Divide
48 / 8 =
48 / 8 = 6
C=59(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) 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=59(F−32)
or
C=59F−59(32)
You can see the slope of the graph is 59, which means that for an increase of 1 degree Fahrenheit, the increase is 59 of 1 degree Celsius.
C=59(F)
C=59(1)=59
Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of 95 degrees Fahrenheit.
C=59(F)
1=59(F)
(F)=95
Since 95 = 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 59 degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true:
C=59(F)
C=59(59)
C=2581(whichis≠1)
An increase of 59 degree Fahrenheit leads to an increase of 2581, not 1 degree, Celsius, and so Statement III is not true.
The final answer is D.
995 x 4 =
3980
5/9x1/2
5/18
3/7 / 2/3
9/14
6 6/10 x 8/12
4 2/5
The equation 24x2+25x−47ax−2=−8x−3−53ax−2 is true for all values of x≠2a, 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.
724 x 2 =
1448
4/9x2/3
8/27
10 4/9 x 1/2
5 2/9
If 3x−y=12, what is the value of 8x2y?
A) 212
B) 44
C) 82
D) The value cannot be determined from the information given.
ANSWER EXPLANATION: One approach is to express
8x2y
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 8x2y gives
(23)x2y
which can be rewritten
23x2y
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
8x2y=212
The final answer is A.
160 x 5
1/3x2/3
2/9
6/5 / 5/8
48/25
9 3/5 x 1/2 =
4 4/5
Points A and B lie on a circle with radius 1, and arc AB⌢ has a length of π3. 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 π3÷2π. This division can be represented by π3*12π=16.
The fraction 16 can also be rewritten as 0.166 or 0.167.
The final answer is 16, 0.166, or 0.167.
827 x 3
2481
1/3x1/2
1/6
6/7 / 10/3
9/35
9 1/2 x 1/3
3 1/9
8−i3−2i
If the expression above is rewritten in the form a+bi, where a and b are real numbers, what is the value of a? (Note: i=−1)
ANSWER EXPLANATION: To rewrite 8−i3−2i in the standard form a+bi, you need to multiply the numerator and denominator of 8−i3−2i by the conjugate, 3+2i. This equals
(8−i3−2i)(3+2i3+2i)=24+16i−3+(−i)(2i)(32)−(2i)2
Since i2=−1, this last fraction can be reduced simplified to
24+16i−3i+29−(−4)=26+13i13
which simplifies further to 2+i. Therefore, when 8−i3−2i is rewritten in the standard form a + bi, the value of a is 2.
The final answer is A.
663 x 3
1989
2/5x2/7
4/35
5/9 / 1/8
40/9