HiSET: Math : Algebraic Concepts

Study concepts, example questions & explanations for HiSET: Math

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Example Questions

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Example Question #1 : Algebraic Concepts

Identify the terms in the following equation:

Possible Answers:

All of these

Correct answer:

All of these

Explanation:

In an equation, a term is a single number or a variable. in our equation we have the following terms:

Example Question #1 : Algebraic Concepts

How many terms are in the following expression: ?

Possible Answers:

None of the Above

Correct answer:

Explanation:

Step 1: We need to separate and arrange the terms in the jumbled expression given to us in the question..

We will separate the terms by the exponent value.

For , there is only one term: 

For , there are no terms.

For , there is two terms: 

For , there are two terms: 

For , there are two terms: 

For , there is only one term: 

For , there are two terms: 

For , there are three terms: 

There are four constant terms: 

Step 2: We will now add up the coefficients in each designation of terms. This will give us the answer.

 

Example Question #1 : Algebraic Concepts

Simplify the polynomial

.

How many terms does the simplified form have?

Possible Answers:

Four

Six

Three

Two

Five

Correct answer:

Four

Explanation:

Arrange and combine like terms (those with the same variable) as follows:

Since each term now has a different exponent for the variable, no further combining is possible. The simplified form has four terms.

Example Question #2 : Algebraic Concepts

Identify the coefficients in the following formula:

Possible Answers:

All of these

Correct answer:

All of these

Explanation:

Generally speaking, in an equation a coefficient is a constant by which a variable is multiplied. For example,  and  are coefficients in the following equation:

In our equation, the following numbers are coefficients:

Example Question #1 : Algebraic Concepts

What is the coefficient of the second highest term in the expression: ?

Possible Answers:

Correct answer:

Explanation:

Step 1: Rearrange the terms from highest power to lowest power. 

We will get: .

Step 2: We count the second term from starting from the left since it is the second highest term in the rearranged expression.

Step 3: Isolate the term.

The second term is 

Step 4: Find the coefficient. The coefficient of a term is considered as the number before any variables. In this case, the coefficient is .

So, the answer is .

Example Question #1 : Perform Arithmetic Operations

Add these two expressions together:  and .

Possible Answers:

Correct answer:

Explanation:

Step 1: Add the terms based on their similarities...

 and  becomes .

 and  becomes .

 and  becomes 

Step 2: Combine all the terms after "becomes" in step 1...

We add and get: .

Example Question #1 : Algebraic Concepts

Subtract  and .

Possible Answers:

Correct answer:

Explanation:

Step 1: Subtract these terms by separating by exponents...

Step 2: Add all the simplified terms together...

Example Question #1 : Algebraic Concepts

Add or subtract: 

Possible Answers:

Correct answer:

Explanation:

Step 1: Find the Least Common Denominator of these fraction. We will list out multiples of each denominator until we find a common number for all three fractions...

The smallest common denominator is .

Step 2: Since the denominator is , we will convert all denominators to .

 

Step 3: Add up all the values of x...

Step 4: The result from step  is the numerator and  is the denominator. We will put these together.

Final Answer: 

 

Example Question #1 : Understand And Apply Concepts Of Expressions

A quadratic function has two zeroes, 3 and 7. What could this function be?

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

Explanation:

A polynomial function with zeroes 3 and 7 has as its factors and . The function is given to be quadratic, so this function is

.

Apply the FOIL method to rewrite the polynomial:

Collect like terms:

,

the correct choice.

 

Example Question #1 : Understand And Apply Concepts Of Equations

Solve. 

Possible Answers:

Correct answer:

Explanation:

In order to solve for the variable, , we need to isolate it on the left side of the equation. We will do this by reversing the operations done to the variable by performing the opposite of each operation on both sides of the equation. 

Let's begin by rewriting the given equation.

Subtract  from both sides of the equation.

Simplify.

Multiply both sides of the equation by .

Solve.

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