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SAT Math

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Answer 50 questions in 15 minutes.
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1. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Average the smallest and largest number
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

2. Definition of Remainder
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
The whole number left over after division.
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.

3. Finding the Distance Between Two Points on a Coordinate Graph
Combine like terms.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
VofaRS=lwh
-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.

4. Counting the Total Number of Possibilities for Several Events to Occur
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.
Sum: Average x Number of 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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

5. Multiplying and Dividing Roots
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.
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
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

6. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Cross multiply.
Combine like terms.
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

7. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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.
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.
VofaC: (pie)r(2)h

8. What are Two Special Pythagorean Triples?

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9. Difference Between a Factor and a Multiple
The whole number left over after division.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
-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.

10. Solving an Inequality
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

11. 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?
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.
-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.
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 each number in the original ratio over the sum of the numbers.

12. Evaluating an Algebraic Expression
Just add or subtract the coefficients in front of the radicals.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
(x1+x2)/2 -(y1+y2)/2

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

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14. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
Put each number in the original ratio over the sum of the numbers.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

15. Finding the Domain and Range of a Function
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.
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.
Sum: Average x Number of Terms

16. Finding the Area of a Circle
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.
(pie)r(squared)
Just add or subtract the coefficients in front of the radicals.
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.

17. Increasing and Decreasing a Number by a Certain Percentage
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 exponents - (x^3)^4=x^3*4=x^12
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.
-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.

18. Multiplying Fractions
Multiply the numerators and multiply the denominators.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
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.

19. Knowing if an Integer is a Multiple of 5 or 10
-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.
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.
2(pie)r
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

20. Converting from part-to-part ratios to part-to-whole ratios
The value that falls in the middle of the set.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Put each number in the original ratio over the sum of the numbers.
FOIL: First - Outer - Inner - Last... Combine Like Terms

21. Adding and Subtracting Roots
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Just add or subtract the coefficients in front of the radicals.
-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. Characteristics of a Square
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

23. Finding the Midpoint Between Two Points
Multiply the numerators and multiply the denominators.
(x1+x2)/2 -(y1+y2)/2
-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 value that appears the most often.

24. 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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Isolate the radical expression and use the standard rules of algebra.

25. Properties of the Interior and Exterior Angles of a Triangle
The whole number left over after division.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

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27. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

28. Counting Consecutive Integers
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
Use simple numbers like 1 and 2 and see what happens.
Multiply the numerators and multiply the denominators.
Subtract the smallest from the largest and add 1

29. Determining Absolute Value of a Number
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

30. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
Subtract the smallest from the largest and add 1
Use the formula distance=rate*time and its variations to help in this question.
Express them with a common denominator.

31. Definition of an Irrational Number
VofaRS=lwh
Cross multiply.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

32. Multiplying Binomials
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Use the distributive property then combine the like terms.
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

33. Definition of a Rational Number
Plug in the given values for the unknowns and calculate according to PEMDAS.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

34. Comparing the values of two or more Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Express them with a common denominator.
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

35. Knowing if an Integer is a Multiple of 2 or 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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
-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.
Four equal acute angles and four equal obtuse angles.

36. Finding the Circumference of a Circle
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
2(pie)r
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

37. Sale Price of a Jacket Marked Down 30% Each Week for 3 Weeks - What % of the Original Price is the Cost of the Jacket After the 3 Week Sale Period
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

38. If 4(x(2)-10x+25) - then what is the value of x?
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
Find a common denominator - then add or subtract the numerators.

39. If (Square Root: x-1)+5=12 - what is the value of x/2?
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

40. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
VofaRS=lwh
Four equal acute angles and four equal obtuse angles.
Get the absolute value equation by itself. Solve.

41. If the average of a - b - and 48 is 48 - what is the value of a + b?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Express them with a common denominator.

42. Adding and Subtracting Polynomials
Combine like terms.
Put each number in the original ratio over the sum of the numbers.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

43. Factoring a Polynomial ('FOIL in Reverse')
Average: Sum of the Terms/Number of the Terms
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

44. 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%.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Isolate the radical expression and use the standard rules of algebra.

45. Finding the Rate of Speed
Put each number in the original ratio over the sum of the numbers.
Use the formula distance=rate*time and its variations to help in this question.
A(2)+b(2)=c(2)
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

46. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
2(pie)r
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

47. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
-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.
Use simple numbers like 1 and 2 and see what happens.

48. Finding the Volume of a Cylinder
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
VofaC: (pie)r(2)h
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

49. Dividing Expressions with Exponents that Have a Common Base
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

50. 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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

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