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ISEE Upper Level Math : ISEE Upper Level (grades 9-12) Mathematics Achievement

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

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All ISEE Upper Level Math Resources

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

Example Questions

Example Question #26 : Percentages

A college has 1200 students. If percent of them are boys, how many girls are there?

Possible Answers:

840

300

800

360

350

Correct answer:

360

Explanation:

percent of the students are boys, so percent of the students are girls.

Let = number of girls.

Then we can set up the following proportion:

$\frac{30}{100}=\frac{x}{1200}\Rightarrow \frac{3}{10}=\frac{x}{1200}\Rightarrow 10x=3\times 1200\Rightarrow x=\frac{3600}{10}=360$

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Example Question #2 : Word Problems

John and Tom are farmers. John can produce $1500\ lb$ of an organic product in six months. Tom can produce $3500\ lb$ of the organic product in one year. How many pounds of organic product can they produce in three years together? (Assume that they can work and produce the organic product all year round.)

Possible Answers:

$20000\ lb$

$18500\ lb$

$19000\ lb$

$19500\ lb$

$18000\ lb$

Correct answer:

$19500\ lb$

Explanation:

John can produce $1500\ lb$ in six month. Therefore we can set up a proportion:

$\frac{1500 \ lb}{0.5\ yr}=\frac{x \ lb}{3\ yr}\Rightarrow 0.5x=3\times 1500\Rightarrow x=9000\ lb$

Tom can produce $3500\ lb$ in one year. Then we can set up another proportion:

$\frac{3500 \ lb}{1\ yr}=\frac{y \ lb}{3\ yr}\Rightarrow 1\times y=3\times 3500 \Rightarrow y=10500\ lb$

$x+y=9000+10500=19500\ lb$

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Example Question #771 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Solve for .

$\frac{1}{7}x-7=49$

Possible Answers:

295

300

294

296

290

Correct answer:

294

Explanation:

$\frac{1}{7}x-7+7=49-7\Rightarrow \frac{x}{7}=42\Rightarrow x=42\times 7=294$

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Example Question #73 : How To Find The Solution To An Equation

Solve the set of equations:

3x-2y=9

4x+y=1

Possible Answers:

x=-1, y=3

x=1, y=3

x=-3, y=1

x=-1, y=-3

x=1, y=-3

Correct answer:

x=1, y=-3

Explanation:

Solve the second equation for :

y=1-4x

Now substitute this expression into the first equation:

$3x-2y=9\Rightarrow 3x-2(1-4x)=9\Rightarrow 3x-2+8x=9\Rightarrow 11x=11$

$\Rightarrow x=1$

Substitute this new value for into the first equation:

$3(1)-2y=9\Rightarrow 3-9=2y\Rightarrow y=-\frac{6}{2}=-3$

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Example Question #72 : Equations

3x+4y=25

If x=4 , find .

Possible Answers:

Correct answer:

Explanation:

$3x+4y=25\Rightarrow 3\times 3+4y=25\Rightarrow 9+4y=25\Rightarrow (9-9)+4y=25-9$

$\Rightarrow 4y=16\Rightarrow y=\frac{16}{4}=4$

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Example Question #73 : Equations

$\frac{1}{3}x+4y^2=45$

If x=15 , find .

Possible Answers:

$\sqrt{10}$

$\sqrt{15}$

$\sqrt{5}$

Correct answer:

$\sqrt{10}$

Explanation:

$\frac{1}{3}x+4y^2=45\Rightarrow \frac{15}{3}+4y^2=45\Rightarrow 5+4y^2=45$

$\Rightarrow (5-5)+4y^2=45-5\Rightarrow 4y^2=40\Rightarrow y^2=\frac{40}{4}=10$

Take the square root of both sides:

$y=\sqrt{10}$

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Example Question #76 : How To Find The Solution To An Equation

Solve the set of equations:

x+7y=39

x-2y=-6

Possible Answers:

x=4, y=5

x=-4, y=5

x=-4, y=-5

x=5, y=4

x=4, y=-5

Correct answer:

x=4, y=5

Explanation:

Solve the second equation for :

$x+6=2y\Rightarrow y=\frac{x+6}{2}$

Now substitute this expression into the first equation:

$x+7y=39\Rightarrow x+7(\frac{x+6}{2})=39\Rightarrow x+\frac{7x}{2}+\frac{7\times 6}{2}=39$

$\Rightarrow \frac{2+7}{2}x+21=39\Rightarrow \frac{9x}{2}=39-21\Rightarrow \frac{9x}{2}=18$

$\Rightarrow x=\frac{18\times 2}{9}=4$

Substitute this new value of into the first equation:

$x+7y=39\Rightarrow 4+7y=39\Rightarrow 4-4+7y=39-4\Rightarrow 7y=35$

$\Rightarrow y=\frac{35}{7}=5$

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Example Question #72 : Algebraic Concepts

Give the slope of the line of the equation: $\frac{}{}$ 5x -7y = 9

Possible Answers:

$\frac{5}{7}$

$-\frac{5}{7}$

$-\frac{7}{5}$

$\frac{7}{5}$

Correct answer:

$\frac{5}{7}$

Explanation:

Rewrite in the slope-intercept form y = mx + b :

5x -7y = 9

5x-5x -7y = 9-5x

-7y = -5x+9

$-7y \div (-7)=\left ( -5x+9 \right )\div (-7)$

$y=\frac{-5}{-7}\cdot x+ \frac{ 9 }{-7}$

$y=\frac{5}{7} x- \frac{ 9 }{7}$

The slope is the coefficient of , which is $\frac{5}{7}$ .

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Example Question #73 : Algebraic Concepts

Give the slope of the line of the equation: 5x = 8y + 7

Possible Answers:

$\frac{7}{5}$

$\frac{5}{7}$

$\frac{8}{5}$

$\frac{8}{7}$

$\frac{5}{8}$

Correct answer:

$\frac{5}{8}$

Explanation:

Rewrite in the slope-intercept form y = mx + b :

8y + 7 = 5x

8y + 7 -7 = 5x-7

8y = 5x-7

$8y \div 8 =\left ( 5x-7 \right )\div 8$

$y =\frac{5x}{8} -\frac{7}{8}$

$y =\frac{5}{8}x -\frac{7}{8}$

The slope is the coefficient of , which is $\frac{5}{8}$ .

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Example Question #74 : Algebraic Concepts

Solve for :

$5^{6x} = 125 ^{2x-1}$

Possible Answers:

x = 6

x = 1

x = 3

x = 2

The equation has no solution.

Correct answer:

The equation has no solution.

Explanation:

$125 = 5^{3}$ , so we can rewrite this equation as:

$5^{6x} = 125 ^{2x-1}$

$5^{6x} = \left ( 5^{3}\right ) ^{2x-1}$

$5^{6x} =5^{3\left ( 2x-1 \right )}$

$5^{6x} =5^{ 6x-3 }$

Therefore, we set the exponents equal.

6x = 6x - 3

6x -6x= 6x-6x - 3

0 = -3

This is identically false. This means that the equation has no solution.

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : ISEE Upper Level (grades 9-12) Mathematics Achievement

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #26 : Percentages

Example Question #2 : Word Problems

Example Question #771 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #73 : How To Find The Solution To An Equation

Example Question #72 : Equations

Example Question #73 : Equations

Example Question #76 : How To Find The Solution To An Equation

Example Question #72 : Algebraic Concepts

Example Question #73 : Algebraic Concepts

Example Question #74 : Algebraic Concepts

All ISEE Upper Level Math Resources

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