SAT- Math LATEST VERSION 173 QUESTIONS AND ANSWERS WITH STUDY
GUIDE DETAILED AND VERIFIED FOR GUARANTEED PASS, LATEST UPDATE
1. How do you solve a To solve a proportion, cross multiply.
proportion? For example:
x/5 = 3/4
4x = 3 x 5
x = 15/4 = 3.75
2. How do you solve To solve a rate problem, use the units to keep things straight. For exam-
a problem involving ple, if asked: If snow is falling at the rate of one foot every four hours,
rates? 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
3. What is the average Average rate is not simply the average of the rates.
rate and how do you Average A per B = Total A/ Total B, so
find it? 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.
, SAT- Math LATEST VERSION 173 QUESTIONS AND ANSWERS WITH STUDY
GUIDE DETAILED AND VERIFIED FOR GUARANTEED PASS, LATEST UPDATE
4. What is the formula To find the average of a set of numbers, add them up and divide by how
used to find average? many there are.
Average = Sum of the terms / Number of the terms
5. How do you quickly For evenly spaced numbers, the average is the middle value. To find the
find the average of a average of evenly spaced numbers, just average the smallest and the
series of evenly spaced largest.
numbers? 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
6. If you have an average Use the formula:
of a series of numbers, Sum = Average x Number of terms
how can you find their If the average of 10 numbers is 50, then they add up to 10 x 50, or 500.
sum?
7. How do you find the To find a missing number when you're given the average, use the sum.
missing number in a Sum = Average x Number of Terms
series when you are For example, if the average of 4 numbers is 7, then the sum of those 4
given the average? 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.
8. How do you find the The median of a set of numbers is the value that falls in the middle of the
median of a set of num- set.
bers? 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.
9. How do you calculate The fundamental counting principle: If there are m ways one event can
the total number of happen and n ways a second event can happen, then there are m x n
, SAT- Math LATEST VERSION 173 QUESTIONS AND ANSWERS WITH STUDY
GUIDE DETAILED AND VERIFIED FOR GUARANTEED PASS, LATEST UPDATE
possibilities for several ways for the 2 events to happen. For example, with 5 shirts and 7 pairs
events to occur? of pants to choose from, you can have 5 x 7 = 35 ditterent outfits.
10. How do you find the The mode of a set of numbers is the value that appears most often.
mode of a set of num- For example, if your test scores were 88, 57, 68, 85, 99, 93, 93, 84, and
bers? 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.
11. How do you multiply To multiply exponential terms with the same base, add the exponents
expressions with expo- and keep the same base:
nents that have a com- x^3 x x^4 = x^3+4 = x^7
mon base?
12. How do you calculate Number of Favorable Outcomes/ Total Possible Outcomes
the probability that an ^ Probability =
event will take place? 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%.
13. How do you divide ex- To divide exponential terms with the same base, subtract the exponents
pressions with expo- and keep the same base:
nents that have a com- y^13 / y^8 = y^13-8 = y^5
mon base?
14. How do you raise a To raise a power to a power, multiply the exponents:
power to a power? (x^3)^4 = x^3 x 4 = x^12
15. How do you simplify To simplify a square root, factor out the perfect squares under the radical.
square roots? Take the square root of the perfect square and put the result in front.
16.
, SAT- Math LATEST VERSION 173 QUESTIONS AND ANSWERS WITH STUDY
GUIDE DETAILED AND VERIFIED FOR GUARANTEED PASS, LATEST UPDATE
How do you add and Only like radicals can be added/subtracted from one another. To combine
subtract roots? radicals, just add or subtract their coeflcients.
17. How do you multiply The product of more than one square root is equal to the square root of
and divide roots? their total product.
The quotient of more than one square root is equal to the square root of
their total quotient.
18. How do you calcu- A negative exponent indicates a reciprocal. To arrive at an equivalent
late negative expo- expression, take the reciprocal of the base and change the sign of the
nents and fractional ex- exponent.
ponents? A fractional exponent indicates a root.
19. How do you determine The absolute value of a number is the distance of the number from zero
the absolute value of a on the number line. Because absolute value is a distance, it is always
number? 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.
20. How do you evaluate To evaluate an algebraic expression, substitute the given values for the
an algebraic expres- unknowns and calculate according to the correct order of operations, or
sion? PEMDAS.
For example, to find the value of x^2 = 5x - 6 when x = -2, replace x with
-2: (-2)^2 + 5 (-2) - 6 = 4 + (-10) - 6 = -12.
21. How do you add and To add or subtract monomials, first make sure that the terms to be
subtract monomials? combined have exactly the same variable(s). This makes them like terms.
Then, to combine like terms, keep the variable part unchanged while
adding or subtracting the coeflcients.
For example: 2a + 3a = (2 + 3)a = 5a
22.
GUIDE DETAILED AND VERIFIED FOR GUARANTEED PASS, LATEST UPDATE
1. How do you solve a To solve a proportion, cross multiply.
proportion? For example:
x/5 = 3/4
4x = 3 x 5
x = 15/4 = 3.75
2. How do you solve To solve a rate problem, use the units to keep things straight. For exam-
a problem involving ple, if asked: If snow is falling at the rate of one foot every four hours,
rates? 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
3. What is the average Average rate is not simply the average of the rates.
rate and how do you Average A per B = Total A/ Total B, so
find it? 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.
, SAT- Math LATEST VERSION 173 QUESTIONS AND ANSWERS WITH STUDY
GUIDE DETAILED AND VERIFIED FOR GUARANTEED PASS, LATEST UPDATE
4. What is the formula To find the average of a set of numbers, add them up and divide by how
used to find average? many there are.
Average = Sum of the terms / Number of the terms
5. How do you quickly For evenly spaced numbers, the average is the middle value. To find the
find the average of a average of evenly spaced numbers, just average the smallest and the
series of evenly spaced largest.
numbers? 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
6. If you have an average Use the formula:
of a series of numbers, Sum = Average x Number of terms
how can you find their If the average of 10 numbers is 50, then they add up to 10 x 50, or 500.
sum?
7. How do you find the To find a missing number when you're given the average, use the sum.
missing number in a Sum = Average x Number of Terms
series when you are For example, if the average of 4 numbers is 7, then the sum of those 4
given the average? 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.
8. How do you find the The median of a set of numbers is the value that falls in the middle of the
median of a set of num- set.
bers? 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.
9. How do you calculate The fundamental counting principle: If there are m ways one event can
the total number of happen and n ways a second event can happen, then there are m x n
, SAT- Math LATEST VERSION 173 QUESTIONS AND ANSWERS WITH STUDY
GUIDE DETAILED AND VERIFIED FOR GUARANTEED PASS, LATEST UPDATE
possibilities for several ways for the 2 events to happen. For example, with 5 shirts and 7 pairs
events to occur? of pants to choose from, you can have 5 x 7 = 35 ditterent outfits.
10. How do you find the The mode of a set of numbers is the value that appears most often.
mode of a set of num- For example, if your test scores were 88, 57, 68, 85, 99, 93, 93, 84, and
bers? 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.
11. How do you multiply To multiply exponential terms with the same base, add the exponents
expressions with expo- and keep the same base:
nents that have a com- x^3 x x^4 = x^3+4 = x^7
mon base?
12. How do you calculate Number of Favorable Outcomes/ Total Possible Outcomes
the probability that an ^ Probability =
event will take place? 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%.
13. How do you divide ex- To divide exponential terms with the same base, subtract the exponents
pressions with expo- and keep the same base:
nents that have a com- y^13 / y^8 = y^13-8 = y^5
mon base?
14. How do you raise a To raise a power to a power, multiply the exponents:
power to a power? (x^3)^4 = x^3 x 4 = x^12
15. How do you simplify To simplify a square root, factor out the perfect squares under the radical.
square roots? Take the square root of the perfect square and put the result in front.
16.
, SAT- Math LATEST VERSION 173 QUESTIONS AND ANSWERS WITH STUDY
GUIDE DETAILED AND VERIFIED FOR GUARANTEED PASS, LATEST UPDATE
How do you add and Only like radicals can be added/subtracted from one another. To combine
subtract roots? radicals, just add or subtract their coeflcients.
17. How do you multiply The product of more than one square root is equal to the square root of
and divide roots? their total product.
The quotient of more than one square root is equal to the square root of
their total quotient.
18. How do you calcu- A negative exponent indicates a reciprocal. To arrive at an equivalent
late negative expo- expression, take the reciprocal of the base and change the sign of the
nents and fractional ex- exponent.
ponents? A fractional exponent indicates a root.
19. How do you determine The absolute value of a number is the distance of the number from zero
the absolute value of a on the number line. Because absolute value is a distance, it is always
number? 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.
20. How do you evaluate To evaluate an algebraic expression, substitute the given values for the
an algebraic expres- unknowns and calculate according to the correct order of operations, or
sion? PEMDAS.
For example, to find the value of x^2 = 5x - 6 when x = -2, replace x with
-2: (-2)^2 + 5 (-2) - 6 = 4 + (-10) - 6 = -12.
21. How do you add and To add or subtract monomials, first make sure that the terms to be
subtract monomials? combined have exactly the same variable(s). This makes them like terms.
Then, to combine like terms, keep the variable part unchanged while
adding or subtracting the coeflcients.
For example: 2a + 3a = (2 + 3)a = 5a
22.
