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SAT Math

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Answer 50 questions in 15 minutes.
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1. Multiplying and Dividing Roots
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.
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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

2. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
-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.
Average the smallest and largest number
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

3. If 4(x(2)-10x+25) - then what is the value of x?
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.
The whole number left over after division.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

4. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the numerators and multiply the denominators.
-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.
VofaC: (pie)r(2)h

5. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

6. Finding the Area of a Triangle

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7. Finding the Reciprocal of a Fraction
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use the units to keep things straight - Snowfall inches/hours
Combine like terms.
Switch the numerator and denominator.

8. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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
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
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

9. Finding the Domain and Range of a Function
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.

10. Solving a Linear Equation
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Do whatever is necessary to both sides to isolate the variable.
Combine like terms.

11. Direct Variation and Inverse Variation
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.
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.

12. Finding the Circumference of a Circle
A(2)+b(2)=c(2)
The value that appears the most often.
(pie)r(squared)
2(pie)r

13. Characteristics of a Square
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Plug in the given values for the unknowns and calculate according to PEMDAS.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

14. Finding the GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Four equal acute angles and four equal obtuse angles.

15. Finding the Distance Between Two Points on a Coordinate Graph
Just add or subtract the coefficients in front of the radicals.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

16. 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?
Express them with a common denominator.
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

17. Adding and Subtracting Polynomials
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.
Combine like terms.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

18. 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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Subtract the smallest from the largest and add 1

19. What is the Triangle Inequality Theorem?
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.
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.
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.
Express them with a common denominator.

20. Finding the Missing Number in a Series When You are Given the Average
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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

21. Dividing Expressions with Exponents that Have a Common Base
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

22. Definition of a Rational Number
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

23. Raising a Power to a Power
-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.
-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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

24. Finding the y-intercept When Given an Equation of a Line
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.
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Put the equation into y=mx+b-- in which case b is the y-intercept.

25. Properties of a 45-45-90 Triangle
Probability: Number of Favorable Outcomes/Total Possible Outcomes
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Express them with a common denominator.
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

26. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-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.

27. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Cancel factors common to the numerator and denominator.
Sum: Average x Number of 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.
Use simple numbers like 1 and 2 and see what happens.

28. How do you know if an integer is a multiple of 3 or 9?
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
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

29. 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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
-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.

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

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31. Multiplying Expressions with Exponents that Have a Common Base
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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
Factor out and cancel all factors the numerator and denominator have in common.

32. Comparing the values of two or more Fractions
Express them with a common denominator.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Multiply the exponents - (x^3)^4=x^3*4=x^12
2(pie)r

33. What are Two Special Pythagorean Triples?

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34. Finding the Surface Area of a Rectangular Solid
Put each number in the original ratio over the sum of the numbers.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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. Converting From a Mixed Number to an Improper Fraction
Sum: Average x Number of Terms
Adjacent angles are supplementary - Vertical angles are equal
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

36. What types of angles are formed when a transversal cross parallel lines?
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.
Four equal acute angles and four equal obtuse angles.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

37. 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?
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Get the absolute value equation by itself. Solve.
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.

38. Finding the Sum of the Interior Angles of a Polygon
Switch the numerator and denominator.
Cross multiply.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

39. Adding a Positive Number to a Negative 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 whole number left over after division.
Two relatively prime numbers are integers that have no common factor other than 1.
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.

40. Calculating the Probability that an Event will Take Place
Express them with a common denominator.
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
-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.

41. Difference Between a Factor and a Multiple
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
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 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.

42. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Just add or subtract the coefficients in front of the radicals.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

43. Finding the Volume of a Cylinder
Cross multiply.
Adjacent angles are supplementary - Vertical angles are equal
Factor out and cancel all factors the numerator and denominator have in common.
VofaC: (pie)r(2)h

44. Finding the Slope of a Line When Given Two Points on the Line
Adjacent angles are supplementary - Vertical angles are equal
Slope=change in y/change in x
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Two relatively prime numbers are integers that have no common factor other than 1.

45. Converting from an Improper Fraction to a Mixed Number
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.
Cross 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.
-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.

46. Simplifying a Fraction to Lowest 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.
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.
Factor out and cancel all factors the numerator and denominator have in common.

47. What is the Pythagorean Theorem?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
A(2)+b(2)=c(2)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

48. Calculating Negative Exponents and Radical Exponents
Put each number in the original ratio over the sum of the numbers.
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.
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

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

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50. 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.
VofaC: (pie)r(2)h
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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

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