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SAT Math

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Answer 50 questions in 15 minutes.
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1. Finding the Surface Area of a Rectangular Solid
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Average the smallest and largest number
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. Finding the Domain and Range of a Function
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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. Converting from part-to-part ratios to part-to-whole ratios
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put each number in the original ratio over the sum of the numbers.

4. Properties of the Interior and Exterior Angles of a Triangle
Two relatively prime numbers are integers that have no common factor other than 1.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
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.

5. Direct Variation and Inverse Variation
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.
Put each number in the original ratio over the sum of the numbers.
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
(x1+x2)/2 -(y1+y2)/2

6. What is the Pythagorean Theorem?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
A(2)+b(2)=c(2)

7. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Plug in the given values for the unknowns and calculate according to PEMDAS.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
VofaC: (pie)r(2)h

8. 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
-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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
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.

9. Solving an Inequality
Multiply the numerators and multiply the denominators.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
(pie)r(squared)

10. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Adjacent angles are supplementary - Vertical angles are equal
VofaRS=lwh
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

11. Average Rate and How Do You Find It
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

12. Multiply and Divide Positive and Negative Numbers
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
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
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

13. Prime Factorization of a Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Factor out and cancel all factors the numerator and denominator have in common.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Put each number in the original ratio over the sum of the numbers.

14. Finding the Median of a Set of Numbers
Combine like terms.
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.
The value that falls in the middle of the set.
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

15. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

16. Definition of a Rational Number
Sum: Average x Number of Terms
Use the distributive property then combine the like terms.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

17. Expressing the Union and Intersection of Sets
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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Put the equation into y=mx+b-- in which case b is the y-intercept.
Use the distributive property then combine the like terms.

18. Finding the Circumference of a Circle
2(pie)r
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

19. Finding a Term in a Geometric Sequence
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Combine like terms.
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

20. Finding the Area of a Circle
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
(pie)r(squared)
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

21. 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?
Combine like terms.
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.
A(2)+b(2)=c(2)
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

22. Finding the Sum of the Average of a Series of Numbers
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Two relatively prime numbers are integers that have no common factor other than 1.
Average the smallest and largest number
Sum: Average x Number of Terms

23. Finding the LCM of Two or More Numbers

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24. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

25. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
FOIL: First - Outer - Inner - Last... Combine Like Terms
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

26. If r#t=t(r)-r(t) - then what is 4#3?
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
Put each number in the original ratio over the sum of the numbers.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

27. 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
-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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.

28. Increasing and Decreasing a Number by a Certain Percentage
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
-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.

29. Adding and Subtracting Monomials
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

30. Adding and Subtracting Polynomials
Find a common denominator - then add or subtract the numerators.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Combine like terms.
Put each number in the original ratio over the sum of the numbers.

31. If x varies directly with y - and the value of x is 12 when y is 11 - what is the value of y when x is 66?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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
Plug in the given values for the unknowns and calculate according to PEMDAS.

32. Finding the Volume of a Cylinder
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
VofaC: (pie)r(2)h
Cancel factors common to the numerator and denominator.

33. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
(pie)r(squared)
Multiply the numerators and multiply the denominators.
Do whatever is necessary to both sides to isolate the variable.
Use simple numbers like 1 and 2 and see what happens.

34. Convert From a Fraction to a Decimal - Vice Versa
Combine like terms.
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.
Multiply the numerators and multiply the denominators.

35. Solving a Radical Equation
(pie)r(squared)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Isolate the radical expression and use the standard rules of algebra.
VofaRS=lwh

36. Converting from an Improper Fraction to a Mixed Number
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
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.
VofaRS=lwh

37. General Procedure for Multiplying Polynomials
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use the distributive property then combine the like terms.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

38. Finding the y-intercept When Given an Equation of a Line
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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.

39. Definition of Remainder
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
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
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.

40. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
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.
Put each number in the original ratio over the sum of the numbers.
Subtract the smallest from the largest and add 1

41. Finding the Missing Number in a Series When You are Given the Average
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

42. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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 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.
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.

43. Finding the Rate of Speed
Use the formula distance=rate*time and its variations to help in this question.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
Four equal acute angles and four equal obtuse angles.

44. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Sum: Average x Number of Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

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

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46. Determining Absolute Value of a 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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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

47. Adding a Positive Number to a Negative Number
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Express them with a common denominator.
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

48. PEMDAS
VofaC: (pie)r(2)h
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
-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.
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.

49. 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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

50. Finding the Area of a Sector

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