### All Algebra 1 Resources

## Example Questions

### Example Question #2 : Counting / Sets

The sum of three consecutive even integers equals 72. What is the product of these integers?

**Possible Answers:**

12144

13728

10560

13800

17472

**Correct answer:**

13728

Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72.

x + (x + 2) + (x + 4) = 72

3x + 6 = 72

3x = 66

x = 22.

This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728.

The answer is 13728.

### Example Question #1 : Counting / Sets

**Possible Answers:**

**Correct answer:**

### Example Question #1 : How To Find The Missing Number In A Set

If the mean of the following set is 12, what is ?

(1,14,3,15,16,,21,10)

**Possible Answers:**

**Correct answer:**

Since we are given the mean, we need to find the sum of the numbers. From there we can figure out . We know

We can use this to find the sum by plugging in

So our sum is 96.

So we know that our total sum minus the sum of the given numbers is equal to .

So, .

### Example Question #2 : How To Find The Missing Number In A Set

There are 5 men and 4 women competing for an executive body consisting of :

- President
- Vice President
- Secretary
- Treasurer

It is required that 2 women and 2 men must be selected

How many ways the executive body can be formed?

**Possible Answers:**

**Correct answer:**

2 men can be selected:

2 women can be selected out of 4 women:

Finally, after the selection process, these men and women can fill the executive body in ways.

This gives us a total of

### Example Question #83 : Summations And Sequences

Which number is needed to complete the following sequence:

1,5,_,13,17

**Possible Answers:**

**Correct answer:**

This is a sequence that features every other positive, odd integers. The missing number in this case is 9.

### Example Question #2 : How To Find The Missing Number In A Set

Find the missing number:

**Possible Answers:**

**Correct answer:**

Find the missing number:

To find the missing number, we need to find the pattern.

If we look closely, our numbers are going up by the same number each time: 13

To check this, find the difference between neighboring numbers

You get the idea.

So, to find the missing number, simply do the following:

### Example Question #3 : How To Find The Missing Number In A Set

Find n in the following sequence:

**Possible Answers:**

**Correct answer:**

You need to evaluate the terms in the sequence to determine the pattern that is shown. In this case, the first term is multiplied by 2 and the second term is found by adding 3.

### Example Question #5 : How To Find The Missing Number In A Set

The first four numbers in the following set are parabolic: . What must the missing numbers, respectively?

**Possible Answers:**

**Correct answer:**

Notice that the world parabolic is given. This means that our parent function will be in the form:

The terms resemble a pattern where the parent function is centered at , and the first term starts at and so forth.

We can find the two missing terms by substituting to determine the missing numbers.

The first number is:

The second number is:

The respective numbers are:

### Example Question #6 : How To Find The Missing Number In A Set

Find the missing numbers in the set of numbers:

**Possible Answers:**

**Correct answer:**

Notice that the second and third terms in the set of numbers can be subtracted to determine the displacement of each number in the set.

Subtract negative three from one. Enclose the negative number with parentheses.

Each number is spaced four units.

Subtract four from negative three to find the first number.

Add four to one to find the number for the second question mark.

This number is also four units from nine.

The answer is:

### Example Question #7 : How To Find The Missing Number In A Set

Find the missing numbers, respectively:

**Possible Answers:**

**Correct answer:**

Determine the distance between each number.

The second and the third number are spaced units.

Check the third and fourth number if this is also has the same displacement.

Since this is true, this means that the numbers are also spaced at units.

Notice the fractions are in decreasing order.

Add units to the second term to obtain the first term.

Reduce this fraction.

The first term is:

Subtract units from to obtain the fifth term.

Reduce this fraction.

The fifth term is:

The correct answer is:

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