MILESTONE
24/25
24/25 that's 96% RETAKE
24 questions were answered correctly.
1 question was answered incorrectly.
1
Jessica bought the ingredients to make chicken soup, and
wanted to make a double batch, which would be 18 cups of soup.
A quick Google search told her that this was 259.9 cubic inches.
She hoped the soup pot below would be big enough.
The soup pot is 9 inches tall with a radius of 3.5 inches.
,What is the volume of the soup pot? Answer choices are
MILESTONE
rounded to the nearest whole cubic inch.
24/25
346 cubic inches
169 cubic inches
890 cubic inches
197 cubic inches
RATIONALE
Recall that the volume of the pot can be
represented with the formula for the volume of a
cylinder, where V is the value, r is the radius of the
base, and h is the height. First, substitute 3.5 for r
and 9 for h.
Once we have the given values plugged into the
appropriate places, we can evaluate the formula.
Following Order of Operations, we will first square
the radius of 3.5.
3.5 squared equals 12.25. Next, we can multiply
the remaining values. Using a calculator with a pi
button (π) will be the most accurate; otherwise we
can use the value 3.14.
Multiplying π times 12.25 times 9 is 346, when
rounded to the nearest whole cubic inch. The
volume of the soup pot is 346 cubic inches.
CONCEPT
Volume
2
,Write the following as a single rational expression.
MILESTONE
24/25
RATIONALE
Just as with numeric fractions, we can
subtract algebraic fractions. To do so, we
need to rewrite the fractions so that they
have a common denominator. One strategy
is to multiply the two denominators
together. But if we change the denominator,
we have to also change the numerator to
keep things equal.
Multiply the numerator and denominator of
the first fraction by the denominator of the
second fraction; repeat for the second
fraction. We now have an equivalent
expression with common denominators.
Before we subtract across the numerators,
let's simplify each numerator.
1 times (x – 2) is equal to x – 2 and 1 times x
is equal to x. We can now subtract across
the numerators.
, The numerator is x – 2 – x and the
MILESTONE denominator is x(x – 2). Finally, simplify the
numerator.
24/25
This is the simplified rational expression.
CONCEPT
Adding and Subtracting Rational Expressions
3
A deposit of $1200 is added to an account that earns 5% interest,
compounded annually. Each year, an additional deposit of $1200
is added to the account.
What is the value of the account after the tenth total deposit if
no withdrawals or additional deposits are made?
$12,004.20
$15,093.47
$11,628.90
$14,624.40
RATIONALE
Start by building a sequence to show
the values in the account each year.
The account starts with an initial
deposit of $1200. After a year, the
initial $1200 deposit grows by 5%
and is now valued at $1260. Then
another deposit of $1200 is added. In
this sequence, the first term is the
24/25
24/25 that's 96% RETAKE
24 questions were answered correctly.
1 question was answered incorrectly.
1
Jessica bought the ingredients to make chicken soup, and
wanted to make a double batch, which would be 18 cups of soup.
A quick Google search told her that this was 259.9 cubic inches.
She hoped the soup pot below would be big enough.
The soup pot is 9 inches tall with a radius of 3.5 inches.
,What is the volume of the soup pot? Answer choices are
MILESTONE
rounded to the nearest whole cubic inch.
24/25
346 cubic inches
169 cubic inches
890 cubic inches
197 cubic inches
RATIONALE
Recall that the volume of the pot can be
represented with the formula for the volume of a
cylinder, where V is the value, r is the radius of the
base, and h is the height. First, substitute 3.5 for r
and 9 for h.
Once we have the given values plugged into the
appropriate places, we can evaluate the formula.
Following Order of Operations, we will first square
the radius of 3.5.
3.5 squared equals 12.25. Next, we can multiply
the remaining values. Using a calculator with a pi
button (π) will be the most accurate; otherwise we
can use the value 3.14.
Multiplying π times 12.25 times 9 is 346, when
rounded to the nearest whole cubic inch. The
volume of the soup pot is 346 cubic inches.
CONCEPT
Volume
2
,Write the following as a single rational expression.
MILESTONE
24/25
RATIONALE
Just as with numeric fractions, we can
subtract algebraic fractions. To do so, we
need to rewrite the fractions so that they
have a common denominator. One strategy
is to multiply the two denominators
together. But if we change the denominator,
we have to also change the numerator to
keep things equal.
Multiply the numerator and denominator of
the first fraction by the denominator of the
second fraction; repeat for the second
fraction. We now have an equivalent
expression with common denominators.
Before we subtract across the numerators,
let's simplify each numerator.
1 times (x – 2) is equal to x – 2 and 1 times x
is equal to x. We can now subtract across
the numerators.
, The numerator is x – 2 – x and the
MILESTONE denominator is x(x – 2). Finally, simplify the
numerator.
24/25
This is the simplified rational expression.
CONCEPT
Adding and Subtracting Rational Expressions
3
A deposit of $1200 is added to an account that earns 5% interest,
compounded annually. Each year, an additional deposit of $1200
is added to the account.
What is the value of the account after the tenth total deposit if
no withdrawals or additional deposits are made?
$12,004.20
$15,093.47
$11,628.90
$14,624.40
RATIONALE
Start by building a sequence to show
the values in the account each year.
The account starts with an initial
deposit of $1200. After a year, the
initial $1200 deposit grows by 5%
and is now valued at $1260. Then
another deposit of $1200 is added. In
this sequence, the first term is the
