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SAT Math

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Answer 50 questions in 15 minutes.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. Finding the Sum of the Average of a Series of Numbers
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Sum: Average x Number of Terms
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.

2. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Use the units to keep things straight - Snowfall inches/hours
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
Part=Percent x Whole

3. Finding the Mode of a Set of Numbers
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the numerators and multiply the denominators.
(pie)r(squared)
The value that appears the most often.

4. Formula to Find Average
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.
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.
Use the distributive property then combine the like terms.
Average: Sum of the Terms/Number of the Terms

5. Factoring a Polynomial ('FOIL in Reverse')
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Use the formula distance=rate*time and its variations to help in this question.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

6. Adding and Subtracting Polynomials
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.
2(pie)r
Combine like 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.

7. Convert From a Fraction to a Decimal - Vice Versa
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.
-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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

8. Numbers that are Relatively Prime
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Express them with a common denominator.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Two relatively prime numbers are integers that have no common factor other than 1.

9. Finding the GCF of Two or More Numbers
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.
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

10. Finding the Area of a Triangle

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11. 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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.

12. PEMDAS
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

13. 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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

14. If r#t=t(r)-r(t) - then what is 4#3?
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

15. General Procedure for Multiplying Polynomials
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Adjacent angles are supplementary - Vertical angles are equal
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.
Use the distributive property then combine the like terms.

16. Finding the Median of a Set of Numbers
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
The value that falls in the middle of the set.
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.

17. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
VofaRS=lwh
A(2)+b(2)=c(2)
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
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.

18. 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.
The value that falls in the middle of the set.
Cross multiply.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

19. Properties of the Interior and Exterior Angles of a Triangle
Get the absolute value equation by itself. Solve.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Switch the numerator and 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.

20. Finding a Term in a Geometric Sequence
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

21. Multiplying and Dividing Roots
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.
Slope=change in y/change in x
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.

22. Calculating the Probability that an Event will Take Place
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

23. Characteristics of a Parallelogram
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Isolate the radical expression and use the standard rules of algebra.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

24. Comparing the values of two or more Fractions
Average: Sum of the Terms/Number of the Terms
Express them with a common denominator.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
VofaRS=lwh

25. Converting From a Mixed Number to an Improper Fraction
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Factor out and cancel all factors the numerator and denominator have in common.
Use the formula distance=rate*time and its variations to help in this question.

26. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the units to keep things straight - Snowfall inches/hours
FOIL: First - Outer - Inner - Last... Combine Like Terms

27. Factoring the Difference of Two Squares
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
(pie)r(squared)
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
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

28. If (Square Root: x-1)+5=12 - what is the value of x/2?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

29. Difference Between a Factor and a Multiple
(x1+x2)/2 -(y1+y2)/2
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.
-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.
Subtract the smallest from the largest and add 1

30. 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.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.

31. Finding the LCM of Two or More Numbers

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32. Solving a System of Equations
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Four equal acute angles and four equal obtuse angles.
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.
Combine like terms.

33. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
-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.
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
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

34. Finding the Volume of a Rectangular Solid
VofaRS=lwh
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Cancel factors common to the numerator and denominator.
Isolate the radical expression and use the standard rules of algebra.

35. 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%.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

36. How do you know if an integer is a multiple of 3 or 9?
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.
-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.
-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.
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.

37. Expressing the Union and Intersection of Sets
Slope=change in y/change in x
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
Isolate the radical expression and use the standard rules of algebra.

38. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Use simple numbers like 1 and 2 and see what happens.
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.

39. Multiplying Expressions with Exponents that Have a Common Base
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Two relatively prime numbers are integers that have no common factor other than 1.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Multiply the numerators and multiply the denominators.

40. Adding and Subtracting Fractions
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
Find a common denominator - then add or subtract the numerators.

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

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42. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
A(2)+b(2)=c(2)
Cross multiply.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

43. Finding the Reciprocal of a Fraction
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Switch the numerator and denominator.
Factor out and cancel all factors the numerator and denominator have in common.

44. An Important Property of a Line Tangent to a Circle
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
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.
Average: Sum of the Terms/Number of the Terms
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

45. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
Just add or subtract the coefficients in front of the radicals.
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
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

46. Setting Up a Ratio
Adjacent angles are supplementary - Vertical angles are equal
Average: Sum of the Terms/Number of the Terms
Multiply the numerators and multiply the denominators.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

47. Properties of a 30-60-90 Triangle
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Switch the numerator and denominator.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

48. If 3(3x)=9(x+2) - what is the value of x?
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

49. Prime Factorization 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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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
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. Increasing and Decreasing a Number by a Certain Percentage
-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.
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.
Four equal acute angles and four equal obtuse angles.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

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