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SAT Math

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Answer 50 questions in 15 minutes.
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1. Properties of a 30-60-90 Triangle
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
(pie)r(squared)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Cross multiply.

2. Solving a Proportion
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
Cross multiply.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

3. Finding the Surface Area of a Rectangular Solid
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Put the equation into y=mx+b-- in which case b is the y-intercept.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

4. Finding the y-intercept When Given an Equation of a Line
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Sum: Average x Number of Terms

5. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
Subtract the smallest from the largest and add 1

6. Dividing Fractions
-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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Put the equation into y=mx+b-- in which case b is the y-intercept.

7. If r#t=t(r)-r(t) - then what is 4#3?
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Multiply the numerators and multiply the denominators.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

8. If x(2)=7x+18 - what is the positive value of x?
Put the equation into y=mx+b-- in which case b is the y-intercept.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Factor out and cancel all factors the numerator and denominator have in common.
2(pie)r

9. Finding the Midpoint Between Two Points
The value that appears the most often.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
(x1+x2)/2 -(y1+y2)/2

10. Solving an Inequality
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Average the smallest and largest number
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

11. Calculating Negative Exponents and Radical Exponents
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Use simple numbers like 1 and 2 and see what happens.
Four equal acute angles and four equal obtuse angles.

12. Dividing Expressions with Exponents that Have a Common Base
-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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
-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.

13. 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?
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.

14. If (Square Root: x-1)+5=12 - what is the value of x/2?
Use simple numbers like 1 and 2 and see what happens.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

15. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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.
Get the absolute value equation by itself. Solve.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.

16. What is the Pythagorean Theorem?
Find a common denominator - then add or subtract the numerators.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
A(2)+b(2)=c(2)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

17. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Cross multiply.
-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

18. Number of Groups - +1 Each Time
Cross multiply.
Get the absolute value equation by itself. Solve.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

19. 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%
Four equal acute angles and four equal obtuse angles.
-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.
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.

20. Definition of an Irrational Number
Use the formula distance=rate*time and its variations to help in this question.
Part=Percent x Whole
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

21. Finding the Sum of the Average of a Series of Numbers
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Sum: Average x Number of Terms
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Four equal acute angles and four equal obtuse angles.

22. 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.
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
Average the smallest and largest number
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

23. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use simple numbers like 1 and 2 and see what happens.

24. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the formula distance=rate*time and its variations to help in this question.

25. Finding the Rate of Speed
The whole number left over after division.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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
Use the formula distance=rate*time and its variations to help in this question.

26. Definition of a Rational Number
Factor out and cancel all factors the numerator and denominator have in common.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Use simple numbers like 1 and 2 and see what happens.

27. Expressing the Union and Intersection of Sets
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.
Part=Percent x Whole
Adjacent angles are supplementary - Vertical angles are equal
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

28. Comparing the values of two or more Fractions
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Express them with a common denominator.

29. What types of angles are formed when a transversal cross parallel lines?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Four equal acute angles and four equal obtuse angles.

30. Finding the Area of a Triangle

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

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32. 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.
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

33. Finding the LCM of Two or More Numbers

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34. Increasing and Decreasing a Number by a Certain Percentage
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
Part=Percent x Whole
Adjacent angles are supplementary - Vertical angles are equal
-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.

35. Characteristics of a Square
Just add or subtract the coefficients in front of the radicals.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

36. Properties of Similar Triangles
Sum: Average x Number of Terms
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 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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

37. Finding the Sum of the Interior Angles of a Polygon
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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

38. Converting from part-to-part ratios to part-to-whole ratios
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.
Just add or subtract the coefficients in front of the radicals.
Put each number in the original ratio over the sum of the numbers.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

39. What is the Triangle Inequality Theorem?
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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. Adding a Positive Number to a Negative Number
Isolate the radical expression and use the standard rules of algebra.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
-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.

41. Finding the Area of a Circle
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
(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.
Use the distributive property then combine the like terms.

42. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Sum: Average x Number of Terms
-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.
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.

43. Factoring a Polynomial ('FOIL in Reverse')
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

45. What types of angles are formed when two lines intersect?
Cross multiply.
Adjacent angles are supplementary - Vertical angles are equal
The value that falls in the middle of the set.
Average the smallest and largest number

46. Finding the Volume of a Rectangular Solid
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
VofaRS=lwh
Average: Sum of the Terms/Number of the Terms

47. 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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Multiply the numerators and multiply the denominators.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

48. Difference Between a Factor and a Multiple
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.

49. What value of x is not in the domain of the function f(x)=x-2/x-3?
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use the units to keep things straight - Snowfall inches/hours
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

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

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