12 and 13 16
Range.................... 15 14
Standard deviation... 4.3 6.72
What can Coach Woods conclude about the comparison of quiz scores?
Answer: There was more variation in scores for 4th period.
#3. The population, in millions, of a city t years after 1990 is given by the equation P(t) = 2.9 + 0.08t. In this function,
Answer- 2.9 million is the population of the city in 1990 and 0.08 million is the increase per year in the population.
Videos: https://www.youtube.com/watch?v=AzM9rAhAaSc
Interpret Differences
72, 80, 74, 68, 65, 66, 72, 70, 65, 80, 75
#1. Jennifer's recent golf scores are shown. What is her mean score, rounded to the nearest tenth?
Answer: 71.5
#2. A student scored an 88, 92, and 76 on three math tests. What does the student need to get on the fourth test to have an average of 85 for all four tests?
James wants to use algebra to solve this problem. Which equation should he use?
Answer- 256 + x4 = 85 <---------Fraction
#3. For a specific type of machine part being produced, the diameter is normally distributed, with a mean of 15.000 cm and a standard deviation of 0.030 cm. Machine parts with a diameter more than 2 standard deviations away from the mean are rejected.
If 15,000 machine parts are manufactured, how many of these will be rejected?
Answer: 2
Videos: https://www.youtube.com/watch?v=_hFrXUGgDf8
72, 80, 74, 68, 65, 66, 72, 70, 65, 80, 75
#1. Jennifer's recent golf scores are shown. What is her mean score, rounded to the nearest tenth?
Answer: 71.5
#2. A student scored an 88, 92, and 76 on three math tests. What does the student need to get on the fourth test to have an average of 85 for all four tests?
James wants to use algebra to solve this problem. Which equation should he use?
Answer- 256 + x4 = 85 <---------Fraction
#3. For a specific type of machine part being produced, the diameter is normally distributed, with a mean of 15.000 cm and a standard deviation of 0.030 cm. Machine parts with a diameter more than 2 standard deviations away from the mean are rejected.
If 15,000 machine parts are manufactured, how many of these will be rejected?
Answer: 2
Videos: https://www.youtube.com/watch?v=_hFrXUGgDf8
Know Definitions
#1. Define parallel lines.
Answer: Lines in the same plane that never intersect.
#2. Defined by distinct lines which intersect at right angles and at exactly one point.
Answer:perpendicular lines
#3. What is the locus of all points that are a fixed distance from a given point?
Answer: circle
Videos: https://www.youtube.com/watch?v=pFGcMIL2NVo
#1. Define parallel lines.
Answer: Lines in the same plane that never intersect.
#2. Defined by distinct lines which intersect at right angles and at exactly one point.
Answer:perpendicular lines
#3. What is the locus of all points that are a fixed distance from a given point?
Answer: circle
Videos: https://www.youtube.com/watch?v=pFGcMIL2NVo
Use Coordinates For Theorems
#1 .The points (5, 3), (3, -4), (10, 3), and (8, -4) are the vertices of a polygon. What type of polygon is formed by these points?
Answer: Parallelogram
#2. Could the points (-4,3), (-1,1) and (1,3) form the vertices of a right triangle? Why or why not?
Answer: No, a2 + b2 ≠ c2.
#3.On a coordinate grid, the movie theater is located at (0,0) and the mall is located at (4,3). If the bowling alley is located at the midpoint between the theater and the mall, what is the approximate distance from the bowling alley to the mall? (Note: 1 unit equals 1 mile)
Answer: 2.5 miles
Videos: https://www.youtube.com/watch?v=UPIBssMqsA8
#1 .The points (5, 3), (3, -4), (10, 3), and (8, -4) are the vertices of a polygon. What type of polygon is formed by these points?
Answer: Parallelogram
#2. Could the points (-4,3), (-1,1) and (1,3) form the vertices of a right triangle? Why or why not?
Answer: No, a2 + b2 ≠ c2.
#3.On a coordinate grid, the movie theater is located at (0,0) and the mall is located at (4,3). If the bowling alley is located at the midpoint between the theater and the mall, what is the approximate distance from the bowling alley to the mall? (Note: 1 unit equals 1 mile)
Answer: 2.5 miles
Videos: https://www.youtube.com/watch?v=UPIBssMqsA8
Correlation And Causation
For 10 weeks Dolly wrote down everything she ate as well as weighed herself each morning. For two separate weeks during the 10 week period when her car was broken down and she was walking to work she was running late each day so she did not have a chance to write down what she ate.
At the end of the 10 weeks she graphed her weight over time and noticed that for the two weeks she didn't write down anything she lost weight. She concluded that for this experiment NOT writing down what she ate would help her lose weight.
#1. Which mistake did Dolly have in her conclusion?
Answer: Confusing causation with correlation.
#2. Which statement is TRUE?
Answer:A correlation does not establish a causal relationship.
#3.Susie gains more weight over Christmas than any other time of the year. Christmas makes Susie gain weight. This conclusion is
Answer: not justifiable, because there is another variable to consider.
Video: https://www.youtube.com/watch?v=5zyruPbgxyM
For 10 weeks Dolly wrote down everything she ate as well as weighed herself each morning. For two separate weeks during the 10 week period when her car was broken down and she was walking to work she was running late each day so she did not have a chance to write down what she ate.
At the end of the 10 weeks she graphed her weight over time and noticed that for the two weeks she didn't write down anything she lost weight. She concluded that for this experiment NOT writing down what she ate would help her lose weight.
#1. Which mistake did Dolly have in her conclusion?
Answer: Confusing causation with correlation.
#2. Which statement is TRUE?
Answer:A correlation does not establish a causal relationship.
#3.Susie gains more weight over Christmas than any other time of the year. Christmas makes Susie gain weight. This conclusion is
Answer: not justifiable, because there is another variable to consider.
Video: https://www.youtube.com/watch?v=5zyruPbgxyM
Rearrange Formulas
#1. Given F = Gm1m2d, solve for G. <-------- Fraction
Answer:G = dFm1m2<------- Fraction
#2. Given A = 12(b1 + b2)h, solve for h. <-------- Fraction
ANswer: h = 2Ab1 + b2 <-------- Fraction
#3. The formula for the circumference of a circle is C = 2πr. Use this formula to write a formula for the RADIUS of a circle.
Answer: r = C2π
#1. Given F = Gm1m2d, solve for G. <-------- Fraction
Answer:G = dFm1m2<------- Fraction
#2. Given A = 12(b1 + b2)h, solve for h. <-------- Fraction
ANswer: h = 2Ab1 + b2 <-------- Fraction
#3. The formula for the circumference of a circle is C = 2πr. Use this formula to write a formula for the RADIUS of a circle.
Answer: r = C2π
Use Units
#1. Lauren is building a tree house with her dad. The dimensions of the floor are 9 feet by 6 feet. What is the area of the floor, measured in square yards?
Answer: 6 square yards
#2. Every substance has a specific value of heat required to change the temperature of 1 gram of the substance by 1 degree Celsius. Specific heat is found by using the equation Q=mcΔt, where Q represents heat in joules, m represents mass in grams, Δt is the change in temperature in Celsius, and c is the coefficient constant for a substance. Find the units for the coefficient c.
Answer: c=J/g·°C
#3. Change 27 centimeters to millim?eters.
Answer: 270 mm
#1. Lauren is building a tree house with her dad. The dimensions of the floor are 9 feet by 6 feet. What is the area of the floor, measured in square yards?
Answer: 6 square yards
#2. Every substance has a specific value of heat required to change the temperature of 1 gram of the substance by 1 degree Celsius. Specific heat is found by using the equation Q=mcΔt, where Q represents heat in joules, m represents mass in grams, Δt is the change in temperature in Celsius, and c is the coefficient constant for a substance. Find the units for the coefficient c.
Answer: c=J/g·°C
#3. Change 27 centimeters to millim?eters.
Answer: 270 mm
Descriptive Modeling
#1. You need to install a new air conditioner in your house. To determine what size you need the company asks you the size of your house. What units of measure should you use when stating the size?
Answer: square feet
#2. If you were to measure the volume of an ice cube in your freezer, what would be a reasonable unit to use?
Answer: cubic inches
#3. Which equation describes the proportion: The number of chickens (c) is four times as many the number of horses (h) on the farm.?
Answer: c = 4h
#1. You need to install a new air conditioner in your house. To determine what size you need the company asks you the size of your house. What units of measure should you use when stating the size?
Answer: square feet
#2. If you were to measure the volume of an ice cube in your freezer, what would be a reasonable unit to use?
Answer: cubic inches
#3. Which equation describes the proportion: The number of chickens (c) is four times as many the number of horses (h) on the farm.?
Answer: c = 4h
Complicated Expressions
#1. If Christopher consumed 600 calories by drinking x number of sodas, which expression represents the number of calories in each soda?
Answer: 600x <----- Fraction
#2. (3 + 4i) (7 + 8i)
Answer: -11 + 52i
#3. Which of the inequalities represents the statement "the absolute value of the difference of x and y is greater than 5"?
Answer: |x - y| > 5
#1. If Christopher consumed 600 calories by drinking x number of sodas, which expression represents the number of calories in each soda?
Answer: 600x <----- Fraction
#2. (3 + 4i) (7 + 8i)
Answer: -11 + 52i
#3. Which of the inequalities represents the statement "the absolute value of the difference of x and y is greater than 5"?
Answer: |x - y| > 5
Standard: Linear Equation
#1. What is the value of x when x + 7 = 21?
ANswer: 14
#2. How many solutions does this equation have?
8x + 7 – 3x = 5 + 5x + 2
Answer: infinitely many solutions
#3. Solve: -12 = 5x
Answer: -2.4
#1. What is the value of x when x + 7 = 21?
ANswer: 14
#2. How many solutions does this equation have?
8x + 7 – 3x = 5 + 5x + 2
Answer: infinitely many solutions
#3. Solve: -12 = 5x
Answer: -2.4
Standard: Create Equation
#1.
#1.