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SAT Math

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Answer 50 questions in 15 minutes.
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1. If 3(3x)=9(x+2) - what is the value of x?
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Subtract the smallest from the largest and add 1
Put the equation into y=mx+b-- in which case b is the y-intercept.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

2. 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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
-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.

3. Definition of an Irrational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Four equal acute angles and four equal obtuse angles.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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

4. Adding and Subtracting Fractions
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Find a common denominator - then add or subtract the numerators.
VofaRS=lwh
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.

5. Adding a Positive Number to a Negative Number
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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
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 Sum of the Average of a Series of Numbers
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 whole number left over after division.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

7. Finding the Rate of Speed
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 the formula distance=rate*time and its variations to help in this question.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

8. What is the Triangle Inequality Theorem?
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
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.

9. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.

10. Formula Used to Find Percent
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
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 radical expression and use the standard rules of algebra.
Part=Percent x Whole

11. 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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

12. Multiply and Divide Positive and Negative Numbers
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

13. If (Square Root: x-1)+5=12 - what is the value of x/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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Adjacent angles are supplementary - Vertical angles are equal
Multiply the numerators and multiply the denominators.

14. Finding the Mode of a Set of Numbers
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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
The value that appears the most often.
2(pie)r

15. Solving a Problem Involving Rates
Average the smallest and largest number
FOIL: First - Outer - Inner - Last... Combine Like Terms
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Use the units to keep things straight - Snowfall inches/hours

16. Solving a Proportion
Cross multiply.
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12

17. If r#t=t(r)-r(t) - then what is 4#3?
Just add or subtract the coefficients in front of the radicals.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Cross multiply.
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

18. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use simple numbers like 1 and 2 and see what happens.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

19. Numbers that are Relatively Prime
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.
Two relatively prime numbers are integers that have no common factor other than 1.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Do whatever is necessary to both sides to isolate the variable.

20. Adding and Subtracting Monomials
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

21. Solving a Linear Equation
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Do whatever is necessary to both sides to isolate the variable.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

22. Scalene - Isosceles - and Equilateral Triangles
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

23. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Multiply the numerators and multiply the denominators.
Do whatever is necessary to both sides to isolate the variable.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

24. Finding the Volume of a Rectangular Solid
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
VofaRS=lwh
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

25. Difference Between a Factor and a Multiple
-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.
Use the units to keep things straight - Snowfall inches/hours
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

26. Average Rate and How Do You Find It
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
-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 A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Get the absolute value equation by itself. Solve.

27. 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?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
(pie)r(squared)
The whole number left over after division.
Sum: Average x Number of Terms

28. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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.
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
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.

29. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use simple numbers like 1 and 2 and see what happens.

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

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31. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Factor out and cancel all factors the numerator and denominator have in common.
Use the distributive property then combine the like terms.
Use simple numbers like 1 and 2 and see what happens.

32. What are Two Special Pythagorean Triples?

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33. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
The value that falls in the middle of the set.
Factor out and cancel all factors the numerator and denominator have in common.

34. Simplifying Square Roots
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
-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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

35. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
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
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

36. What types of angles are formed when a transversal cross parallel lines?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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 number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Four equal acute angles and four equal obtuse angles.

37. Raising a Power to a Power
Subtract the smallest from the largest and add 1
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the exponents - (x^3)^4=x^3*4=x^12

38. Characteristics of a Square
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Isolate the radical expression and use the standard rules of algebra.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

39. Knowing if an Integer is a Multiple of 5 or 10
Subtract the smallest from the largest and add 1
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
-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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

40. Expressing the Union and Intersection of Sets
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
Get the absolute value equation by itself. Solve.

41. Comparing the values of two or more Fractions
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.
Part=Percent x Whole
Express them with a common denominator.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

42. Characteristics of a Parallelogram
Use simple numbers like 1 and 2 and see what happens.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

43. PEMDAS
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

44. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Factor out and cancel all factors the numerator and denominator 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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

45. Adding and Subtracting Roots
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Just add or subtract the coefficients in front of the radicals.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

46. 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.
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

47. Finding the GCF of Two or More Numbers
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The whole number left over after division.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

48. Finding the Distance Between Two Points on a Coordinate Graph
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
(x1+x2)/2 -(y1+y2)/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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

49. 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.
Switch the numerator and denominator.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

50. Dividing Expressions with Exponents that Have a Common Base
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
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 the exponents - (x^3)^4=x^3*4=x^12
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

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