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Algebra II : Number Lines

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Example Questions

Example Question #1 : Number Lines

For all negative values of $\displaystyle x$ , where y = |x| $\displaystyle y = |x|$ , what is the correct order, from least to greatest, for the following expressions?

a) $y^{2}-x$ $\displaystyle y^{2}-x$

b) $x^{2}+x$ $\displaystyle x^{2}+x$

c) $x^{2}-y^{2}+y$ $\displaystyle x^{2}-y^{2}+y$

Possible Answers:

a,b,c

c,b,a

a,c,b

b,a,c

c,a,b

Correct answer:

c,b,a

Explanation:

The easiest approach to this problem is to pick a value for X, and plug it in.

If we use x=-3 $\displaystyle x=-3$ , then then expression

a) $\displaystyle 3^2--3=9+3=12$ .

b) $\displaystyle (-3)^2+-3=9-3=6$

c) $\displaystyle (-3)^2-(3)^2+3=9-9+3=3$

The order from least to greatest is C,B,A

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Example Question #1 : Number Lines

Put the following numbers in order from least to greatest:

$\displaystyle 2i^2 , 3i^2, 4i^2, 5i^2$

Possible Answers:

$\displaystyle 5i^2, 4i^2, 3i^2, 2i^2$

$\displaystyle 2i^2, 3i^2, 4i^2, 5i^2$

$\displaystyle 2i^2 , 3i^2, 5i^2$

$\displaystyle 5i^2, 3i^2, 2i^2, 4i^2$

Correct answer:

$\displaystyle 5i^2, 4i^2, 3i^2, 2i^2$

Explanation:

$\displaystyle i^2 = -1$ , remembering that, then the most negative number is first, the least negative is last.

Therefore,

$\displaystyle 2i^2 , 3i^2, 4i^2, 5i^2=-2,-3,-4,-5$ .

Thus when we put them in order we get,

$\displaystyle 5i^2,4i^2, 3i^2, 2i^2$

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Example Question #2 : Number Lines

What are integers?

Possible Answers:

Positive whole numbers only.

Negative whole numbers only.

Just $\displaystyle 0$ .

Positive, negative whole numbers and $\displaystyle 0$ .

Any number that is real.

Correct answer:

Positive, negative whole numbers and $\displaystyle 0$ .

Explanation:

Integers are values you would find on a number line.

They are whole numbers that exist in positive and negative values. What divides them is the number $\displaystyle 0$ .

So integers are essentially positive, negative whole numbers and $\displaystyle 0$ .

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Example Question #5145 : Algebra Ii

Which of the following numbers is between $\displaystyle -1$ and $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ ?

Possible Answers:

i^4 $\displaystyle i^4$

log(0) $\displaystyle log(0)$

$150\%$ $\displaystyle 150\%$

$\textup{All values are out of bounds.}$

$\sqrt{\frac{1}{9}}$ $\displaystyle \sqrt{\frac{1}{9}}$

Correct answer:

$\sqrt{\frac{1}{9}}$ $\displaystyle \sqrt{\frac{1}{9}}$

Explanation:

The answer will lie in the range between negative one and a half. Convert all the values given to integer or fractional form.

$150\%=\frac{3}{2}$ $\displaystyle 150\%=\frac{3}{2}$

$i^4= i^2\cdot i^2 = -1\cdot -1=1$ $\displaystyle i^4= i^2\cdot i^2 = -1\cdot -1=1$

$\sqrt{\frac{1}{9}}= \frac{1}{3}$ $\displaystyle \sqrt{\frac{1}{9}}= \frac{1}{3}$

log(0) $\displaystyle log(0)$ is undefined.

Of all the possible answers, $\sqrt{\frac{1}{9}}$ $\displaystyle \sqrt{\frac{1}{9}}$ will fall between the given range.

The answer is: $\sqrt{\frac{1}{9}}$ $\displaystyle \sqrt{\frac{1}{9}}$

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Algebra II : Number Lines

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Number Lines

Example Question #1 : Number Lines

Example Question #2 : Number Lines

Example Question #5145 : Algebra Ii

All Algebra II Resources

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