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ISEE Upper Level Math : Algebraic Concepts

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 #181 : How To Find The Solution To An Equation

Solve the following equation for y

3y+7=49

Possible Answers:

Correct answer:

Explanation:

Solve the following equation for y

3y+7=49

Begin by subtracting 7 from both sides

3y=49-7

3y=42

Next, divide both sides by 3 to get our final answer:

$y=\frac{42}{3}=14$

So, our answer is 14

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Example Question #881 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Which of the following makes this equation true:

4x+9=65

Possible Answers:

x=13

x=12

x=9

x=14

x=8

Correct answer:

x=14

Explanation:

To answer the question, we will solve for x.

4x+9=65

4x+9-9=65-9

4x+0=56

4x=56

$\frac{4x}{4} = \frac{56}{4}$

x=14

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Example Question #182 : How To Find The Solution To An Equation

Solve for a in the following:

6a-8=64

Possible Answers:

a=8

a=14

a=13

a=9

a=12

Correct answer:

a=12

Explanation:

To solve for a, we want a to stand alone. So,

6a-8=64

6a-8+8=64+8

6a-0=72

6a=72

$\frac{6a}{6} = \frac{72}{6}$

a=12

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Example Question #183 : How To Find The Solution To An Equation

Which of the following makes this equation true:

12x – 11 = 145

Possible Answers:

x=12

x=11

x=9

x=13

x=14

Correct answer:

x=13

Explanation:

To answer the question, we will solve for x. We get

12x-11+11=145+11

12x-0=156

12x=156

$\frac{12x}{12} = \frac{156}{12}$

x = 13

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Example Question #184 : How To Find The Solution To An Equation

Solve for a in the following equation:

13a-8=109

Possible Answers:

x=12

x=8

x=7

a=9

x=11

Correct answer:

a=9

Explanation:

To solve, we want a to stand alone.

So, we get

13a-8=109

13a-8+8=109+8

13a-0=117

13a=117

$\frac{13a}{13} = \frac{117}{13}$

a=9

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Example Question #185 : How To Find The Solution To An Equation

Which of the following makes this equation true:

12x+9=141

Possible Answers:

x=12

x=8

x=9

x=13

x=11

Correct answer:

x=11

Explanation:

To answer the question, we will solve for x.

So, we get

12x+9=141

12x+9-9=141-9

12x+0=132

12x=132

$\frac{12x}{12} = \frac{132}{12}$

x=11

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Example Question #186 : How To Find The Solution To An Equation

Solve the equation: $\frac{3}{x}+4 = -1$

Possible Answers:

$-\frac{3}{5}$

$-\frac{2}{3}$

$\frac{1}{3}$

Correct answer:

$-\frac{3}{5}$

Explanation:

Subtract four on both sides.

$\frac{3}{x}+4 -(4)= -1-(4)$

Simplify both sides.

$\frac{3}{x} =-5$

Multiply by on both sides.

$\frac{3}{x} \cdot x=-5\cdot x$

3=-5x

Divide by negative five on both sides.

$\frac{3}{-5}=\frac{-5x}{-5}$

The answer is: $-\frac{3}{5}$

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Example Question #187 : How To Find The Solution To An Equation

Solve for $x: 3x^2 + 4 = 31$

Possible Answers:

Correct answer:

Explanation:

We first subtract 4 from both sides. This gives us 3x^2 = 27 . Now, dividing both sides by 3 leaves us with x^2 = 9 . Solve for x: x=3.

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Example Question #1 : How To Multiply Variables

Machine A can produce 4 buttons in 2 days. Machine B can produce 20 buttons in 4 days. How many buttons can Machine A and B, working together, produce in 40 days?

Possible Answers:

$\dpi{100} 280$

$\dpi{100} 7$

$\dpi{100} 70$

$\dpi{100} 200$

Correct answer:

$\dpi{100} 280$

Explanation:

First determine how many buttons each machine can produce in a day.

Machine A: $\dpi{100} \frac{4}{2}=2\ buttons\ per\ day$

Machine B: $\dpi{100} \frac{20}{4}=5\ buttons\ per\ day$

Machine A and B can produce 7 buttons per day when they are working together.

$\dpi{100} 7\times 40=280\ buttons$

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Example Question #2 : Variables

Brian has 3 siblings. When his family orders pizza, each of the 4 children is given $\dpi{100} \frac{1}{4}$ of the pizza. Brian does not feel well so he only finishes $\dpi{100} \frac{1}{3}$ of his pizza. If the original pizza consisted of 12 slices of pizza, how many slices did Brian eat?

Possible Answers:

$\dpi{100} 1$

$\dpi{100} 4$

$\dpi{100} 6$

$\dpi{100} 3$

Correct answer:

$\dpi{100} 1$

Explanation:

Brian eats $\dpi{100} \frac{1}{3}\times \frac{1}{4}\times 12\ slices\ of\ pizza$ .

So Brian eats

$\dpi{100} \frac{1}{12}\cdot 12=1\ slice\ of\ pizza.$

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All ISEE Upper Level Math Resources

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

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ISEE Upper Level Math : Algebraic Concepts

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #181 : How To Find The Solution To An Equation

Example Question #881 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #182 : How To Find The Solution To An Equation

Example Question #183 : How To Find The Solution To An Equation

Example Question #184 : How To Find The Solution To An Equation

Example Question #185 : How To Find The Solution To An Equation

Example Question #186 : How To Find The Solution To An Equation

Example Question #187 : How To Find The Solution To An Equation

Example Question #1 : How To Multiply Variables

Example Question #2 : Variables

All ISEE Upper Level Math Resources

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