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ISEE Upper Level Math : Equations

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6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #141 : How To Find The Solution To An Equation

What is the value of the expression $\sqrt{169-144}$ ?

Possible Answers:

Correct answer:

Explanation:

The first step here is to recognize you need to simplify within the radical before moving outside of the radical (avoid a common mistake of getting the square root of 169 and 144 before subtracting). Thus, you subtract 144 from 169, which gives you a difference of 25:

$\sqrt{169-144}$ = $\sqrt{25}$ =

Then you can take the square root of 25, which gives you the answer of 5.

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Example Question #141 : Equations

Solve for :

$\sqrt{x}+7=9$

Possible Answers:

x=-2

x=4

x=2

$x=\sqrt2$

Correct answer:

x=4

Explanation:

$\sqrt{x}+7=9$

$\sqrt{x}+7-7=9-7$

$\sqrt{x}=2$

$(\sqrt{x})^2=2^2$

x=4

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Example Question #142 : Equations

A sweater was originally $25, but then marked down to $22. What is the percent decrease?

Possible Answers:

14%

19%

25%

12%

Correct answer:

12%

Explanation:

To find the percent decrease, remember this formula: difference/original. First, find the difference between the prices. This is $3. Then divide that by the original price, which is $25. $\frac{3}{25}=.12$ . Since the question is asking for a percentage, move the decimal over to the right two places and you get 12%.

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Example Question #143 : Equations

Solve for x.

$\frac{x}{3}+0.4=1.2$

Possible Answers:

x=1.3

x=24

x=8

x=.24

x=2.4

Correct answer:

x=2.4

Explanation:

To solve for x, first subtract 0.4 from both sides. This gives you $\frac{x}{3}=0.8$ . Then, multiply both sides by 3. This yields 2.4 for x.

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Example Question #845 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify:

$\frac{\sqrt{24}}{144}$

Possible Answers:

$\frac{\sqrt{6}}{72}$

$\sqrt{6}$

$\frac{\sqrt{2}}{36}$

$\frac{1}{}6$

Correct answer:

$\frac{\sqrt{6}}{72}$

Explanation:

First, simplify the radical on the numerator. $\sqrt{24}$ can be simplified to $\sqrt{4} \cdot \sqrt{6}$ , which is also $2\sqrt{6}$ . Then, put that over the denominator: $\frac{2\sqrt{6}}{144}$ . Then, simplify like terms. 2 goes into both the numerator and denominator, so that final answer is $\frac{\sqrt{6}}{72}$ .

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Example Question #144 : How To Find The Solution To An Equation

Solve for x in the equation below:

$\sqrt{x}=\frac{4+5\cdot2-18\div2}{5}$

Possible Answers:

Correct answer:

Explanation:

The first step is to simplify the numerator in the right side of the equation.

$\sqrt{x}=\frac{4+5\cdot2-18\div2}{5}$

$\sqrt{x}=\frac{4+10-9}{5}$

$\sqrt{x}=\frac{5}{5}$

$\sqrt{x}=1$

Next, we square each side of the equation.

x=1

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Example Question #145 : How To Find The Solution To An Equation

Which of the answer choices below has a value that is different from the others?

Possible Answers:

$\sqrt{16}$

$2^{2}$

$4\div \frac{1}{4}$

$\frac{8}{2}$

Correct answer:

$4\div \frac{1}{4}$

Explanation:

$4\div \frac{1}{4}=16$

$\sqrt{16}=4$

$\frac{8}{2}=4$

$2^{2}=4$

Therefore, $4\div \frac{1}{4}$ has a value that is different from the other expressions.

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Example Question #144 : Equations

Solve for in this equation:

$\frac{5x}{2}=\frac{8}{x}$

Possible Answers:

$\frac{4\sqrt{5}}{5}$

$\frac{4}{5}$

$\frac{5}{4}$

$\frac{\sqrt{5}}{4}$

Correct answer:

$\frac{4\sqrt{5}}{5}$

Explanation:

In order to solve for $\frac{5x}{2}=\frac{8}{x}$ , cross multiplication must be used. Applying this, the equestion to be solved will be:

$5x^{2}=16$

Next, each side must be divided by 5. This results in:

$x^{2}=\frac{16}{5}$

The square root of each side is now taken. This gives us:

$x=\sqrt{}\frac{16}{5}$

This reduces to:

$\frac{4}{\sqrt{5}}$

Finally, we rationalize the denominator:

$\frac{4}{\sqrt{5}}\cdot\frac{\sqrt{5}}{\sqrt{5}}=\frac{4\sqrt{5}}{5}$

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Example Question #145 : Equations

On average, 1 in 9 peanuts that are harvested will only have one pod instead of two pods. Of those one-pod peanuts, three quarters of them will be smaller than the average peanut.

If 900 peanuts are harvested, how many will be one-pod peanuts that are smaller than average in size?

Possible Answers:

100

Correct answer:

Explanation:

If there are 900 peanuts and 1 in 9 will be one-podded, that means that 100 will be one-podded.

$900\cdot \frac{1}{9}=100$

Three quarters of these 100 one-podded peanuts will be of smaller than average size. Three quarters of of 100 is 75. Therefore, 75 is the correct answer.

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Example Question #144 : How To Find The Solution To An Equation

A small bakery sells two flavors of muffins: chocolate and banana.

At the end of the day, there are 13 muffins left.

There are chocolate muffins and banana muffins.

$x=\frac{7}{2}\cdot \frac{4}{7}-1$

how many banana muffins are left?

Possible Answers:

Correct answer:

Explanation:

The first step is to solve for x.

$x=\frac{7}{2}\cdot \frac{4}{7}-1$

x=2-1

x=1

If there are 1x chocolate muffins and 2y banana muffins, for a total of 13 muffins then:

1x+2y=13

1+2y=13

2y=12

Since the number of banana muffins remaining is 2y, there are 12 banana muffins left.

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Equations

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #141 : How To Find The Solution To An Equation

Example Question #141 : Equations

Example Question #142 : Equations

Example Question #143 : Equations

Example Question #845 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #144 : How To Find The Solution To An Equation

Example Question #145 : How To Find The Solution To An Equation

Example Question #144 : Equations

Example Question #145 : Equations

Example Question #144 : How To Find The Solution To An Equation

All ISEE Upper Level Math Resources

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