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ISEE Upper Level Math : Variables

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Example Questions

Example Question #11 : Variables

Simplify:

$(-\frac{5}{3})^{-3}$

Possible Answers:

$-\frac{27}{125}$

$-\frac{125}{27}$

$\frac{125}{27}$

$-\frac{25}{9}$

$\frac{27}{125}$

Correct answer:

$-\frac{27}{125}$

Explanation:

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

$(-\frac{5}{3})^{-3}=(-\frac{3}{5})^3$

Apply the exponent within the parentheses and simplify. The negative in the fraction can be applied to either the numerator or the denominator, but not both; we will apply it to the numerator.

$\frac{(-3)^3}{(5)^3}$

$\frac{-27}{125}=-\frac{27}{125}$

The fraction cannot be simplified further.

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Example Question #12 : Variables

Solve for $\dpi{100} x$ :

$\dpi{100} \frac{1}{3}x-14=7$

Possible Answers:

$\dpi{100} 63$

$\dpi{100} 3$

$\dpi{100} 21$

$\dpi{100} 7$

Correct answer:

$\dpi{100} 63$

Explanation:

$\dpi{100} \frac{1}{3}x-14=7$

$\dpi{100} \frac{1}{3}x-14+14=7+14$

$\dpi{100} \frac{1}{3}x=21$

$\dpi{100} 3\cdot \frac{1}{3}x=21\cdot 3$

$\dpi{100} x=63$

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Example Question #13 : Variables

If the product of three consecutive numbers is 990, what is the smallest number?

Possible Answers:

Correct answer:

Explanation:

If the product of three consecutive numbers is 990, then the smallest number can be found by plugging in each answer choice into the scenario to see whether it is correct.

If we plug in 9 as the smallest number, then the two consecutive numbers would be 10 and 11.

Given that 9 times 10 times 11 equals 990, that is the correct answer.

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Example Question #14 : Variables

What is the simplified version of the expression below?

$(\frac{5}{4}\cdot8+6\div3)^{2}-12$

Possible Answers:

132

Correct answer:

132

Explanation:

The first step is to simplify the values in the parentheses:

$(\frac{5}{4}\cdot8+6\div3)^{2}-12$

$(10+2)^{2}-12$

$12^{2}-12$

144-12

132

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Example Question #15 : Variables

Simplify:

$4xy^2-2xy+y^{2}x+y^3-8xy+4yx$

Possible Answers:

4xy^2-6xy+y^3

xy^2-4xy+y^3

5xy^2-6xy+y^3

4xy^2-10xy+yx^2+y^3+4yx

4xy^2-10xy+y^3

Correct answer:

5xy^2-6xy+y^3

Explanation:

Reorder the expression to group like-terms together.

$4xy^2-2xy+y^{2}x+y^3-8xy+4yx$

$(4xy^2+y^{2}x)+(-2xy+-8xy+4yx)+y^3$

Simplify by combining like-terms.

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Example Question #16 : Variables

If $x^{2}-12x$ is a positive number, what is a possible value of ?

Possible Answers:

Correct answer:

Explanation:

If x is equal to , then the equation could be written as follows:

$x^{2}-12x$

$-4^{2}-(12*-4)$

16+48=64

Given that is a positive number, is a possible value of .

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Example Question #17 : Variables

Megan teaches a cooking class. Every time a student takes a class, the student receives a 10% discount off of the price he paid for the previous class. The first class that Jose took cost $50. What will be the first class in which Jose pays less than $38?

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, the price of $50 must be discounted by 10% until we get to a price of $38 or less.

The first class is 50.

The second class, being 10 percent less than the previous one, is $50-.1\cdot 50=50-5=45$

The third class, being 10 percent less than the previous one, is $45-.1\cdot45=45-4.5 = 40.5$

The fourth class, being 10 percent less than the previous one, is $40.5-.1\cdot40.5=40.5-4.05=36.45$

Therefore, the answer is 4.

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Example Question #907 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify the following expression

(6x^2)*(3x^3)

Possible Answers:

9x^6

18x^5

18x^6

9x^5

Correct answer:

18x^5

Explanation:

Simplify the following expression

(6x^2)*(3x^3)

Let's begin by multiplying our coefficients:

6*3=18

Next, we need to realize that we can combine our x's by adding the exponents.

$x^2*x^3=x^{3+2}=x^5$

Put it all together to get:

18x^5

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Example Question #18 : Variables

Simplify the following:

(9q^3n^3)(q^5n^6)

Possible Answers:

81q^8n^9

$9qn^{72}$

9q^8n^9

9q^9n^8

Correct answer:

9q^8n^9

Explanation:

Simplify the following:

(9q^3n^3)(q^5n^6)

To begin, our coefficient will not change. We have just one integer (the 9) and nothing to multiply it by.

To combine our exponents, we will add them. This is because we are multiplying them

$q^3*q^5=q^{3+5}=q^8$

$n^3*n^6=n^{3+6}=n^9$

Put it together to get:

9q^8n^9

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Example Question #19 : Variables

$x^{2} = 18$

$y^{2} = 2$

and are both positive.

Evaluate (2x+ 3y) (3x-2y) .

Possible Answers:

150

126

Correct answer:

126

Explanation:

Multiply the binomials using the FOIL method - first, outer, inner, last - then combine like terms:

(2x+ 3y) (3x-2y)

$= 2x \cdot 3x - 2x \cdot 2y+ 3y \cdot 3x-3y \cdot 2y$

$=6 x ^{2}-4 x y+ 9xy-6y^{2}$

$=6 x ^{2}+ 5 xy-6y^{2}$

$x^{2} = 18$ and $y^{2} = 2$ ; also, by the Power of a Product Principle:

$(xy) ^{2} = x^{2}y^{2}$ .

and are both positive, so, substituting:

$xy = \sqrt{x^{2}y^{2}} = \sqrt{18 \cdot 2} = \sqrt{36} = 6$ .

Again, using substitution:

(2x+ 3y) (3x-2y)

$=6 x ^{2}+ 5 xy-6y^{2}$

=6 (18)+ 5 (6)-6 (2)

=108 +30-12

=126

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Variables

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #11 : Variables

Example Question #12 : Variables

Example Question #13 : Variables

Example Question #14 : Variables

Example Question #15 : Variables

Example Question #16 : Variables

Example Question #17 : Variables

Example Question #907 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #18 : Variables

Example Question #19 : Variables

All ISEE Upper Level Math Resources

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