SAT Math

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• Answer 50 questions in 15 minutes.
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• Match each statement with the correct term.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. If the average of a - b - and 48 is 48 - what is the value of a + b?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Multiply the exponents - (x^3)^4=x^3*4=x^12
Switch the numerator and denominator.


2. Multiplying and Dividing Roots
Multiplying: Multiply the numbers under the different radicals. The product goes under one radical - Dividing: The quotient of more than one square root is equal to the square root of their total quotient.
VofaC: (pie)r(2)h
Remember that any non-zero base to the power of zero is equal to one. Set the exponent equal to zero and solve for x.
Factor out and cancel all factors the numerator and denominator have in common.


3. Finding the Area of a Sector

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4. What types of angles are formed when two lines intersect?
Express them with a common denominator.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Scalene- No sides or angles are equal - Isosceles- Have two equal sides. The angles opposite the equal sides are also equal - Equilateral- All three sides and angles are equal.
Adjacent angles are supplementary - Vertical angles are equal


5. Solving a Proportion
VofaC: (pie)r(2)h
Multiplying: Multiply the numbers under the different radicals. The product goes under one radical - Dividing: The quotient of more than one square root is equal to the square root of their total quotient.
Cross multiply.
Average: Sum of the Terms/Number of the Terms


6. Adding and Subtracting Polynomials
Just add or subtract the coefficients in front of the radicals.
-An integer is divisible by 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
-The Factors of integer n are the positive integers that divide into n with no remainder - The Multiples of n are the positive integers that n divides into with no remainder.
Combine like terms.


7. Raising a Power to a Power
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Multiply the exponents - (x^3)^4=x^3*4=x^12
Multiply and/or divide positives and negatives treat the number parts as usual - and attach a negative sign if there is an odd number of negatives
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


8. What is the Pythagorean Theorem?
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
A(2)+b(2)=c(2)
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


9. Finding the Area of a Circle
(pie)r(squared)
Cancel factors common to the numerator and denominator.
The whole number left over after division.
-The Factors of integer n are the positive integers that divide into n with no remainder - The Multiples of n are the positive integers that n divides into with no remainder.


10. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
FOIL: First - Outer - Inner - Last... Combine Like Terms
In a 30-60-90 triangle - the measure of the longer leg is 7(square root: 3) - then the length of the shorter side or shorter leg must be 7.
Average: Sum of the Terms/Number of the Terms


11. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


12. Finding the Volume of a Rectangular Solid
Values of x the take the denominator of a faction equal to zero - thereby dividing by zero which is not possible - are not in the domain of a function. Set the denominator equal to zero and solve for x. Ans: 3
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
VofaRS=lwh
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


13. Finding the Missing Number in a Series When You are Given the Average
Use the sum... If the average of 4 numbers is 7 - then the sum of those 4 numbers is 4*7 - or 28. Suppose that 3 of the numbers are 3 -5 - and 9. These 3 numbers add up to 16 of that 28 - 12 is the fourth number.
-Increasing: Add the percent to 100 percent - convert to a decimal - and multiply - Decrease: Subtract the percent from 100 percent - convert to a decimal - and multiply.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Set the quadratic equation equal to zero with the terms in order of decreasing exponents - and solve for the roots by factoring. Don't forget to then find the difference in the roots by subtracting them. Ans: 2


14. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Set the quadratic equation equal to zero with the terms in order of decreasing exponents - and solve for the roots by factoring. Don't forget to then find the difference in the roots by subtracting them. Ans: 2
Use simple numbers like 1 and 2 and see what happens.


15. Finding the Length of an Arc in a Circle

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16. Dividing Fractions
Use simple numbers like 1 and 2 and see what happens.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Average the smallest and largest number


17. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

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18. If (Square Root: x-1)+5=12 - what is the value of x/2?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Do whatever is necessary to both sides to isolate the variable.
When a line is tangent to a circle - or touches the circle at just one point - the radius of the circle is perpendicular to the line at the point of contact.
2(pie)r


19. What is the Triangle Inequality Theorem?
Combine the equations so that one of the variables cancels out. 4x+3y=8 and x+y=3. Multiply equation 2 by -3... then add the two equations.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
The whole number left over after division.
The length of one side of a triangle must be greater than the difference and less of the sum of the lengths of the other two sides.


20. Finding the Reciprocal of a Fraction
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the formula distance=rate*time and its variations to help in this question.
The union of Set A and Set B is the set of elements that are in either or both Set A and Set B - The intersection of Set A and Set B is the set of elements common to both Set A and Set B
Switch the numerator and denominator.


21. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
FOIL: First - Outer - Inner - Last... Combine Like Terms
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Cancel factors common to the numerator and denominator.


22. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The 3 interior angles of a any triangle add up to 180 degrees. An exterior angle of a triangle is equal to the sum of the remote - that is - non-adjacent - interior angles.
Don't be confused by all the variables. Recall that (x-y)(x+y)=x(2)-y(2). Then - x(2)-y(2)=5*7=35. x(2)+1-y(2)=x(2)-y(2)+1=35+1=36.


23. Calculating the Probability that an Event will Take Place
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Multiply and/or divide positives and negatives treat the number parts as usual - and attach a negative sign if there is an odd number of negatives


24. Properties of Similar Triangles
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


25. What are Two Special Pythagorean Triples?

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26. Definition of Remainder
Just add or subtract the coefficients in front of the radicals.
Get the absolute value equation by itself. Solve.
The whole number left over after division.
Consecutive odd integers are odd integers in order in a row - such as 1 - 3 - and 5. The difference between any two consecutive odd integers is 2. Translate the question into an equation that expresses the relationship between the integers.


27. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


28. Let N represent the smallest positive integer that is a multiple of 6 and 8 - but leaves a remainder of 2 when divided by 7. What is the value of N?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
(pie)r(squared)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


29. Simplifying a Fraction to Lowest Terms
Use the units to keep things straight - Snowfall inches/hours
In a 30-60-90 triangle - the measure of the longer leg is 7(square root: 3) - then the length of the shorter side or shorter leg must be 7.
An integer is divisible by 3 if the sum of its digits is divisible by 3 - - An integer is divisible by 9 is the sum of its digits is divisible by 9.
Factor out and cancel all factors the numerator and denominator have in common.


30. Sale Price of a Jacket Marked Down 30% Each Week for 3 Weeks - What % of the Original Price is the Cost of the Jacket After the 3 Week Sale Period
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Use the units to keep things straight - Snowfall inches/hours
Express them with a common denominator.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


31. Counting the Total Number of Possibilities for Several Events to Occur
Sum: Average x Number of Terms
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Multiply and/or divide positives and negatives treat the number parts as usual - and attach a negative sign if there is an odd number of negatives
If there are m ways one event can happen and n ways a second event can happen - then there are m*n ways for the 2 events to happen.


32. Finding the Midpoint Between Two Points
Get the absolute value equation by itself. Solve.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
(x1+x2)/2 -(y1+y2)/2
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


33. What is the positive difference between the answers to the equation 35+x(2)=12x?

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34. Finding the Median of a Set of Numbers
Use the distributive property then combine the like terms.
Use the formula distance=rate*time and its variations to help in this question.
The value that falls in the middle of the set.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


35. Multiplying Binomials
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Don't be confused by all the variables. Recall that (x-y)(x+y)=x(2)-y(2). Then - x(2)-y(2)=5*7=35. x(2)+1-y(2)=x(2)-y(2)+1=35+1=36.
FOIL: First - Outer - Inner - Last... Combine Like Terms


36. General Procedure for Multiplying Polynomials
Put each number in the original ratio over the sum of the numbers.
Use the distributive property then combine the like terms.
Combine like terms.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


37. Evaluating an Algebraic Expression
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Multiply the numerators and multiply the denominators.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


38. Definition of a Rational Number
Subtract the smallest from the largest and add 1
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use the formula distance=rate*time and its variations to help in this question.


39. Knowing if an Integer is a Multiple of 5 or 10
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
-An integer is divisible by 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
-Increasing: Add the percent to 100 percent - convert to a decimal - and multiply - Decrease: Subtract the percent from 100 percent - convert to a decimal - and multiply.
The value that falls in the middle of the set.


40. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Values of x the take the denominator of a faction equal to zero - thereby dividing by zero which is not possible - are not in the domain of a function. Set the denominator equal to zero and solve for x. Ans: 3
Direct Variation- y=kx - where k is constant. As x gets larger - y gets larger. If the number of units of B were to double - the number of units of A would double - Inverse Variation- xy=k - where k is a constant. As x gets larger - y gets smaller. A
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Average the smallest and largest number


41. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Use the units to keep things straight - Snowfall inches/hours
Set the quadratic equation equal to zero with the terms in order of decreasing exponents - and solve for the roots by factoring. Don't forget to then find the difference in the roots by subtracting them. Ans: 2


42. Characteristics of a Parallelogram
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


43. Simplifying Square Roots
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
The whole number left over after division.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


44. Dividing Expressions with Exponents that Have a Common Base
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
VofaC: (pie)r(2)h
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
-An integer is divisible by 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.


45. How do you know if an integer is a multiple of 3 or 9?
When a line is tangent to a circle - or touches the circle at just one point - the radius of the circle is perpendicular to the line at the point of contact.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
An integer is divisible by 3 if the sum of its digits is divisible by 3 - - An integer is divisible by 9 is the sum of its digits is divisible by 9.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


46. Finding the Rate of Speed
Put the equation into y=mx+b-- in which case b is the y-intercept.
An integer is divisible by 3 if the sum of its digits is divisible by 3 - - An integer is divisible by 9 is the sum of its digits is divisible by 9.
The whole number left over after division.
Use the formula distance=rate*time and its variations to help in this question.


47. Finding the Volume of a Cylinder
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
VofaC: (pie)r(2)h
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


48. Finding the Domain and Range of a Function
Domain- The domain of a a function is the set of values for which the function is defined - Range- The range of a function is the set of outputs or results of the function.
Area of a Triangle=1/29(base)(height) - The height is the perpendicular distance between the side that's chosen as the base and the opposite vertex.
Use the formula distance=rate*time and its variations to help in this question.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


49. Average Rate and How Do You Find It
Cross multiply.
(pie)r(squared)
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Adjacent angles are supplementary - Vertical angles are equal


50. Finding the Surface Area of a Rectangular Solid
Divide the denominator into the numerator to get a whole number quotient with a remainder. The quotient becomes the whole number of the mixed number. Remainder becomes the numerator.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Values of x the take the denominator of a faction equal to zero - thereby dividing by zero which is not possible - are not in the domain of a function. Set the denominator equal to zero and solve for x. Ans: 3
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)