Variables and Exponents

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ISEE Upper Level Quantitative Reasoning › Variables and Exponents

Questions 1 - 10
1

Simplify:

Explanation

Break the fraction up and apply the quotient of powers rule:

2

Simplify:

Explanation

The cube of a sum pattern can be applied here:

3

Simplify:

Explanation

Break the fraction up and apply the quotient of powers rule:

4

Factor completely:

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:

5

Fill in the box to form a perfect square trinomial:

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

6

Fill in the box to form a perfect square trinomial:

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

7

Factor completely:

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:

8

Simplify:

Explanation

The cube of a sum pattern can be applied here:

9

Half of one hundred divided by five and multiplied by one-tenth is __________.

1

5

2

10

Explanation

Let's take this step by step. "Half of one hundred" is 100/2 = 50. Then "half of one hundred divided by five" is 50/5 = 10. "Multiplied by one-tenth" really is the same as dividing by ten, so the last step gives us 10/10 = 1.

10

Half of one hundred divided by five and multiplied by one-tenth is __________.

1

5

2

10

Explanation

Let's take this step by step. "Half of one hundred" is 100/2 = 50. Then "half of one hundred divided by five" is 50/5 = 10. "Multiplied by one-tenth" really is the same as dividing by ten, so the last step gives us 10/10 = 1.

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