### All HSPT Math Resources

## Example Questions

### Example Question #1 : Algebra

If you rewrite the phrase "the product of nine and a number added to the sum of six and twice the number" as an algebraic expression, then *simplify* the expression, the result is:

**Possible Answers:**

**Correct answer:**

"The product of nine and a number" is . "Twice the number" is , and "The sum of six and twice the number" is .

"The product...added to the sum..." is ; simplify to get

### Example Question #2 : Algebra

Simplify the expression:

**Possible Answers:**

**Correct answer:**

### Example Question #1 : Algebra

Simplify:

**Possible Answers:**

**Correct answer:**

### Example Question #1 : How To Add Variables

**Possible Answers:**

**Correct answer:**

Add the numbers and keep the variable:

Answer:

### Example Question #2 : Algebra

**Possible Answers:**

**Correct answer:**

Add the numbers and keep the variable:

Answer:

### Example Question #1 : How To Add Variables

Simplify

**Possible Answers:**

Already simplified

**Correct answer:**

In order to add variables the terms must be like. In order for terms to be like, the variables must be exactly alike also being raised to the same power by the exponent.

In this case the like terms are and . Just because there is a 1 in the exponent for the first term doesnt mean it is different from the second term. With exponents if a variable does not show an exponent, that means it is still to the first power.

We add the coefficients of the like terms. The coefficient is the number in front of the first variable, in this case it is 1 for both terms because of the identity property of multiplication stating any variable, term, or number multiplied by 1 is itself.

Our last term is not like because the variable is raised to a different power than the other two. In this case we do not combine it to the like terms, we just add it to the end of the term.

### Example Question #1 : How To Add Variables

**Possible Answers:**

**Correct answer:**

Remember, for exponent problems, you group together different exponents and different combinations of variables as though each were a different type of variable. Therefore, you can group your problem as follows:

Now, just combine like terms:

### Example Question #21 : Variables

Simplify:

**Possible Answers:**

**Correct answer:**

You should begin by distributing through the *whole* group that it precedes:

Now, move your like variables next to each other:

Finally, combine the like terms:

### Example Question #1 : Algebra

Simplify:

**Possible Answers:**

**Correct answer:**

First, group together your like variables:

The only like variables needing to be combined are the x-variables. You can do this in steps or all at once:

### Example Question #3 : Algebra

Simplify:

**Possible Answers:**

**Correct answer:**

First, move the like terms to be next to each other:

Now, combine the x-variables and the y-variables:

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