ISEE Upper Level Math : How to find the solution to an equation

Study concepts, example questions & explanations for ISEE Upper Level Math

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Example Questions

Example Question #81 : Algebraic Concepts

What is  ?

Possible Answers:

 can be any real number.

Correct answer:

Explanation:

Add the left and right sides of the equations separately:

  

 

Divide:

Example Question #82 : Algebraic Concepts

Give the -intercept of the line through points  and .

Possible Answers:

The line has no -intercept.

Correct answer:

Explanation:

The slope of this line is 

.

Let the -intercept be . Then, using the slope and point , we know that:

Take the reciprocal of both sides:

The -intercept is .

Example Question #81 : Algebraic Concepts

A line through points  and  has slope . What is ?

Possible Answers:

Correct answer:

Explanation:

Substitute  into the slope formula:

Example Question #781 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Give the -intercept of the line through points  and .

Possible Answers:

The line has no -intercept.

Correct answer:

Explanation:

The slope of this line is 

.

Let the -intercept be . Then, using the slope and point , we know that:

The -intercept is .

Example Question #81 : How To Find The Solution To An Equation

Give the -intercept of the line of the equation: 

Possible Answers:

The line has no -intercept.

Correct answer:

Explanation:

Substitute :

The -intercept is .

Example Question #782 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Solve for , giving all real solutions:

Possible Answers:

The equation has no real solution.

Correct answer:

Explanation:

Substitute  and, subsequently, .

Factor as , replacing the two question marks with integers whose product is  and whose sum is . These integers are , so

.

Break this up into two equations, replacing  for  in each:

or 

Example Question #782 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Give the -intercept of the line through points  and .

Possible Answers:

The line has no -intercept.

Correct answer:

The line has no -intercept.

Explanation:

The slope of this line is 

.

A line with slope 0 is horizontal, and therefore has no -intercept. 

Example Question #82 : How To Find The Solution To An Equation

What is ?

 

Possible Answers:

Correct answer:

Explanation:

Substitute  into the second equation:

Example Question #784 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Solve for , giving all real solutions:

Possible Answers:

The equation has no real solutions.

Correct answer:

Explanation:

Write the equation in standard form:

 can be factored out of each term:

Factor the trinomial by writing , replacing the question marks with two integers with product  and sum . These integers are , so the above becomes

.

We can disregard the , as it does not contribute a solution. Set each of the other two factors equal to and solve separately:

The solution set is .

Example Question #83 : Algebraic Concepts

For what value of is ?

 

Possible Answers:

Correct answer:

Explanation:

We need to use logarithms.

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