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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. Finding a Term in a Geometric Sequence
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Find a common denominator - then add or subtract the numerators.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

2. Raising a Power to a Power
Put each number in the original ratio over the sum of the numbers.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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 exponents - (x^3)^4=x^3*4=x^12

3. If 3(3x)=9(x+2) - what is the value of x?
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Cross multiply.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

4. Simplifying Square Roots
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
-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.

5. Finding the Area of a Circle
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
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.
Sum: Average x Number of Terms
(pie)r(squared)

6. Finding the Reciprocal of a Fraction
Multiply the numerators and multiply the denominators.
(pie)r(squared)
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.
Switch the numerator and denominator.

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

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8. Finding the Length of an Arc in a Circle

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9. Factoring a Polynomial ('FOIL in Reverse')
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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

10. What is the Triangle Inequality Theorem?
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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
VofaC: (pie)r(2)h

11. Convert From a Fraction to a Decimal - Vice Versa
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

12. Numbers that are Relatively Prime
Part=Percent x Whole
Just add or subtract the coefficients in front of the radicals.
Two relatively prime numbers are integers that have no common factor other than 1.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

13. Properties of a 45-45-90 Triangle
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 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

14. Number of Groups - +1 Each Time
The value that falls in the middle of the set.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
VofaRS=lwh

15. Solving a Proportion
VofaC: (pie)r(2)h
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Cross multiply.

16. Counting the Total Number of Possibilities for Several Events to Occur
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
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.

17. What types of angles are formed when two lines intersect?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Adjacent angles are supplementary - Vertical angles are equal

18. Scalene - Isosceles - and Equilateral Triangles
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Switch the numerator and denominator.

19. Solving an Inequality
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.
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.
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.

20. Multiplying Monomials
Do whatever is necessary to both sides to isolate the variable.
Use simple numbers like 1 and 2 and see what happens.
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 distributive property then combine the like terms.

21. Adding and Subtracting Roots
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Just add or subtract the coefficients in front of the radicals.
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.
Use simple numbers like 1 and 2 and see what happens.

22. Finding the GCF of Two or More Numbers
Use simple numbers like 1 and 2 and see what happens.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

23. General Procedure for Multiplying Polynomials
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Use the distributive property then combine the like terms.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

24. Definition of a Rational Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
The value that falls in the middle of the set.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.

25. If x(2)=7x+18 - what is the positive value of x?
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Do whatever is necessary to both sides to isolate the variable.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

26. 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?
Average the smallest and largest number
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the whole number part by the denominator - then add the numerator. Keep the same 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.

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

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28. Converting from an Improper Fraction to a Mixed 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.
-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.
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.
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. Adding and Subtracting Monomials
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 whole number left over after division.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Cross multiply.

30. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Factor out and cancel all factors the numerator and denominator have in common.
Average the smallest and largest number
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

31. Characteristics of a Parallelogram
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Put the equation into y=mx+b-- in which case b is the y-intercept.

32. Average Rate and How Do You Find It
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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

33. 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.
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
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

34. What value of x is not in the domain of the function f(x)=x-2/x-3?
Sum: Average x Number of Terms
Just add or subtract the coefficients in front of the radicals.
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.
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

35. What types of angles are formed when a transversal cross parallel lines?
Do whatever is necessary to both sides to isolate the variable.
Four equal acute angles and four equal obtuse angles.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
-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.

36. Knowing if an Integer is a Multiple of 5 or 10
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The value that appears the most often.
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
-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.

37. 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
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.
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

38. Knowing if an Integer is a Multiple of 2 or 4
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

39. 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
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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
The value that appears the most often.

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.
Use simple numbers like 1 and 2 and see what happens.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-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.

41. Adding a Positive Number to a Negative Number
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Combine like terms.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

42. Finding the Rate of Speed
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Use the formula distance=rate*time and its variations to help in this question.
Isolate the radical expression and use the standard rules of algebra.

43. PEMDAS
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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 the formula distance=rate*time and its variations to help in this question.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

44. Finding the Sum of the Average of a Series of Numbers
(pie)r(squared)
Sum: Average x Number of Terms
The value that falls in the middle of the set.
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

45. Finding the Sum of the Interior Angles of a Polygon
Multiply the numerators and multiply the denominators.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

46. Finding the Domain and Range of a Function
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

47. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
(pie)r(squared)
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

48. Finding the y-intercept When Given an Equation of a Line
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.
Subtract the smallest from the largest and add 1
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.

49. Calculating the Probability that an Event will Take Place
Get the absolute value equation by itself. Solve.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Probability: Number of Favorable Outcomes/Total Possible Outcomes

50. Finding the Distance Between Two Points on a Coordinate Graph
Four equal acute angles and four equal obtuse angles.
2(pie)r
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

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