SAT Math

Instructions:

• 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. 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.
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.
Two relatively prime numbers are integers that have no common factor other than 1.
-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.


2. Simplifying an Algebraic Equation
Switch the numerator and denominator.
Cancel factors common to the numerator and denominator.
Multiply the numerators and multiply the denominators.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


3. Finding the Volume of a Rectangular Solid
VofaRS=lwh
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


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

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5. Finding the Domain and Range of a Function
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
Just add or subtract the coefficients in front of the radicals.


6. Solving a Proportion
Cross multiply.
Multiply the exponents - (x^3)^4=x^3*4=x^12
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
(x1+x2)/2 -(y1+y2)/2


7. Converting from an Improper Fraction to a Mixed Number
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


8. Properties of the Interior and Exterior Angles of a Triangle
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
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.


9. What is the greatest of three consecutive odd integers where the sum of the third and twice the first is equal to nine more than twice the second?
Multiply the numerators and multiply the denominators.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Switch the numerator and denominator.
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.


10. Counting the Total Number of Possibilities for Several Events to Occur
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.
Get the absolute value equation by itself. Solve.
The value that appears the most often.
Combine like terms.


11. Number of Groups - +1 Each Time
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
(x1+x2)/2 -(y1+y2)/2
Factor out and cancel all factors the numerator and denominator have in common.


12. Multiply and Divide Positive and Negative Numbers
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
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


13. General Procedure for Multiplying Polynomials
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use the distributive property then combine the like terms.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


14. Difference Between a Factor and a Multiple
Factor out and cancel all factors the numerator and denominator have in common.
Subtract the smallest from the largest and add 1
-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.
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


15. Adding and Subtracting Polynomials
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 variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Combine like terms.
If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side.


16. Multiplying Fractions
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Multiply the numerators and multiply the denominators.
-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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


17. Properties of a 45-45-90 Triangle
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


18. Counting Consecutive Integers
Use the formula distance=rate*time and its variations to help in this question.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Use the distributive property then combine the like terms.
Subtract the smallest from the largest and add 1


19. 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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
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.


20. Calculating the Probability that an Event will Take Place
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


21. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Put the equation into y=mx+b-- in which case b is the y-intercept.
Get the absolute value equation by itself. Solve.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.


22. Finding the Surface Area of a Rectangular Solid
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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


23. Finding the Slope of a Line When Given Two Points on the Line
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
Find a common denominator - then add or subtract the numerators.
Slope=change in y/change in x
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.


24. Finding the Median of a Set of Numbers
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
The value that falls in the middle of the set.
Use the distributive property then combine the like terms.


25. Solving a Radical Equation
Use the distributive property then combine the like terms.
Adjacent angles are supplementary - Vertical angles are equal
Average the smallest and largest number
Isolate the radical expression and use the standard rules of algebra.


26. What types of angles are formed when a transversal cross parallel lines?
Slope=change in y/change in x
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Four equal acute angles and four equal obtuse angles.
Use simple numbers like 1 and 2 and see what happens.


27. Finding the Area of a Sector

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28. Finding the GCF of Two or More Numbers
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
Subtract the smallest from the largest and add 1
Combine like terms.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


29. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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.
Use simple numbers like 1 and 2 and see what happens.
-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 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. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
-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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
-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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


31. Characteristics of a Rectangle
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
FOIL: First - Outer - Inner - Last... Combine Like Terms


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

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33. Dividing Fractions
Just add or subtract the coefficients in front of the radicals.
The value that appears the most often.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
2(pie)r


34. Simplifying a Fraction to Lowest Terms
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.
Factor out and cancel all factors the numerator and denominator have in common.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.


35. If r#t=t(r)-r(t) - then what is 4#3?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


36. Increasing and Decreasing a Number by a Certain Percentage
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
-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.
Adjacent angles are supplementary - Vertical angles are equal
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.


37. Finding the Reciprocal of a Fraction
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 value that appears the most often.
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
Switch the numerator and denominator.


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

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39. Finding the Sum of the Interior Angles of a Polygon
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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
FOIL: First - Outer - Inner - Last... Combine Like Terms
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


40. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.


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?
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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
Four equal acute angles and four equal obtuse angles.
Just add or subtract the coefficients in front of the radicals.


42. Multiplying Binomials
Subtract the smallest from the largest and add 1
Get the absolute value equation by itself. Solve.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


43. Finding the LCM of Two or More Numbers

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44. Factoring a Polynomial ('FOIL in Reverse')
If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side.
FOIL: First - Outer - Inner - Last... Combine Like 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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


45. 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
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


46. Prime Factorization of a Number
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 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.
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


47. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Cancel factors common to the numerator and denominator.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.


48. What Does Solving In Terms of Mean?
Average: Sum of the Terms/Number of the Terms
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


49. What types of angles are formed when two lines intersect?
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.
Adjacent angles are supplementary - Vertical angles are equal
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


50. Scalene - Isosceles - and Equilateral Triangles
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction