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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Solving Systems Of Equations In Word Problems

Mark is three times as old as his son Brian. In ten years, Mark will be years old. In how many years will Mark be twice as old as Brian?

Possible Answers:

Correct answer:

Explanation:

In ten years, Mark will be years old, so Mark is 43-10 = 33 years old now, and Brian is one-third of this, or $33 \div 3 = 11$ years old.

Let be the number of years in which Mark will be twice Brian's age. Then Brian will be N + 11 , and Mark will be N + 33 . Since Mark will be twice Brian's age, we can set up and solve the equation:

2 (N + 11) = N + 33

2N + 22 = N + 33

2N + 22-N - 22 = N + 33 -N - 22

N = 11

Mark will be twice Brian's age in years.

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Example Question #1 : Solving Systems Of Equations In Word Problems

Gary is twice as old as his niece Candy. How old will Candy will be in five years when Gary is years old?

Possible Answers:

Not enough information is given to determine the answer.

Correct answer:

Explanation:

Since Gary will be 37 in five years, he is 37 - 5 = 32 years old now. He is twice as old as Cathy, so she is $32 \div 2 =16$ years old, and in five years, she will be 16 + 5 = 21 years old.

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Example Question #562 : Algebraic Concepts

Solve for b when f is equal to 0

$b^3=\frac{4}{f}+2$

Possible Answers:

$b=\sqrt[3]{2}$

No real solutions

b=-2

b=8

Correct answer:

No real solutions

Explanation:

Solve for b when f is equal to 0

$b^3=\frac{4}{f}+2$

Let's start by plugging in 0 for f

$b^3=\frac{4}{(0)}+2$

Now, we cannot go any further, because we cannot divide by zero.

This means that there is no value of b for which f will equal zero.

This means we have no real solutions.

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Example Question #563 : Algebraic Concepts

Solve the following equation for u when y is equal to 6.

$\frac{4y}{u}=12$

Possible Answers:

Correct answer:

Explanation:

Solve the following equation for u when y is equal to 6.

$\frac{4y}{u}=12$

To begin, let's plug in 6 for y.

$\frac{4*6}{u}=12$

Next, bring the u over to the other side by multiplying both sides by u

24=12u

Finally, divide both sides by 12 to see what u is

$\frac{24}{12}=u=2$

So we get u=2 as our answer.

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Example Question #564 : Algebraic Concepts

Solve for x in the following equation:

2x = 10

Possible Answers:

Correct answer:

Explanation:

To solve for x, we want x to stand alone or to be by itself. So in the equation

2x = 10

we want x to stand alone. To do that, we need to cancel the that is next to it. The is being multiplied to x, so to cancel it out, we will need to divide by . If we divide by on the left side of the equal sign, we have to divide by on the right side of the equal sign. So,

$\frac{2x}{2} = \frac{10}{2}$

Now, we simplify.

x = 5

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Example Question #565 : Algebraic Concepts

A + B = 100

A = -40

Evaluate .

Possible Answers:

B = 140

B = -140

B = -60

B = 60

Correct answer:

B = 140

Explanation:

A + B = 100

To evaluate, substitute -40 in for A.

-40 + B = 100

Add 40 to each side to isolate and solve for B.

-40 + B + 40 = 100 + 40

B = 140

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Example Question #361 : How To Find The Solution To An Equation

Solve the equation:

5x+ 7 = 89

Possible Answers:

x = 14.4

x = 12.4

x = 16.4

x = 18.4

Correct answer:

x = 16.4

Explanation:

To solve the equation, isolate the variable on one side of the equation and all other constants on the other side. To accomplish this, perform the opposite operation to manipulate the equation.

5x+ 7 = 89

First add seven to both sides.

5x+ 7 - 7 = 89 - 7

5x = 82

Now divide by five on both sides.

$5x \div 5 = 82 \div 5$

x = 16.4

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Example Question #362 : How To Find The Solution To An Equation

Solve the following equation for y when z=3

12y+6=2z^3-26

Possible Answers:

188

$1.8\bar{3}$

$18.\bar{3}$

Correct answer:

$1.8\bar{3}$

Explanation:

Solve the following equation for y when z=3

12y+6=2z^3-26

Let's begin by rearranging the equation to get y by itself.

12y+6(-6)=2z^3-26(-6)

$12y(\div12)=(2z^3-32)(\div12)$

$y=\frac{2z^3-32}{12}$

Next, just plug in 3 for z and solve.

$y=\frac{2(3)^3-32}{12}=\frac{54-32}{12}=\frac{22}{12}=1.8\bar{3}$

So our answer is

$1.8\bar{3}$

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Example Question #363 : How To Find The Solution To An Equation

Solve for :

-0.04 z + (-7) = - 121

Possible Answers:

z = - 3,200

z=- 2,850

z= 2,850

z = 3,200

Correct answer:

z= 2,850

Explanation:

-0.04 z + (-7) = - 121

-0.04 z + (-7) - (-7) = - 121 - (-7)

-0.04 z = - 121+ 7

-0.04 z = - (121- 7)

-0.04 z = -114

$-0.04 z \div (-0.04 ) = -114 \div (-0.04 )$

$z = 114 \div 0.04$

To divide, move the decimal point in both numbers two units to the right;

$z = 11400 \div 4$

z= 2,850

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Example Question #364 : How To Find The Solution To An Equation

Solve the following equation for h, when l is equal to 5

$3h+12=\frac{l^3-25}{5}$

Possible Answers:

$h=\frac{4}{3}$

$h=\frac{8}{3}$

h=3

$h=\frac{5}{3}$

Correct answer:

$h=\frac{8}{3}$

Explanation:

Solve the following equation for h, when l is equal to 5

$3h+12=\frac{l^3-25}{5}$

Let's begin by substituting in 5 for l

$3h+12=\frac{5^3-25}{5}$

Simplify

$3h+12=\frac{125-25}{5}=\frac{100}{5}=20$

3h+12=20

Next, move the twelve over:

3h=20-12=8

3h=8

Finally, we get:

$h=\frac{8}{3}$

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #1 : Solving Systems Of Equations In Word Problems

Example Question #1 : Solving Systems Of Equations In Word Problems

Example Question #562 : Algebraic Concepts

Example Question #563 : Algebraic Concepts

Example Question #564 : Algebraic Concepts

Example Question #565 : Algebraic Concepts

Example Question #361 : How To Find The Solution To An Equation

Example Question #362 : How To Find The Solution To An Equation

Example Question #363 : How To Find The Solution To An Equation

Example Question #364 : How To Find The Solution To An Equation

All ISEE Middle Level Math Resources

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