# MAP 7th Grade Math : MAP 7th Grade Math

## Example Questions

### Example Question #1 : Statistics And Probability

Kelly spun a spinner, which is pictured below,  times. She recorded her results in the table provided. What is the experimental probability of the spinner landing on the yellow section?

Explanation:

The experimental probability is what actually happened in an experiment. In this case, Kelly spun the spinner  times, and she landed on yellow  times; thus, our experimental probability is

### Example Question #2 : Statistics And Probability

Samantha has a bag of marbles containing  pink marbles,  orange marble,  red marbles,  purple marbles,  white marbles,  black marble,  green marbles, and  yellow marble. What is the probability that Samantha will pick a red marble out of the bag?

Explanation:

In this problem we have a total of  marbles. That means that each marble, regardless of color, has a  chance of being picked, as shown in the images below. This image shows equal probability because each marble has a  chance of being drawn, which is equal to the probability of all of the other marbles.

Samantha wants to know what her probability is of drawing a red marble out of her bag. Remember, probability is the number of favorable outcomes over the total number of outcomes:

For this problem there are  red marbles; therefore,

### Example Question #3 : Statistics And Probability

A university wanted to compare the heights of women on the basketball team and women on the swim team. The data is in the dot plots provided.

Using the dot plots provided, what is the mean absolute deviation of the height of basketball players, rounded to the nearest tenth?

Explanation:

The mean absolute deviation is the average distance between each data point and the mean. So the first step to solving for the mean absolute deviation is to solve for the mean.

The mean is the average of a data set. In order to solve for the mean, we add all of our heights together, and divide by the number of people in our data set.

Next, we subtract to find the distance between each data point and , which is shown in the following table:

Now that we have all of the distances from the mean, we find the average of those differences to find the mean absolute deviation:

### Example Question #1 : Geometry

What is the area of the circle provided?

Explanation:

In order to solve this problem, we need to recall the formula for the area of a circle:

The circle in this question provides us with the radius, so we can use the formula to solve:

Solve:

### Example Question #1 : Geometry

The figure represents a set of complementary angles, solve for .

Explanation:

Complementary angles are defined as two angles that when added together equal

From the question, we know that the two angles are complimentary, and thus equal , so we can set up the following equation:

Next we can solve for :

### Example Question #3 : Geometry

Calculate the volume of the provided figure.

Explanation:

In order to solve this problem, we need to recall the volume formula for a cube:

Now that we have the correct formula, we can substitute in our known values and solve:

### Example Question #1 : The Real And Complex Number Systems

If a server at a restaurant gets a  tip on a bill of , then what will be the amount of the tip?

Explanation:

The first step to solving this problem is determining what operation we are going to use.

Think:we know that the tip is going to be  of .  The keyword "of" gives us a clue and indicates that we are going to multiply.

As we have learned in previous lessons, we need to convert our percentage into a decimal before we are able to multiply:

Next, we can perform the multiplication operation and find the tip:

The server's tip will be

### Example Question #1 : The Real And Complex Number Systems

Solve:

Explanation:

In order to solve this problem, we need to start at  on the number line.

Next, we have  which means we need to move  places to the right on the number line. When we have an addition sign   we move to the right because that is towards the positive side of the number line. When we have a subtraction sign  we move to the left because that is towards the negative side of the number line.

The orange arrow moved  places to the right, and ended at ; thus,

### Example Question #3 : The Real And Complex Number Systems

Does the table provided show a direct proportional relationship? If so, then identify the proportion.

Yes,

No

Yes,

Yes,

Yes,

Explanation:

In order to determine whether or not the table shows a direct proportion, we will divide the quantities in the  coordinate column by the quantities in the  coordinate column. In order for the table to show direct proportion, each quotient should be the same value.

In this example, each quotient is the same value; therefore, this table does show direct proportion.

The proportion is

### Example Question #1 : Operations And Algebraic Thinking

Elizabeth is going to buy concert tickets. The concert tickets costs  plus a  sales tax. What is the total price that Elizabeth will pay for her concert tickets?

Explanation:

We know that Elizabeth is going to pay  of the  concert because that is the total cost. Plus, she is going to pay  of the  because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

Next, we can write a numeric expression and solve: