### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #1 : Algebraic Concepts

Solve for x:

**Possible Answers:**

**Correct answer:**

First, subtract 4 from both sides:

Next, divide both sides by 3:

Now take the square root of both sides:

### Example Question #1 : Algebraic Concepts

Solve for :

**Possible Answers:**

**Correct answer:**

### Example Question #1 : Algebraic Concepts

Solve for :

**Possible Answers:**

**Correct answer:**

Rewrite this as a compound statement and solve each separately:

### Example Question #1 : Algebraic Concepts

Solve for :

**Possible Answers:**

**Correct answer:**

FOIL each of the two expressions, then solve:

Solve the resulting linear equation:

### Example Question #2 : Algebraic Concepts

Solve for :

**Possible Answers:**

**Correct answer:**

First, rewrite the quadratic equation in standard form by moving all nonzero terms to the left:

Now factor the quadratic expression into two binomial factors , replacing the question marks with two integers whose product is and whose sum is . These numbers are , so:

or

The solution set is .

### Example Question #1 : Algebraic Concepts

Solve for :

**Possible Answers:**

**Correct answer:**

First, rewrite the quadratic equation in standard form by FOILing out the product on the left, then collecting all of the terms on the left side:

Use the method to factor the quadratic expression ; we are looking to split the linear term by finding two integers whose sum is and whose product is . These integers are , so:

Set each expression equal to 0 and solve:

or

The solution set is .

### Example Question #2 : Algebraic Concepts

Solve for :

Give all solutions.

**Possible Answers:**

**Correct answer:**

Rewrite this quadratic equation in standard form:

Factor the expression on the left. We want two integers whose sum is and whose product is . These numbers are , so the equation becomes

.

Set each factor equal to 0 separately, then solve:

### Example Question #1 : How To Find The Solution To An Equation

Solve for :

**Possible Answers:**

The equation has the set of all real numbers as its solution set.

The equation has no solution.

**Correct answer:**

Simplify both sides, then solve:

### Example Question #1 : How To Find The Solution To An Equation

**Possible Answers:**

The equation has no solution.

The equation has the set of all real numbers as its solution set.

**Correct answer:**

The equation has the set of all real numbers as its solution set.

Simplify both sides, then solve:

This is an identically true statement, so the original equation has the set of all real numbers as its solution set.

### Example Question #10 : Algebraic Concepts

Solve for :

**Possible Answers:**

**Correct answer:**

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