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SAT Math

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Answer 50 questions in 15 minutes.
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1. If r#t=t(r)-r(t) - then what is 4#3?
Sum: Average x Number of Terms
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

2. Finding the Domain and Range of a Function
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
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.
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.

3. 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
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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

4. Dividing Expressions with Exponents that Have a Common Base
Express them with a common denominator.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

5. Finding the Volume of a Rectangular Solid
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
VofaRS=lwh
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.

6. Finding the Midpoint Between Two Points
Find a common denominator - then add or subtract the numerators.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
(x1+x2)/2 -(y1+y2)/2
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

7. Direct Variation and Inverse Variation
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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

8. Properties of Similar Triangles
(x1+x2)/2 -(y1+y2)/2
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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)

9. Solving an Inequality
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

10. If (Square Root: x-1)+5=12 - what is the value of x/2?
Put each number in the original ratio over the sum of the numbers.
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

11. Knowing if an Integer is a Multiple of 5 or 10
VofaC: (pie)r(2)h
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.
-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.
FOIL: First - Outer - Inner - Last... Combine Like Terms

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

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13. Adding and Subtracting Monomials
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
VofaC: (pie)r(2)h
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

14. Adding and Subtracting Fractions
Do whatever is necessary to both sides to isolate the variable.
The whole number left over after division.
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
Find a common denominator - then add or subtract the numerators.

15. How do you know if an integer is a multiple of 3 or 9?
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
-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.

16. Numbers that are Relatively Prime
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
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.
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

17. Converting from an Improper Fraction to a Mixed Number
Use the formula distance=rate*time and its variations to help in this question.
Part=Percent x Whole
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
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.

18. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Cancel factors common to the numerator and denominator.

19. Multiply and Divide Positive and Negative Numbers
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.
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 group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

20. Scalene - Isosceles - and Equilateral Triangles
A(2)+b(2)=c(2)
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.
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.

21. Calculating Negative Exponents and Radical Exponents
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

22. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Adjacent angles are supplementary - Vertical angles are equal
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

23. Properties of the Interior and Exterior Angles of a Triangle
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.
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 y=mx+b-- in which case b is the y-intercept.
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.

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

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25. Finding the Circumference of 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.
2(pie)r
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 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.

26. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
-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.
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

27. Factoring the Difference of Two Squares
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.
Average: Sum of the Terms/Number of the Terms
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

28. Finding the Rate of Speed
(pie)r(squared)
Do whatever is necessary to both sides to isolate the variable.
Use the formula distance=rate*time and its variations to help in this question.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

29. If 3(3x)=9(x+2) - what is the value of x?
The value that appears the most often.
Switch the numerator and denominator.
Part=Percent x Whole
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

30. What are Two Special Pythagorean Triples?

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31. 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.
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.
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
Sum: Average x Number of Terms

32. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

33. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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 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.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

34. Finding the Missing Number in a Series When You are Given the Average
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
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.
Use the formula distance=rate*time and its variations to help in this question.

35. Finding the Median of a Set of Numbers
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The value that falls in the middle of the set.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
(pie)r(squared)

36. Finding the Slope When Given an Equation of a Line
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.
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.
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.

37. Multiplying and Dividing Roots
(x1+x2)/2 -(y1+y2)/2
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use the distributive property then combine the like terms.

38. Finding the LCM of Two or More Numbers

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39. Number of Groups - +1 Each Time
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Subtract the smallest from the largest and add 1
Put each number in the original ratio over the sum of the numbers.
Use the units to keep things straight - Snowfall inches/hours

40. Adding and Subtracting Polynomials
Combine like terms.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
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.

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

42. 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?
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

43. Definition of Remainder
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Combine like terms.
The whole number left over after division.

44. Raising a Power to a Power
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Multiply the exponents - (x^3)^4=x^3*4=x^12
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
Slope=change in y/change in x

45. Counting Consecutive Integers
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use the units to keep things straight - Snowfall inches/hours
Subtract the smallest from the largest and add 1
-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.

46. Finding the Reciprocal of a Fraction
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
Subtract the smallest from the largest and add 1
VofaC: (pie)r(2)h
Switch the numerator and denominator.

47. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Cross multiply.

48. Simplifying an Algebraic Equation
Sum: Average x Number of Terms
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Cancel factors common to the numerator and denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

49. An Important Property of a Line Tangent to a Circle
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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 value that falls in the middle of the set.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

50. Solving a Radical 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.
Isolate the radical expression and use the standard rules of algebra.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

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