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. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


2. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
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
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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


3. Characteristics of a Square
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
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


4. Finding the Slope When Given an Equation of a Line
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
VofaC: (pie)r(2)h


5. Multiplying and Dividing Roots
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.
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.
Use simple numbers like 1 and 2 and see what happens.
Get the absolute value equation by itself. Solve.


6. Finding the Circumference of a Circle
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.
The value that appears the most often.
2(pie)r
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


7. Finding the LCM of Two or More Numbers

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8. Solving a System of Equations
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.
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.
Sum: Average x Number of 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.


9. Finding the Domain and Range of a Function
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
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


10. Simplifying a Fraction to Lowest Terms
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Factor out and cancel all factors the numerator and denominator have in common.


11. If the average of a - b - and 48 is 48 - what is the value of a + b?
(pie)r(squared)
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Switch the numerator and denominator.
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.


12. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
Average: Sum of the Terms/Number of the Terms
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
(x1+x2)/2 -(y1+y2)/2


13. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
Find a common denominator - then add or subtract the numerators.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


14. What is the Pythagorean Theorem?
A(2)+b(2)=c(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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
FOIL: First - Outer - Inner - Last... Combine Like Terms


15. Factoring the Difference of Two Squares
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
(x1+x2)/2 -(y1+y2)/2
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


16. Definition of Remainder
Multiply the exponents - (x^3)^4=x^3*4=x^12
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
A(2)+b(2)=c(2)
The whole number left over after division.


17. 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.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


18. Definition of an Integer
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
-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.


19. 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.
The value that falls in the middle of the set.
Combine like terms.
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.


20. Simplifying Square Roots
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


21. If 4(x(2)-10x+25) - then what is the value of x?
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.
Use simple numbers like 1 and 2 and see what happens.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


22. 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.
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
Use the formula distance=rate*time and its variations to help in this question.
The value that falls in the middle of the set.


23. What value of x is not in the domain of the function f(x)=x-2/x-3?
Two relatively prime numbers are integers that have no common factor other than 1.
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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


24. If 3(3x)=9(x+2) - what is the value of x?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
A(2)+b(2)=c(2)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.


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

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26. Increasing and Decreasing a Number by a Certain Percentage
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
-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.


27. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Isolate the radical expression and use the standard rules of algebra.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Subtract the smallest from the largest and add 1
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.


28. Multiplying Monomials
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Find a common denominator - then add or subtract the numerators.
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


29. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


30. Multiplying Binomials
Get the absolute value equation by itself. Solve.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use simple numbers like 1 and 2 and see what happens.
FOIL: First - Outer - Inner - Last... Combine Like Terms


31. Difference Between a Factor and a Multiple
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
-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.


32. Finding the Length of an Arc in a Circle

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33. Evaluating an Algebraic Expression
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Combine like terms.
Plug in the given values for the unknowns and calculate according to PEMDAS.


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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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


35. If (Square Root: x-1)+5=12 - what is the value of x/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.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
VofaC: (pie)r(2)h


36. Definition of an Irrational Number
Slope=change in y/change in x
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.


37. Adding and Subtracting Polynomials
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.
Combine like terms.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


38. 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?
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
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.


39. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Do whatever is necessary to both sides to isolate the variable.


40. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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
-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.


41. Finding the Mode of a Set of Numbers
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The value that appears the most often.
Find a common denominator - then add or subtract the numerators.


42. What are Two Special Pythagorean Triples?

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

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44. Dividing Fractions
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


45. Finding the Sum of the Average of a Series of 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
Average: Sum of the Terms/Number of the Terms
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Sum: Average x Number of Terms


46. 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?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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 appears the most often.
The whole number left over after division.


47. Characteristics of a Parallelogram
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Subtract the smallest from the largest and add 1
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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. Multiplying Expressions with Exponents that Have a Common Base
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.
Average: Sum of the Terms/Number of the 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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


49. 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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
-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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


50. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
Switch the numerator and denominator.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.