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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. Solving an Inequality
Just add or subtract the coefficients in front of the radicals.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
Adjacent angles are supplementary - Vertical angles are equal

2. Finding the LCM of Two or More Numbers

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3. Properties of Similar Triangles
-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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

4. 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
-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.
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 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.

5. Calculating the Probability that an Event will Take Place
VofaC: (pie)r(2)h
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

6. Finding the y-intercept When Given an Equation of a Line
Multiply the numerators and multiply the denominators.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

7. Finding a Term in a Geometric Sequence
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.
Express them with a common denominator.
Plug in the given values for the unknowns and calculate according to PEMDAS.
(x1+x2)/2 -(y1+y2)/2

8. Multiplying and Dividing Roots
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use the units to keep things straight - Snowfall inches/hours
VofaC: (pie)r(2)h

9. Finding the Volume of a Cylinder
Use simple numbers like 1 and 2 and see what happens.
Multiply the numerators and multiply the denominators.
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.
VofaC: (pie)r(2)h

10. Finding the Domain and Range of a Function
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
-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.
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.

11. Multiply and Divide Positive and Negative Numbers
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Average: Sum of the Terms/Number of the Terms
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

12. Difference Between a Factor and a Multiple
VofaC: (pie)r(2)h
-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.
(x1+x2)/2 -(y1+y2)/2
VofaRS=lwh

13. What is the Triangle Inequality Theorem?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
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.

14. Formula to Find Average
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.
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

15. Scalene - Isosceles - and Equilateral Triangles
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Do whatever is necessary to both sides to isolate the variable.
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.

16. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Multiply the numerators and multiply the denominators.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

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

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18. Factoring the Difference of Two Squares
Two relatively prime numbers are integers that have no common factor other than 1.
2(pie)r
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

19. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
VofaC: (pie)r(2)h

20. 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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
Factor out and cancel all factors the numerator and denominator have in common.

21. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Do whatever is necessary to both sides to isolate the variable.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The value that appears the most often.

22. Properties of a 45-45-90 Triangle
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

23. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
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
Do whatever is necessary to both sides to isolate the variable.
Find a common denominator - then add or subtract the numerators.

24. Converting From a Mixed Number to an Improper Fraction
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

25. Knowing if an Integer is a Multiple of 5 or 10
Put the equation into y=mx+b-- in which case b is the y-intercept.
-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 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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

26. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

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

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28. Adding a Positive Number to a Negative Number
Put each number in the original ratio over the sum of the numbers.
(pie)r(squared)
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

29. Definition of Remainder
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The whole number left over after division.
Cross multiply.
Multiply the numerators and multiply the denominators.

30. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Sum: Average x Number of Terms
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Use the distributive property then combine the like terms.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

31. Solving a Radical Equation
2(pie)r
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.
Slope=change in y/change in x
Isolate the radical expression and use the standard rules of algebra.

32. Knowing if an Integer is a Multiple of 2 or 4
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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
-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.
Do whatever is necessary to both sides to isolate the variable.

33. Formula Used to Find Percent
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Part=Percent x Whole

34. Dividing Expressions with Exponents that Have a Common Base
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use the distributive property then combine the like terms.
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.

35. Evaluating an Algebraic Expression
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.

36. Adding and Subtracting Polynomials
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.

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

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38. Factoring a Polynomial ('FOIL in Reverse')
-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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Plug in the given values for the unknowns and calculate according to PEMDAS.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

39. General Procedure for Multiplying Polynomials
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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Use the distributive property then combine the like terms.
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.

40. If (Square Root: x-1)+5=12 - what is the value of x/2?
Use the units to keep things straight - Snowfall inches/hours
Combine like terms.
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

41. Finding the Median of a Set of Numbers
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
The value that falls in the middle of the set.

42. Definition of an Irrational Number
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

43. 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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Average: Sum of the Terms/Number of the Terms

44. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use simple numbers like 1 and 2 and see what happens.
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.

45. Raising a Power to a Power
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

46. Finding the Mode of a Set of Numbers
-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.
The value that appears the most often.
Put each number in the original ratio over the sum of the numbers.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

47. 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%.
Multiply the numerators and multiply the denominators.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

48. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

49. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Isolate the radical expression and use the standard rules of algebra.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

50. Finding the Area of a Circle
-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.
Just add or subtract the coefficients in front of the radicals.
Use simple numbers like 1 and 2 and see what happens.
(pie)r(squared)

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