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SAT Math

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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. Knowing if an Integer is a Multiple of 5 or 10
Combine like terms.
The value that falls in the middle of the set.
2(pie)r
-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.

2. What is the Triangle Inequality Theorem?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
Cross 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.

3. 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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
The whole number left over after division.
Subtract the smallest from the largest and add 1

4. Difference Between a Factor and a Multiple
Multiply the exponents - (x^3)^4=x^3*4=x^12
-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.
Do whatever is necessary to both sides to isolate the variable.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

5. What types of angles are formed when a transversal cross parallel lines?
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 y=mx+b-- in which case b is the y-intercept.
Use the formula distance=rate*time and its variations to help in this question.
Four equal acute angles and four equal obtuse angles.

6. Finding the Length of an Arc in a Circle

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7. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Just add or subtract the coefficients in front of the radicals.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

8. Setting Up a Ratio
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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. Direct Variation and Inverse Variation
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Slope=change in y/change in x
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
Put each number in the original ratio over the sum of the numbers.

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

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11. Converting from part-to-part ratios to part-to-whole ratios
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.
Put each number in the original ratio over the sum of the numbers.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
-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.

12. 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?
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
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Four equal acute angles and four equal obtuse angles.

13. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
Cross multiply.

14. Properties of Similar Triangles
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
-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.

15. An Important Property of a Line Tangent to a Circle
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.
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 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.
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.

16. What is the Pythagorean Theorem?
Adjacent angles are supplementary - Vertical angles are equal
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Cancel factors common to the numerator and denominator.
A(2)+b(2)=c(2)

17. 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.
Express them with a common denominator.
-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.
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. Definition of an Irrational Number
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Do whatever is necessary to both sides to isolate the variable.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

19. Finding the Area of a Sector

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20. Counting the Total Number of Possibilities for Several Events to Occur
Multiply the numerators and multiply the denominators.
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use the distributive property then combine the like terms.

21. Solving a Radical Equation
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
Isolate the radical expression and use the standard rules of algebra.
FOIL: First - Outer - Inner - Last... Combine Like Terms
-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.

22. Finding the Mode of a Set of Numbers
The value that appears the most often.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
2(pie)r

23. Finding the Distance Between Two Points on a Coordinate Graph
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Plug in the given values for the unknowns and calculate according to PEMDAS.

24. Finding the Reciprocal of a Fraction
-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
Switch the numerator and denominator.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

25. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Cross multiply.
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
FOIL: First - Outer - Inner - Last... Combine Like Terms

26. Adding and Subtracting Polynomials
Combine like 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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime 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

27. Multiply and Divide Positive and Negative Numbers
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
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

28. 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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
-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.
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.

29. 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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

30. Definition of an Integer
(pie)r(squared)
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Get the absolute value equation by itself. Solve.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

31. Calculating Negative Exponents and Radical Exponents
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Sum: Average x Number of Terms
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

32. Finding the Surface Area of a Rectangular Solid
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: 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.
Four equal acute angles and four equal obtuse angles.

33. Formula Used to Find Percent
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Multiply the numerators and multiply the denominators.
Part=Percent x Whole
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

34. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The value that appears the most often.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

35. Properties of the Interior and Exterior Angles of a Triangle
FOIL: First - Outer - Inner - Last... Combine Like Terms
Average the smallest and largest number
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

36. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
Use simple numbers like 1 and 2 and see what happens.
-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.

37. General Procedure for Multiplying Polynomials
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Use the distributive property then combine the like terms.
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.
Cross multiply.

38. Finding the Domain and Range of a Function
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Subtract the smallest from the largest and add 1

39. Simplifying Square Roots
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
'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.

40. Factoring the Difference of Two Squares
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.
VofaC: (pie)r(2)h
A(2)+b(2)=c(2)
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

41. If 4(x(2)-10x+25) - then what is the value of x?
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
Slope=change in y/change in x

42. Calculating the Probability that an Event will Take Place
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Express them with a common denominator.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

43. Properties of a 30-60-90 Triangle
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Four equal acute angles and four equal obtuse angles.

44. Finding the Slope When Given an Equation of a Line
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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

45. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
Slope=change in y/change in x
Put each number in the original ratio over the sum of the numbers.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

46. Definition of a Rational Number
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Isolate the radical expression and use the standard rules of algebra.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

47. What are Two Special Pythagorean Triples?

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48. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.

49. Solving an Inequality
Slope=change in y/change in x
Part=Percent x Whole
Do whatever is necessary to both sides to isolate the variable.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

50. Solving a Proportion
Cross multiply.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Plug in the given values for the unknowns and calculate according to PEMDAS.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

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