NC Check-In 2 Review

NC Check-In 2 Review

Probability

• Recall: Probability = something happening ÷ total happenings

• Example: I have a bag of 10 marbles: 6 white, 3 red, and 1 blue. The probability of me choosing a blue marble at random is 1/10.

• An impossible event has a probability of 0.

• A certain event has the probability of 100% or 1.

Multiple Choice

Your teacher is letting you choose a candy from a bag. You cannot see the candies. What is the probability of choosing a non-chocolate candy?

• 4/20

• 3/20

• 2/20

• 1/20

Multiple Choice

Flipping a coin AND rolling a die is an example of what kind of event?

• Probability

• Simple

• Compound

• Tree Diagram

Multiple Choice

I roll a fair 6-sided die 50 times. What is the probability that I rolled an even number?

• 1/2

• 10

• 25

• 50

Multiple Choice

You flip 2 coins. What is the probability of the coin landing on heads twice?

• 1/4

• 2/4

• 3/4

• 4/4

Rational numbers

• When adding/subtracting/multiplying/dividing rational numbers, remember that all the numbers must be in the same form (either fractions OR decimals).

• Rational numbers can be fractions OR decimals. [Rational = Ratio]

• Either repeating or terminating decimals have a fraction form.

Multiple Select

Which of these fractions are repeating decimals? There may be more than one answer.

• 1/4

• 2/7

• 1/8

• 1/3

Multiple Choice

Three rock climbers started a climb with each person carrying 8kg of climbing equipment. A fourth climber joins them that wasn't carrying any equipment. The group decides to distribute the equipment equally amongst the group. How much equipment is each climber carrying now?

• 2 kg

• 4 kg

• 6 kg

• 8 kg

Multiple Choice

Your teacher gave a test with 50 questions, each worth the same amount of points. Donovan got 39 out of 50 questions correct. Marci's score was 10 percentage points higher than Donovan's. What was Marci's score?

• 39%

• 49%

• 78%

• 88%

Algebraic Expressions

• Expressions can be added or subtracted by rearranging terms to combine like terms

• You can undo the distributive property by finding the greatest common factor of each term in an expression

Multiple Choice

Which of these are equivalent to 2x + 6?

• 2(x + 6)

• x(2 + 6)

• 6(x + 2)

• 2(x + 3)

Multiple Select

Which of these expressions are equivalent to

 $x^2\ +\ x\ +\ 3$  ? More than one choice may be correct.

•  $2x^2\ -\ \left(x^2\ +\ x\right)\ +\ 2x\ +\ 3$  

•  $3\left(x^2\ +\ x\right)$  

•  $4\left(x^2-2x+6\right)-3\left(x^2-3x+7\right)$  

•  $x^2\ +\ x\ -3\left(x^2\ +\ x\ +3\right)$  

Multiple Choice

Which of these is equivalent to

 $10x\ +\ 15y\ -\ 25z$  

•  $15\left(x\ +\ y\ -\ z\right)$  

•  $5\left(2x\ +\ 3y\ -\ 5z\right)$  

•  $5\left(x\ +\ y\ -\ z\right)$  

•  $10\left(x\ +\ y\ +\ z\right)$  

Proportions

• Recall: two things are proportional if they simplify to the same ratio

• You can compare tables, graphs, or equations for proportionality by checking for ratios individually.

Checking a table for proportions

To determine if a table is proportional, you divide each y number by the x number and reduce.

For this table:

10/1 = 10

20/2 = 10

70/7 = 10

100/10 = 10

This table is proportional.

Multiple Choice

Is this table proportional?

• Yes

• No

Checking an Equation for Proportionality

An equation show proportionality IF it is the form of y = kx, where k is the constant of proportionality.

The equation y = 2x is proportional, with a k = 2.

The equation y = 2x + 3 is NOT proportional.

Constant of Proportionality

A constant of proportionality is the ratio between 2 proportional quantities. We call this value k. For this table, the constant of proportionality is the ratio of y/x, which is 10.

Multiple Choice

What is the constant of proportionality for this table?

• $-7$

• $-\frac{1}{7}$

• $\frac{1}{7}$

• This table is not proportional.

Checking a graph for proportionality

A graph is proportional if it shows a straight line AND goes through the origin.

This graph shows a straight line. It will pass through the origin, so it is proportional.

Multiple Choice

Is this graph proportional? If yes, what is the constant of proportionality?

• Yes, with a k = 3

• Yes, with a k = 1/3

• Yes, with a k = -3

• Not proportional

Multiple Choice

Is this graph proportional? If yes, what is the constant of proportionality?

• Yes, with a k = -1/5

• Yes, with a k = 1/5

• Yes, with a k = 5

• Not proportional

Checking an Equation for Proportionality

An equation show proportionality IF it is the form of y = kx, where k is the constant of proportionality.

The equation y = 2x is proportional, with a k = 2.

The equation y = 2x + 3 is NOT proportional.

Multiple Select

Which of these equations are proportional? More than one answer may be correct.

• $y\ =\ \frac{2}{3}x\ +\ 5$

• $y\ =\ x^2$

• $y\ =\ -\frac{1}{2}x$

• $y\ =\ 5$

Multiple Choice

Which of the following is proportional to the equation

 $y\ =\ \frac{1}{2}x$  ?

Multiple Select

Which of the following are proportional?

• $y\ =\ -x$

Multiple Choice

I went to an ice cream shop and was able to choose from the following:

flavors: chocolate/vanilla

sauce: strawberry/hot fudge

toppings: whipped cream/peanuts

What is the probability of me choosing a chocolate ice cream with hot fudge and peanuts, if I choose each at random?

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{1}{6}$

• $\frac{1}{8}$

Multiple Choice

Which fraction is equivalent to the decimal

 $0.\overline{1}$  ? 

• 1/5

• 1/7

• 1/9

• 1/11

Multiple Choice

What is the GCF of the following numbers: 12x, 14x, 16x ?

• x

• 2

• 2x

• 4x