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Answers
Answer:
Question 1
C=
5
9
(F−32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5
9
degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
ANSWER EXPLANATION: Think of the equation as an equation for a line
y=mx+b
where in this case
C=
5
9
(F−32)
or
C=
5
9
F−
5
9
(32)
You can see the slope of the graph is
5
9
, which means that for an increase of 1 degree Fahrenheit, the increase is
5
9
of 1 degree Celsius.
C=
5
9
(F)
C=
5
9
(1)=
5
9
Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of
9
5
degrees Fahrenheit.
C=
5
9
(F)
1=
5
9
(F)
(F)=
9
5
Since
9
5
= 1.8, statement II is true.
The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of
5
9
degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true:
C=
5
9
(F)
C=
5
9
(
5
9
)
C=
25
81
(whichis≠1)
An increase of
5
9
degree Fahrenheit leads to an increase of
25
81
, not 1 degree, Celsius, and so Statement III is not true.
The final answer is D.
Question 2
The equation
24x2+25x−47
ax−2
=−8x−3−
53
ax−2
is true for all values of x≠
2
a
, where a is a constant.
What is the value of a?
A) -16
B) -3
C) 3
D) 16
ANSWER EXPLANATION: There are two ways to solve this question. The faster way is to multiply each side of the given equation by ax−2 (so you can get rid of the fraction). When you multiply each side by ax−2, you should have:
24x2+25x−47=(−8x−3)(ax−2)−53
You should then multiply (−8x−3) and (ax−2) using FOIL.
24x2+25x−47=−8ax2−3ax+16x+6−53
Then, reduce on the right side of the equation
24x2+25x−47=−8ax2−3ax+16x−47
Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.
The other option which is longer and more tedious is to attempt to plug in all of the answer choices for a and see which answer choice makes both sides of the equation equal. Again, this is the longer option, and I do not recommend it for the actual SAT as it will waste too much time.
The final answer is B.
Question 3
If 3x−y=12, what is the value of
8x
2y
?
A) 212
B) 44
C) 82
D) The value cannot be determined from the information given.
ANSWER EXPLANATION: One approach is to express
8x
2y
so that the numerator and denominator are expressed with the same base. Since 2 and 8 are both powers of 2, substituting 23 for 8 in the numerator of
8x
2y
gives
(23)x
2y
which can be rewritten
23x
2y
Since the numerator and denominator of have a common base, this expression can be rewritten as 2(3x−y). In the question, it states that 3x−y=12, so one can substitute 12 for the exponent, 3x−y, which means that
8x
2y
=212
The final answer is A.
Question 4
Points A and B lie on a circle with radius 1, and arc
⌢
AB
has a length of
π
3
. What fraction of the circumference of the circle is the length of arc
⌢
AB
?
ANSWER EXPLANATION: To figure out the answer to this question, you'll first need to know the formula for finding the circumference of a circle.
The circumference, C, of a circle is C=2πr, where r is the radius of the circle. For the given circle with a radius of 1, the circumference is C=2(π)(1), or C=2π.
To find what fraction of the circumference the length of
⌢
AB
is, divide the length of the arc by the circumference, which gives
π
3
÷2π. This division can be represented by
π
3
*
1
2
π=
1
6
.
The fraction
1
6
can also be rewritten as 0.166 or 0.167.
The final answer is
1
6
, 0.166, or 0.167.