1
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SAT- Math Questions and Answers (100%
Correct Answers) Already Graded A+
How do you convert from part-to-part ratios to part-to-whole
ratios?Ans: If the parts add up to the whole, a part-to-part ratio
can be turned into two part-to-whole ratios by putting each
number in the original ratio over the sum of the numbers. For
example, if the ratio of males to females is 1 to 2, then the males-
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to-people ratio is 1/ (1+2) = 1/3 and the females-to-people ratio is
2/ (1+2) = 2/3
In other words, 2/3 of all the people are female.
How do you solve a proportion?Ans: To solve a proportion, cross
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multiply.
For example:
x/5 = 3/4
4x = 3 x 5
x = 15/4 = 3.75
How do you solve a problem involving rates?Ans: To solve a rate
problem, use the units to keep things straight. For example, if
asked: If snow is falling at the rate of one foot every four hours,
how many inches of snow will fall in seven hours?
Your setup would be:
1 foot/ 4 hours = x inches/ 7 hours
12 inches/ 4 hours = x inches/ 7 hours
4x = 12 x 7
x = 21
What is the average rate and how do you find it?Ans: Average
rate is not simply the average of the rates.
, 2
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Average A per B = Total A/ Total B, so
Average Speed = Total distance/ Total time
For example, to find the average speed for 120 miles at 40 mph
and 120 miles at 60 mph, don't just average the two speeds. First,
figure out the total distance and the total time. The total distance
is 120 + 120 = 240 miles. The times are three hours for the first leg
and two hours for the second leg, or five hours total. The average
speed, then, is 240/5 = 48 miles per hour.
What is the formula used to find average?Ans: To find the
average of a set of numbers, add them up and divide by how
many there are.
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Average = Sum of the terms / Number of the terms
How do you quickly find the average of a series of evenly spaced
numbers?Ans: For evenly spaced numbers, the average is the
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middle value. To find the average of evenly spaced numbers, just
average the smallest and the largest.
For example, the average of all the integers from 13 through 77 is
the same as the average of 13 and 77.
13 + 77/ 2 = 90/ 2 = 45
If you have an average of a series of numbers, how can you find
their sum?Ans: Use the formula:
Sum = Average x Number of terms
If the average of 10 numbers is 50, then they add up to 10 x 50, or
500.
How do you find the missing number in a series when you are
given the average?Ans: To find a missing number when you're
given the average, use the sum.
Sum = Average x Number of Terms
For example, if the average of 4 numbers is 7, then the sum of
those 4 numbers is 4 x 7, or 28. Suppose that 3 of the numbers are
3, 5, and 8. These 3 numbers add up to 16 of that 28, which leaves
12 for the fourth number.
, 3
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How do you find the median of a set of numbers?Ans: The
median of a set of numbers is the value that falls in the middle of
the set.
For example, if you have 5 test scores, and they are 88, 86, 57, 94,
and 73, you must first list the scores in increasing or decreasing
order: 57, 73, 86, 88, 94. The median is the middle number, or 86. If
there is an even number of values in a set (6 test scores, for
instance), simply take the average of the two middle numbers.
How do you calculate the total number of possibilities for several
events to occur?Ans: The fundamental counting principle: If there
are m ways one event can happen and n ways a second event
can happen, then there are m x n ways for the 2 events to
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happen. For example, with 5 shirts and 7 pairs of pants to choose
from, you can have 5 x 7 = 35 different outfits.
How do you find the mode of a set of numbers?Ans: The mode of
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a set of numbers is the value that appears most often.
For example, if your test scores were 88, 57, 68, 85, 99, 93, 93, 84,
and 81, the mode of the scores would be 93 because it appear
more often than any other score.
If there is a tie for the most common value in a set, the set has
more than one mode.
How do you multiply expressions with exponents that have a
common base?Ans: To multiply exponential terms with the same
base, add the exponents and keep the same base:
x^3 x x^4 = x^3+4 = x^7
How do you calculate the probability that an event will take
place?Ans: Number of Favorable Outcomes/ Total Possible
Outcomes
^ Probability =
For example, if you have 12 shirts in a drawer and 9 of them are
white, the probability of picking a white shirt at random is 9/ 12 =
3/ 4. This probability can also be expressed as .75 or 75%.
, 4
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How do you divide expressions with exponents that have a
common base?Ans: To divide exponential terms with the same
base, subtract the exponents and keep the same base:
y^13 / y^8 = y^13-8 = y^5
How do you raise a power to a power?Ans: To raise a power to a
power, multiply the exponents:
(x^3)^4 = x^3 x 4 = x^12
How do you simplify square roots?Ans: To simplify a square root,
factor out the perfect squares under the radical. Take the square
root of the perfect square and put the result in front.
How do you add and subtract roots?Ans: Only like radicals can
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be added/subtracted from one another. To combine radicals, just
add or subtract their coefficients.
How do you multiply and divide roots?Ans: The product of more
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than one square root is equal to the square root of their total
product.
The quotient of more than one square root is equal to the square
root of their total quotient.
How do you calculate negative exponents and fractional
exponents?Ans: A negative exponent indicates a reciprocal. To
arrive at an equivalent expression, take the reciprocal of the base
and change the sign of the exponent.
A fractional exponent indicates a root.
How do you determine the absolute value of a number?Ans: The
absolute value of a number is the distance of the number from
zero on the number line. Because absolute value is a distance, it is
always positive.
The absolute value of 7 is 7. Similarly the absolute value of -7 is 7.
Every positive number is the absolute value of two numbers: itself
and its opposite.
How do you evaluate an algebraic expression?Ans: To evaluate
an algebraic expression, substitute the given values for the
For Expert help and assignment solutions, +254707240657
SAT- Math Questions and Answers (100%
Correct Answers) Already Graded A+
How do you convert from part-to-part ratios to part-to-whole
ratios?Ans: If the parts add up to the whole, a part-to-part ratio
can be turned into two part-to-whole ratios by putting each
number in the original ratio over the sum of the numbers. For
example, if the ratio of males to females is 1 to 2, then the males-
© 2025 Assignment Expert
to-people ratio is 1/ (1+2) = 1/3 and the females-to-people ratio is
2/ (1+2) = 2/3
In other words, 2/3 of all the people are female.
How do you solve a proportion?Ans: To solve a proportion, cross
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multiply.
For example:
x/5 = 3/4
4x = 3 x 5
x = 15/4 = 3.75
How do you solve a problem involving rates?Ans: To solve a rate
problem, use the units to keep things straight. For example, if
asked: If snow is falling at the rate of one foot every four hours,
how many inches of snow will fall in seven hours?
Your setup would be:
1 foot/ 4 hours = x inches/ 7 hours
12 inches/ 4 hours = x inches/ 7 hours
4x = 12 x 7
x = 21
What is the average rate and how do you find it?Ans: Average
rate is not simply the average of the rates.
, 2
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Average A per B = Total A/ Total B, so
Average Speed = Total distance/ Total time
For example, to find the average speed for 120 miles at 40 mph
and 120 miles at 60 mph, don't just average the two speeds. First,
figure out the total distance and the total time. The total distance
is 120 + 120 = 240 miles. The times are three hours for the first leg
and two hours for the second leg, or five hours total. The average
speed, then, is 240/5 = 48 miles per hour.
What is the formula used to find average?Ans: To find the
average of a set of numbers, add them up and divide by how
many there are.
© 2025 Assignment Expert
Average = Sum of the terms / Number of the terms
How do you quickly find the average of a series of evenly spaced
numbers?Ans: For evenly spaced numbers, the average is the
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middle value. To find the average of evenly spaced numbers, just
average the smallest and the largest.
For example, the average of all the integers from 13 through 77 is
the same as the average of 13 and 77.
13 + 77/ 2 = 90/ 2 = 45
If you have an average of a series of numbers, how can you find
their sum?Ans: Use the formula:
Sum = Average x Number of terms
If the average of 10 numbers is 50, then they add up to 10 x 50, or
500.
How do you find the missing number in a series when you are
given the average?Ans: To find a missing number when you're
given the average, use the sum.
Sum = Average x Number of Terms
For example, if the average of 4 numbers is 7, then the sum of
those 4 numbers is 4 x 7, or 28. Suppose that 3 of the numbers are
3, 5, and 8. These 3 numbers add up to 16 of that 28, which leaves
12 for the fourth number.
, 3
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How do you find the median of a set of numbers?Ans: The
median of a set of numbers is the value that falls in the middle of
the set.
For example, if you have 5 test scores, and they are 88, 86, 57, 94,
and 73, you must first list the scores in increasing or decreasing
order: 57, 73, 86, 88, 94. The median is the middle number, or 86. If
there is an even number of values in a set (6 test scores, for
instance), simply take the average of the two middle numbers.
How do you calculate the total number of possibilities for several
events to occur?Ans: The fundamental counting principle: If there
are m ways one event can happen and n ways a second event
can happen, then there are m x n ways for the 2 events to
© 2025 Assignment Expert
happen. For example, with 5 shirts and 7 pairs of pants to choose
from, you can have 5 x 7 = 35 different outfits.
How do you find the mode of a set of numbers?Ans: The mode of
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a set of numbers is the value that appears most often.
For example, if your test scores were 88, 57, 68, 85, 99, 93, 93, 84,
and 81, the mode of the scores would be 93 because it appear
more often than any other score.
If there is a tie for the most common value in a set, the set has
more than one mode.
How do you multiply expressions with exponents that have a
common base?Ans: To multiply exponential terms with the same
base, add the exponents and keep the same base:
x^3 x x^4 = x^3+4 = x^7
How do you calculate the probability that an event will take
place?Ans: Number of Favorable Outcomes/ Total Possible
Outcomes
^ Probability =
For example, if you have 12 shirts in a drawer and 9 of them are
white, the probability of picking a white shirt at random is 9/ 12 =
3/ 4. This probability can also be expressed as .75 or 75%.
, 4
For Expert help and assignment solutions, +254707240657
How do you divide expressions with exponents that have a
common base?Ans: To divide exponential terms with the same
base, subtract the exponents and keep the same base:
y^13 / y^8 = y^13-8 = y^5
How do you raise a power to a power?Ans: To raise a power to a
power, multiply the exponents:
(x^3)^4 = x^3 x 4 = x^12
How do you simplify square roots?Ans: To simplify a square root,
factor out the perfect squares under the radical. Take the square
root of the perfect square and put the result in front.
How do you add and subtract roots?Ans: Only like radicals can
© 2025 Assignment Expert
be added/subtracted from one another. To combine radicals, just
add or subtract their coefficients.
How do you multiply and divide roots?Ans: The product of more
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than one square root is equal to the square root of their total
product.
The quotient of more than one square root is equal to the square
root of their total quotient.
How do you calculate negative exponents and fractional
exponents?Ans: A negative exponent indicates a reciprocal. To
arrive at an equivalent expression, take the reciprocal of the base
and change the sign of the exponent.
A fractional exponent indicates a root.
How do you determine the absolute value of a number?Ans: The
absolute value of a number is the distance of the number from
zero on the number line. Because absolute value is a distance, it is
always positive.
The absolute value of 7 is 7. Similarly the absolute value of -7 is 7.
Every positive number is the absolute value of two numbers: itself
and its opposite.
How do you evaluate an algebraic expression?Ans: To evaluate
an algebraic expression, substitute the given values for the
