SAT Math

Instructions:

• Answer 50 questions in 15 minutes.
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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. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

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2. Properties of a 30-60-90 Triangle
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
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


3. Characteristics of a Square
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


4. If the average of a - b - and 48 is 48 - what is the value of a + b?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Just add or subtract the coefficients in front of the radicals.


5. Characteristics of a Parallelogram
The value that falls in the middle of the set.
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


6. Finding the Sum of the Interior Angles of a Polygon
Average: Sum of the Terms/Number of the Terms
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Just add or subtract the coefficients in front of the radicals.


7. What is a Function and how do you Evaluate one?

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8. Prime Factorization of a Number
Subtract the smallest from the largest and add 1
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.


9. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Average: Sum of the Terms/Number of the Terms


10. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Use simple numbers like 1 and 2 and see what happens.
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 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.


11. Finding the Sum of the Average of a Series of Numbers
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Sum: Average x Number of Terms
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
(x1+x2)/2 -(y1+y2)/2


12. Finding the Circumference of a Circle
2(pie)r
Average: Sum of the Terms/Number of the 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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


13. Finding a Term in a Geometric Sequence
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.
Use the formula - a(n)=a(1)r(n-1) - where a(n) is the nth term - a1 is the first term - and r is the ratio between the terms.
Cancel factors common to the numerator and denominator.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


14. Finding the Volume of a Rectangular Solid
VofaRS=lwh
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Switch the numerator and denominator.


15. Finding the Mode of a Set of Numbers
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
The value that appears the most often.


16. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Just add or subtract the coefficients in front of the radicals.
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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


17. Adding a Positive Number to a Negative Number
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Isolate the radical expression and use the standard rules of algebra.


18. Multiplying Monomials
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
A(2)+b(2)=c(2)
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


19. Difference Between a Factor and a Multiple
VofaRS=lwh
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
-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.
Slope=change in y/change in x


20. PEMDAS
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.
-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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


21. Multiplying Binomials
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Slope=change in y/change in x
FOIL: First - Outer - Inner - Last... Combine Like Terms


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

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23. Adding and Subtracting Polynomials
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Combine like terms.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


24. Finding the Reciprocal of a Fraction
Probability: Number of Favorable Outcomes/Total Possible Outcomes
(x1+x2)/2 -(y1+y2)/2
Switch the numerator and denominator.
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.


25. Factoring the Difference of Two Squares
Cancel factors common to the numerator and denominator.
The whole number left over after division.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


26. Properties of a 45-45-90 Triangle
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Average: Sum of the Terms/Number of the Terms
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


27. Calculating Negative Exponents and Radical Exponents
Switch the numerator and denominator.
(pie)r(squared)
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


28. Expressing the Union and Intersection of Sets
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.
(pie)r(squared)
FOIL: First - Outer - Inner - Last... Combine Like Terms
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


29. If r#t=t(r)-r(t) - then what is 4#3?
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.
Just add or subtract the coefficients in front of the radicals.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


30. Formula to Find Average
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Average: Sum of the Terms/Number of the Terms
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Use simple numbers like 1 and 2 and see what happens.


31. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
Cancel factors common to the numerator and denominator.
VofaC: (pie)r(2)h
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


32. Adding and Subtracting Monomials
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Isolate the radical expression and use the standard rules of algebra.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


33. If x varies directly with y - and the value of x is 12 when y is 11 - what is the value of y when x is 66?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
The value that falls in the middle of the set.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


34. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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
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.
Use the units to keep things straight - Snowfall inches/hours
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


35. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


36. Counting the Total Number of Possibilities for Several Events to Occur
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
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.


37. Finding the Length of an Arc in a Circle

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38. Finding the LCM of Two or More Numbers

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39. Dividing Fractions
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.
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.
Do whatever is necessary to both sides to isolate the variable.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


40. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
Slope=change in y/change in x
Isolate the radical expression and use the standard rules of algebra.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


41. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
Get the absolute value equation by itself. Solve.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


42. What is the Pythagorean Theorem?
Adjacent angles are supplementary - Vertical angles are equal
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.
A(2)+b(2)=c(2)
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.


43. Finding the Distance Between Two Points on a Coordinate Graph
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Factor out and cancel all factors the numerator and denominator have in common.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Average: Sum of the Terms/Number of the Terms


44. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Two relatively prime numbers are integers that have no common factor other than 1.
Four equal acute angles and four equal obtuse angles.


45. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Use the units to keep things straight - Snowfall inches/hours
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


46. Finding the Missing Number in a Series When You are Given the Average
Combine like terms.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


47. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Cancel factors common to the numerator and denominator.
Average the smallest and largest number
Get the absolute value equation by itself. Solve.
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.


48. What value of x is not in the domain of the function f(x)=x-2/x-3?
Average the smallest and largest number
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime 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


49. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
The value that falls in the middle of the set.
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.
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


50. 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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Switch the numerator and denominator.
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