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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 #111 : Numbers And Operations

Solve: $3^5 \cdot 3^{-8}$

Possible Answers:

$3^{13}$

$\frac{1}{3^{13}}$

$\frac{1}{9}$

$\frac{1}{27}$

Correct answer:

$\frac{1}{27}$

Explanation:

It is not necessary to evaluate both terms and multiply.

According to the rules of exponents, when we have the same bases raised to some power that are multiplied with each other, we can add the powers.

$3^5 \cdot 3^{-8} = 3^{5+( -8)} = 3^{-3}$

This term can be rewritten as a fraction.

$3^{-3 } = \frac{1}{3^3} = \frac{1}{27}$

The answer is: $\frac{1}{27}$

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Example Question #551 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Which of the following is equivalent to the expression below?

$4^{x}\cdot2^{5}$

Possible Answers:

$8^{10x}$

$2^{2x+5}$

$8^{5x}$

$6^{5x}$

Correct answer:

$2^{2x+5}$

Explanation:

When exponents are multiplied by one another, and the base is the same, the exponents can be added together.

The first step is to try to create a common base.

$4^{x}\cdot2^{5}$

Given that the square of 2 is for, the expression can be rewritten as:

$2^{2}^{x}\cdot 2^{5}$

$2^{2x+5}$

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Example Question #111 : Numbers And Operations

Simplify:

$(6a^3)(\frac{1}{3}a^2)$

Possible Answers:

a^6

a^5

2a^4

2a^5

2a^6

Correct answer:

2a^5

Explanation:

Based on the product rule for exponents in order to multiply two exponential terms with the same base, add their exponents:

$(x)^a(x)^b=x^{a+b}$

So we can write:

$(6a^3)\left(\frac{1}{3}a^2\right)=\left(\frac{6}{3}\right)\times a^{3+2}=2a^5$

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Example Question #551 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Venn

Refer to the above Venn diagram.

Define universal set $U = \mathbb{N}$ , the set of natural numbers.

Define sets and as follows:

$A = \left \{ 1,5,9,13,17,21,... \right \}$

$B = \left \{ 2,5,8,11,14,17...\right \}$

Which of the following numbers is an element of the set represented by the gray area in the diagram?

Possible Answers:

101

105

103

102

104

Correct answer:

104

Explanation:

The gray area represents the set of all elements that are in but not in .

is the set of integers that, when divided by 3, yield remainder 2. Therefore, we can eliminate 102 and 105, both multiples of 3, and 103, which, when divided by 3, yields remainder 1.

is the set of integers that, when divided by 4, yield remainder 1. Since we do not want an element from this set, we can eliminate 101, but not 104.

104 is the correct choice.

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Example Question #552 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Venn

In the above Venn diagram, the universal set is defined as $U = \left \{ a, b, c, d, e, f, g, h\right \}$ . Each of the eight letters is placed in its correct region.

What is $A \cap B$ ?

Possible Answers:

$A \cap B = \left \{ a,b,d,e,f,g,h \right \}$

$A \cap B = \left \{ a,c,f \right \}$

$A \cap B = \left \{ b,d,e,g,h \right \}$

$A \cap B = \left \{ a,f \right \}$

$A \cap B = \left \{ b,c,d,e,g,h \right \}$

Correct answer:

$A \cap B = \left \{ a,f \right \}$

Explanation:

$A \cap B$ is the intersection of sets and - that is, the set of all elements of that are elements of both and . We want all of the letters that fall in both circles, which from the diagram can be seen to be and . Therefore,

$A \cap B = \left \{ a,f \right \}$

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Example Question #553 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Venn

In the above Venn diagram, the universal set is defined as $U = \left \{ a, b, c, d, e, f, g, h\right \}$ . Each of the eight letters is placed in its correct region. Which of the following is equal to $\overline{A\cap B}$ ?

Possible Answers:

$\overline{A\cap B} = \left \{ a,f\right \}$

$\overline{A\cap B} = \left \{ c\right \}$

$\overline{A\cap B} = \left \{ b,d,e,g,h\right \}$

$\overline{A\cap B} = \left \{ a,c,f\right \}$

$\overline{A\cap B} = \left \{ b,c,d,e,g,h\right \}$

Correct answer:

$\overline{A\cap B} = \left \{ b,c,d,e,g,h\right \}$

Explanation:

$\overline{A \cap B}$ is the complement of $A \cap B$ - the set of all elements in not in $A \cap B$ .

$A \cap B$ is the intersection of sets and - that is, the set of all elements of that are elements of both and . Therefore, $\overline{A \cap B}$ is the set of all elements that are not in both and , which can be seen from the diagram to be all elements except and . Therefore,

$\overline{A\cap B} = \left \{ b,c,d,e,g,h\right \}$ .

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Example Question #4 : Data Analysis And Probability

Venn

Possible Answers:

$\overline{A\cup B} = \left \{ b,c,d,e,g,h\right \}$

$\overline{A\cup B} = \left \{ b,d,e,g,h\right \}$

$\overline{A\cup B} = \left \{ c\right \}$

$\overline{A\cup B} = \left \{ a,c,f\right \}$

$\overline{A\cup B} = \left \{ a,f\right \}$

Correct answer:

$\overline{A\cup B} = \left \{ c\right \}$

Explanation:

$\overline{A\cup B}$ is the complement of $A\cup B$ - the set of all elements in not in $A\cup B$ .

$A\cup B$ is the union of sets and - the set of all elements in either or . Therefore, $\overline{A\cup B}$ is the set of all elements in neither nor , which can be seen from the diagram to be only one element - . Therefore,

$\overline{A\cup B} = \left \{ c\right \}$

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Example Question #554 : Isee Upper Level (Grades 9 12) Mathematics Achievement

The following Venn diagram depicts the number of students who play hockey, football, and baseball. How many students play football and baseball?

Problem_9

Possible Answers:

Correct answer:

Explanation:

The number of students who play football or baseball can by finding the summer of the number of students who play football alone, baseball alone, baseball and football, and all three sports.

30+20+3+3=56

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Example Question #1 : Data Analysis And Probability

A class of students was asked whether they have cats, dogs, or both.The results are depicted in the following Venn diagram. How many students do not have a dog?

Question_5

Possible Answers:

Correct answer:

Explanation:

First, calculate the number of students with a dog:
9+2=11

Next, subtract the number of students with a dog from the total number of students.

30-11=19

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Example Question #1 : How To Find The Answer From A Table

If a standard die is rolled, what is the probability of getting a 1 or a 2?

Possible Answers:

$\dpi{100} \frac{1}{3}$

$\dpi{100} 2$

$\dpi{100} \frac{1}{2}$

$\dpi{100} \frac{1}{6}$

Correct answer:

$\dpi{100} \frac{1}{3}$

Explanation:

We need to know the total number of possibilities, and the total number of ways to achieve our goal.

A standard die has 6 faces, so there are a total of 6 numbers that we could roll.

We want to roll a 1 or a 2, which means there are 2 ways that we can succeed (rolling a 1 or a 2).

Thus, we have a probability of success as $\dpi{100} \frac{2}{6}$ which reduces to $\dpi{100} \frac{1}{3}$ .

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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 : 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 #111 : Numbers And Operations

Example Question #551 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #111 : Numbers And Operations

Example Question #551 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #552 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #553 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #4 : Data Analysis And Probability

Example Question #554 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #1 : Data Analysis And Probability

Example Question #1 : How To Find The Answer From A Table

All ISEE Upper Level Math Resources

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