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. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Standard function notation is written f(x) and read 'f of x.' To evaluate the function f(x)=2x+3 for f(4) - replace every x with 4 and simplify. f(4)=2(4)+3=11.
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. Solving an Inequality
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Sector is a piece of the area of a circle. Area of a Sector: (n/360)((pie)r2) - n is the degree measure of the sector's central angle
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


3. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Slope=change in y/change in x
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


4. What is the Triangle Inequality Theorem?
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Ue the formula y=mx+b - and remember that the value of m is the slope of the line. The slopes of two perpendicular lines are negative reciprocals of one another.


5. Comparing the values of two or more Fractions
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Express them with a common denominator.


6. How do you know if an integer is a multiple of 3 or 9?
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.
Part=Percent x Whole
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
FOIL: First - Outer - Inner - Last... Combine Like Terms


7. Finding the Area of a Triangle

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8. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


9. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


10. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The whole number left over after division.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


11. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Two relatively prime numbers are integers that have no common factor other than 1.
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
Ue the formula y=mx+b - and remember that the value of m is the slope of the line. The slopes of two perpendicular lines are negative reciprocals of one another.
FOIL: First - Outer - Inner - Last... Combine Like Terms


12. Finding the LCM of Two or More Numbers

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13. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Cross multiply.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
(pie)r(squared)


14. Setting Up a Ratio
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Put each number in the original ratio over the sum of the numbers.


15. Solving a Linear Equation
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Variables that have an inverse relationship will always have the same product. As one value gets larger - the other gets smaller. Set up and solve the equation 310=6x. Answer: 5
Do whatever is necessary to both sides to isolate the variable.


16. Convert From a Fraction to a Decimal - Vice Versa
Fraction to a Decimal: Divide the Denominator into the numerator - Decimal to a Fraction: Set the decimal over 1 and multiply the numerator and denominator by 10 raised to the number of digits to the right of the decimal point.
Subtract the smallest from the largest and add 1
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Combine like terms.


17. Converting from an Improper Fraction to a Mixed Number
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Part=Percent x Whole
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.


18. Properties of a 30-60-90 Triangle
Subtract the smallest from the largest and add 1
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.
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


19. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


20. Raising a Power to a Power
Express them with a common denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12


21. General Procedure for Multiplying Polynomials
(x1+x2)/2 -(y1+y2)/2
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.
Put each number in the original ratio over the sum of the numbers.
Use the distributive property then combine the like terms.


22. If 4(x(2)-10x+25) - then what is the value of x?
Just add or subtract the coefficients in front of the radicals.
Standard function notation is written f(x) and read 'f of x.' To evaluate the function f(x)=2x+3 for f(4) - replace every x with 4 and simplify. f(4)=2(4)+3=11.
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.
-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.


23. Finding the Volume of a Rectangular Solid
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
VofaRS=lwh


24. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Use the units to keep things straight - Snowfall inches/hours
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


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

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26. What are Two Special Pythagorean Triples?

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27. If (Square Root: x-1)+5=12 - what is the value of x/2?
FOIL: First - Outer - Inner - Last... Combine Like Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Four equal acute angles and four equal obtuse angles.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


28. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Average the smallest and largest number
-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.
Factor out and cancel all factors the numerator and denominator have in common.


29. PEMDAS
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Just add or subtract the coefficients in front of the radicals.
-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.


30. Determining Absolute Value of a Number
-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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


31. Finding the GCF of Two or More Numbers
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Fraction to a Decimal: Divide the Denominator into the numerator - Decimal to a Fraction: Set the decimal over 1 and multiply the numerator and denominator by 10 raised to the number of digits to the right of the decimal point.


32. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Ue the formula y=mx+b - and remember that the value of m is the slope of the line. The slopes of two perpendicular lines are negative reciprocals of one another.


33. Finding the Slope When Given an Equation of a Line
Standard function notation is written f(x) and read 'f of x.' To evaluate the function f(x)=2x+3 for f(4) - replace every x with 4 and simplify. f(4)=2(4)+3=11.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Sector is a piece of the area of a circle. Area of a Sector: (n/360)((pie)r2) - n is the degree measure of the sector's central angle
Combine like terms.


34. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Find a common denominator - then add or subtract the numerators.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


35. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Use the units to keep things straight - Snowfall inches/hours


36. Counting Consecutive Integers
The whole number left over after division.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Subtract the smallest from the largest and add 1
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle


37. Simplifying an Algebraic Equation
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
Express them with a common denominator.
Cancel factors common to the numerator and denominator.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


38. Calculating the Probability that an Event will Take Place
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Ue the formula y=mx+b - and remember that the value of m is the slope of the line. The slopes of two perpendicular lines are negative reciprocals of one another.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


39. Dividing Fractions
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.
-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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


40. Adding and Subtracting Monomials
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Express them with a common denominator.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


41. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

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42. Increasing and Decreasing a Number by a Certain Percentage
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
-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.


43. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Get the absolute value equation by itself. Solve.
Just add or subtract the coefficients in front of the radicals.
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


44. Finding the Median of a Set of Numbers
Average: Sum of the Terms/Number of the Terms
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
The value that falls in the middle of the set.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


45. Factoring a Polynomial ('FOIL in Reverse')
Use the distributive property then combine the like terms.
Just add or subtract the coefficients in front of the radicals.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


46. Simplifying a Fraction to Lowest Terms
Average the smallest and largest number
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Ue the formula y=mx+b - and remember that the value of m is the slope of the line. The slopes of two perpendicular lines are negative reciprocals of one another.
Factor out and cancel all factors the numerator and denominator have in common.


47. Calculating Negative Exponents and Radical Exponents
The whole number left over after division.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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
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


48. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
A(2)+b(2)=c(2)
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.
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.
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.


49. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
Adjacent angles are supplementary - Vertical angles are equal
Cross multiply.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


50. Multiplying Monomials
The value that falls in the middle of the set.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
-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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2