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. Raising a Power to a Power
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 exponents - (x^3)^4=x^3*4=x^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
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4


2. Prime Factorization of a Number
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Part=Percent x Whole
Use simple numbers like 1 and 2 and see what happens.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


3. 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?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Factor out and cancel all factors the numerator and denominator have in common.


4. Adding and Subtracting Polynomials
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Combine like terms.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


5. Definition of an Irrational Number
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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


6. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


7. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.


8. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
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.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


9. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^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.


10. Difference Between a Factor and a Multiple
Put the equation into y=mx+b-- in which case b is the y-intercept.
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
-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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


11. Factoring the Difference of Two Squares
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 the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


12. Dividing Expressions with Exponents that Have a Common Base
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
Get the absolute value equation by itself. Solve.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


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

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14. Characteristics of a Square
Do whatever is necessary to both sides to isolate the variable.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.


15. 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%.
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.
Use the distributive property then combine the like terms.
Put the equation into y=mx+b-- in which case b is the y-intercept.


16. 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?
Cancel factors common to the numerator and denominator.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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


17. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
The whole number left over after division.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


18. Finding the Sum of the Interior Angles of a Polygon
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Subtract the smallest from the largest and add 1


19. 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?
Cross multiply.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Four equal acute angles and four equal obtuse angles.
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.


20. If (Square Root: x-1)+5=12 - what is the value of x/2?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Put each number in the original ratio over the sum of the numbers.
Factor out and cancel all factors the numerator and denominator have in common.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


21. Convert From a Fraction to a Decimal - Vice Versa
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
VofaC: (pie)r(2)h
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.


22. Increasing and Decreasing a Number by a Certain Percentage
Multiply the exponents - (x^3)^4=x^3*4=x^12
The sides of a 45-45-90 triangle are in a ratio of x:x:x(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.
Find a common denominator - then add or subtract the numerators.


23. Solving an Inequality
Use the formula distance=rate*time and its variations to help in this question.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


24. Finding the Surface Area of a Rectangular Solid
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
-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.
Four equal acute angles and four equal obtuse angles.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


25. Finding the Volume of a Rectangular Solid
VofaRS=lwh
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Combine like terms.


26. Knowing if an Integer is a Multiple of 5 or 10
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
-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 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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


27. How do you know if an integer is a multiple of 3 or 9?
Use the formula distance=rate*time and its variations to help in this question.
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.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


28. 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
Use the units to keep things straight - Snowfall inches/hours
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


29. Determining Absolute Value of a Number
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
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
The value that appears the most often.


30. Properties of Similar Triangles
The value that appears the most often.
Express them with a common denominator.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
A(2)+b(2)=c(2)


31. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Two relatively prime numbers are integers that have no common factor other than 1.
Isolate the radical expression and use the standard rules of algebra.


32. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


33. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


34. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
VofaC: (pie)r(2)h


35. Quickly Finding the Average of a Series of Evenly Spaced Numbers
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
Average the smallest and largest number
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


36. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
The whole number left over after division.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


37. Finding the LCM of Two or More Numbers

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38. Characteristics of a Rectangle
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Express them with a common denominator.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.


39. 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
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.
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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


40. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
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
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.
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


41. Multiplying Fractions
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Multiply the numerators and multiply the denominators.


42. Average Rate and How Do You Find It
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


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

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44. Dividing Fractions
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
The value that appears the most often.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle


45. Finding the Sum of the Average of a Series of Numbers
Cross multiply.
Average: Sum of the Terms/Number of the Terms
2(pie)r
Sum: Average x Number of Terms


46. What are Two Special Pythagorean Triples?

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47. Finding the Circumference of a Circle
2(pie)r
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Average the smallest and largest number
Probability: Number of Favorable Outcomes/Total Possible Outcomes


48. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Cancel factors common to the numerator and denominator.
Factor out and cancel all factors the numerator and denominator have in common.
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.


49. Finding the Length of an Arc in a Circle

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50. 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.
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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2