ISEE Upper Level Quantitative : How to multiply exponential variables

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

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Example Questions

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Example Question #1 : How To Multiply Exponential Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #2 : How To Multiply Exponential Variables

Expand: 

Possible Answers:

Correct answer:

Explanation:

A binomial can be cubed using the pattern:

Set 

Example Question #3 : How To Multiply Exponential Variables

Factor completely:

Possible Answers:

Correct answer:

Explanation:

A trinomial whose leading term has a coefficent other than 1 can be factored using the -method. We split the middle term using two numbers whose product is  and whose sum is . These numbers are , so:

Example Question #4 : How To Multiply Exponential Variables

Multiply:

Possible Answers:

Correct answer:

Explanation:

This can be achieved by using the pattern of difference of squares:

Applying the binomial square pattern:

Example Question #5 : How To Multiply Exponential Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

The cube of a sum pattern can be applied here:

Example Question #6 : How To Multiply Exponential Variables

Fill in the box to form a perfect square trinomial:

Possible Answers:

Correct answer:

Explanation:

To obtain the constant term of a perfect square trinomial, divide the linear coefficient, which here is , by 2, and square the quotient. The result is 

Example Question #7 : How To Multiply Exponential Variables

Fill in the box to form a perfect square trinomial:

Possible Answers:

Correct answer:

Explanation:

To obtain the constant term of a perfect square trinomial, divide the linear coefficient, which here is , by 2, and square the quotient. The result is 

Example Question #8 : How To Multiply Exponential Variables

Expand: 

Which is the greater quantity?

(a) The coefficient of  

(b) The coefficient of  

Possible Answers:

(a) and (b) are equal.

(a) is greater.

(b) is greater.

It is impossible to tell from the information given.

Correct answer:

(a) is greater.

Explanation:

Using the Binomial Theorem, if  is expanded, the  term is 

.

This makes  the coefficient of .

We compare the values of this expression at  for both  and :

(a) 

(b) 

(a) is the greater quantity.

 

Example Question #9 : How To Multiply Exponential Variables

Which is the greater quantity?

(a) 

(b) 8

Possible Answers:

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(a) is greater

Correct answer:

(a) is greater

Explanation:

 

Since 

, so

making (a) greater. 

Example Question #10 : How To Multiply Exponential Variables

Which is the greater quantity?

(a) 

(b) 

Possible Answers:

It is impossible to tell from the information given.

(a) and (b) are equal.

(b) is greater.

(a) is greater.

Correct answer:

It is impossible to tell from the information given.

Explanation:

We show that either polynomial can be greater by giving two cases:

Case 1: 

Case 2: 

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