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# CAHSEE practice: Problems 1-3

Video transcript

Problem number 1. Which number has the greatest
absolute value? Absolute value is just the
distance that the number is from 0, or how large the number
is, regardless of its sign or its direction. So if you kind of visualize it
on a number line, the absolute value of minus 17. Minus 17 is 17 to
the left of 0. So its absolute value
is just 17. The absolute value
of minus 13? Well, it's 13 to the left of
0, if you imagine it on a number line. So it's just going to be 13. Absolute value of 15? Well, that's just
going to be 15. It's 15 to the right of
0 on the number line. I think you see a
pattern here. When you take the absolute
value of a number, you essentially just disregard
the sign. The absolute value of a negative
number is going to be positive, and the absolute value
of a positive number is going to be positive. The absolute value is always
going to be positive, because you're just measuring how far
you are away from 0 on the number line. And then finally, the absolute
value of 19 is going to be equal to 19. So the number that has the
greatest absolute value? Well, the greatest absolute
value is right there, it's 19. So 19 has the greatest
absolute value. So it also happens to be the
largest number here. Just like that. Problem number 2. Maybe I'll do this in gray. Between which two integers
is the value of the square root of 61? So the way you think about this
is that you know there's some number-- the square root
of 61 is going to be some decimal number, I don't know
what it is-- but there's going to be some number that if I
square it, is going to be a little bit lower than 61. And then some other integer,
if I square it, should be a little bit greater than 61. So let's see if we can
figure this out. So 6 squared is going
to be 36. And then 7 squared is
going to be 49. That number is not
dark enough. Do a darker color. So this isn't going to
be the case, right? Because the square of 61-- or 61
is greater than 49-- so the square root of 61 is going to
be greater than the square root of 49. Or actually let me write
it this way. I could rewrite 6 and 7 as the
square root of 36 and the square root of 49. I can rewrite 7 and 8 as the
square root of 49 and the square root of 64, right? 7 squared is 49, so the square
root of 49 is 7. 8 squared is 64, so the square
root of 64 is going to be 8. So I just rewrote 7 and 8 as the
square root of 49 and the square root of 64. Well, the square root of 61 is
clearly going to be between these two numbers, right? It's going to be between the
square root of 49 and the square root of 64. The 61 is between 49 and 64. So our answer is B. Square root of 61 is between
these two numbers, but these two numbers are the same
thing as 7 and 8. Next problem, number 3. Use the addition problems below
to answer the question. All right, so they wrote some
addition problems right there. We're dealing with fractions. Let's see where this goes. Based on this pattern, what is
the sum of 1/2 plus 1/4 plus 1/8 plus 1/16, all the
way to 1/1024? So let's see if we can discern
some type of a pattern here. Maybe I'll do this in red just
to keep things interesting. So when I took the first
two terms, I got 3/4. When I took the next two terms,
or not the next two terms. When I add another
term to it. When I add the 1/8 term to this
over here, I got 7/8. Then when I add a 1/16 to
7/8, I get a 15/16. So the general pattern here is
that whenever I add it up, my denominator and my sum-- I guess
you could call it that way-- my denominator is going
to be the same denominator that I have right there. And then my numerator, if I
just look at all of the pattern here, just turns out to
be 1 less than that, right? So when I added 1/2 plus 1/4, I
got 4 in the denominator and 3 in the numerator. When I had 1/2 plus 1/4 plus
1/8, 8 in the denominator and 1 less than that in
the numerator. When I added it all the way
to 1/16, I got 16 in the denominator and 1 less
in the numerator. When I added it all the way
to 32, I got 32 in the denominator and 1 less
in the numerator. And this only worked when I'm
adding successive powers of, I guess you could call
it 1/2, right? This is 1/2, 1/2 squared,
1/2 to the third, 1/2 to the fourth. So based on this pattern, what
is the sum if I were to go all the way to 1/1024? Well, based on this pattern, my
denominator is going to be 1,024, and my numerator is going
to be 1 less than 1,024. So it's going to be 1,023. And that is choice
C right there.