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ISEE Middle Level Math : Algebraic Concepts

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 #105 : Equations

Solve for :

0.7t + 0.23 = 0.3 t - 3.21

Possible Answers:

t = - 3.44

t = -7.45

t = - 8.6

t = -2.98

Correct answer:

t = - 8.6

Explanation:

0.7t + 0.23 = 0.3 t - 3.21

0.7t + 0.23 - 0.3t = 0.3 t - 3.21 - 0.3t

0.4t + 0.23 = - 3.21

0.4t + 0.23- 0.23 = - 3.21 - 0.23

0.4t = - 3.44

$0.4t \div 0.4 = - 3.44 \div 0.4$

$t = - 3.44 \div 0.4$

Move each decimal point one digit right:

$t = - 34.4 \div 4 = - 8.6$

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Example Question #102 : Equations

Let be the temperature expressed in degrees Celsius. Then the equivalent temperature in degrees Fahrenheit can be calculated using the formula:

$F = \frac{9}{5} C + 32$

What is $65^{\circ } C$ expressed in degrees Fahrenheit?

Possible Answers:

$149 ^{\circ } F$

$174.6^{\circ } F$

$85 ^{\circ } F$

$59.4^{\circ } F$

Correct answer:

$149 ^{\circ } F$

Explanation:

$F = \frac{9}{5} C + 32$

$F = \frac{9}{5} \cdot 65 + 32 = 117+32 = 149 ^{\circ } F$

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Example Question #106 : Equations

Solve for :

4 t - 1.9 = 8.3

Possible Answers:

t = 2.55

t = 0.16

t = 1.6

t = 0.255

Correct answer:

t = 2.55

Explanation:

4 t - 1.9 = 8.3

4 t - 1.9 + 1.9 = 8.3 + 1.9

4 t = 10.2

$4 t \div 4= 10.2 \div 4$

t = 2.55

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Example Question #107 : Equations

Solve for :

$\frac{4}{5} d > - \frac{7}{10}$

Possible Answers:

$d > - \frac{7}{8}$

$d > - \frac{14}{25}$

$d < - \frac{7}{8}$

$d < - \frac{14}{25}$

Correct answer:

$d > - \frac{7}{8}$

Explanation:

$\frac{4}{5} d > - \frac{7}{10}$

$\frac{5}{4} \cdot \frac{4}{5} d >\frac{5}{4} \cdot \left ( - \frac{7}{10} \right )$

$d > - \left (\frac{5}{4} \cdot \frac{7}{10} \right )$

$d > - \left (\frac{1}{4} \cdot \frac{7}{2} \right )$

$d > - \frac{7}{8}$

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Example Question #311 : Algebraic Concepts

$f (x) = x^{2} + 4x - 10$

Evaluate: f (-3)

Possible Answers:

Correct answer:

Explanation:

$f (x) = x^{2} + 4x - 10$

$f (-3) = (-3)^{2} + 4(-3) - 10$

f (-3) =9-12 - 10

f (-3) =-13

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Example Question #2 : How To Solve Two Step Equations

Let be the temperature expressed in degrees Fahrenheit. Then the equivalent temperature in degrees Celsius can be calculated using the formula:

$C = \frac{5}{9} (F-32)$

What is $80^{\circ } F$ expressed in degrees Celsius (to the nearest degree)?

Possible Answers:

$12^{\circ } C$

$27^{\circ } C$

$112^{\circ } C$

$87^{\circ } C$

Correct answer:

$27^{\circ } C$

Explanation:

$C = \frac{5}{9} (F-32)$

$C = \frac{5}{9} (80-32)$

$C = \frac{5}{9} \cdot 48 \approx 26.7$ , which rounds to $27^{\circ } C$

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Example Question #312 : Algebraic Concepts

$2^{2}*3^{2}=$

Possible Answers:

Correct answer:

Explanation:

First, solve the exponents:

$2^{2}=4$

$3^{2}=9$

Then, solve the equation:

4*9=36

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Example Question #313 : Algebraic Concepts

$5^{2}*4^2=$

Possible Answers:

400

Correct answer:

400

Explanation:

First, solve the exponents:

$5^{2}=25$

$4^{2}=16$

Then, solve the equation:

25*16=400

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Example Question #314 : Algebraic Concepts

6r*11r=

Possible Answers:

$5r^{3}$

$17r^{2}$

$611r^{2}$

$66r^{2}$

Correct answer:

$66r^{2}$

Explanation:

First, multiply the whole numbers.

Then, keep the variable the same and add an exponent totalling the number of variables in the equation:

$6r*11r=66r^{2}$

Answer: $66r^{2}$

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Example Question #315 : Algebraic Concepts

21s*15s=

Possible Answers:

$300s^{2}$

315s

$315s^{2}$

Correct answer:

$315s^{2}$

Explanation:

First, multiply the whole numbers.

Then, keep the variable the same and add an exponent totalling the number of variables in the equation:

$21s*15s=315s^{2}$

Answer: $315s^{2}$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Algebraic Concepts

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #105 : Equations

Example Question #102 : Equations

Example Question #106 : Equations

Example Question #107 : Equations

Example Question #311 : Algebraic Concepts

Example Question #2 : How To Solve Two Step Equations

Example Question #312 : Algebraic Concepts

Example Question #313 : Algebraic Concepts

Example Question #314 : Algebraic Concepts

Example Question #315 : Algebraic Concepts

All ISEE Middle Level Math Resources

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