SAT Math

Instructions:

• Answer 50 questions in 15 minutes.
• If you are not ready to take this test, you can study here.
• 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. Formula Used to Find Percent
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Part=Percent x Whole
Use the formula distance=rate*time and its variations to help in this question.


2. Increasing and Decreasing a Number by a Certain Percentage
Use the formula distance=rate*time and its variations to help in this question.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
-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.


3. Convert From a Fraction to a Decimal - Vice Versa
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
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.
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.


4. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Do whatever is necessary to both sides to isolate the variable.


5. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Switch the numerator and denominator.
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


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

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7. 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?
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.


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

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9. 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
Four equal acute angles and four equal obtuse angles.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


10. Multiply and Divide Positive and Negative Numbers
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Use the formula distance=rate*time and its variations to help in this question.
Average the smallest and largest number


11. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Plug in the given values for the unknowns and calculate according to PEMDAS.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


12. Adding and Subtracting Fractions
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Two relatively prime numbers are integers that have no common factor other than 1.
Find a common denominator - then add or subtract the numerators.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


13. Finding the Volume of a Cylinder
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.
VofaC: (pie)r(2)h
Four equal acute angles and four equal obtuse angles.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


14. Knowing if an Integer is a Multiple of 2 or 4
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
-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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Put the equation into y=mx+b-- in which case b is the y-intercept.


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

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16. 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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Subtract the smallest from the largest and add 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.


17. If 3(3x)=9(x+2) - what is the value of x?
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


18. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


19. What types of angles are formed when two lines intersect?
Use the units to keep things straight - Snowfall inches/hours
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.
-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.
Adjacent angles are supplementary - Vertical angles are equal


20. Properties of a 45-45-90 Triangle
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Switch the numerator and denominator.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.


21. Quickly Finding the Average of a Series of Evenly Spaced Numbers
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Average the smallest and largest number
Do whatever is necessary to both sides to isolate the variable.


22. How do you know if an integer is a multiple of 3 or 9?
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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.


23. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Switch the numerator and denominator.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


24. Finding the LCM of Two or More Numbers

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25. Counting the Total Number of Possibilities for Several Events to Occur
(x1+x2)/2 -(y1+y2)/2
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.


26. Solving a System of Equations
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
A(2)+b(2)=c(2)


27. Finding the Slope of a Line When Given Two Points on the Line
-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 whole number part by the denominator - then add the numerator. Keep the same denominator.
Slope=change in y/change in x
-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.


28. Finding the Sum of the Interior Angles of a Polygon
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.
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Adjacent angles are supplementary - Vertical angles are equal


29. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


30. Finding the Circumference of a Circle
2(pie)r
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Express them with a common denominator.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


31. What Does Solving In Terms of Mean?
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


32. What types of angles are formed when a transversal cross parallel lines?
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Four equal acute angles and four equal obtuse angles.
Use the units to keep things straight - Snowfall inches/hours
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


33. What are Two Special Pythagorean Triples?

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34. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
VofaC: (pie)r(2)h
Do whatever is necessary to both sides to isolate the variable.


35. Characteristics of a Square
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Four equal acute angles and four equal obtuse angles.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


36. Evaluating an Algebraic Expression
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


37. 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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
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


38. Calculating the Probability that an Event will Take Place
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


39. An Important Property of a Line Tangent to a Circle
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Part=Percent x Whole
Slope=change in y/change in x


40. Factoring the Difference of Two Squares
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.
Find a common denominator - then add or subtract the numerators.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


41. Simplifying an Algebraic Equation
Find a common denominator - then add or subtract the numerators.
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)
Cancel factors common to the numerator and denominator.


42. Solving an Inequality
-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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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
(pie)r(squared)


43. Average Rate and How Do You Find It
Adjacent angles are supplementary - Vertical angles are equal
2(pie)r
VofaRS=lwh
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


44. If 4(x(2)-10x+25) - then what is the value of x?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


45. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Slope=change in y/change in x
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
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


46. 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.
The value that appears the most often.
Combine like terms.
Average the smallest and largest number


47. Comparing the values of two or more Fractions
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Express them with a common denominator.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


48. PEMDAS
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
-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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


49. Definition of a Rational Number
Sum: Average x Number of Terms
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Find a common denominator - then add or subtract the numerators.


50. Simplifying Square Roots
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Multiply the numerators and multiply the denominators.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.