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SAT Math

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. Solving a Linear Equation
-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.
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.
Do whatever is necessary to both sides to isolate the variable.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

2. 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.
Average: Sum of the Terms/Number of the Terms
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.

3. Solving an Inequality
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
A(2)+b(2)=c(2)
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

4. Knowing if an Integer is a Multiple of 2 or 4
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.
Slope=change in y/change in x
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
-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.

5. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

6. Finding the Length of an Arc in a Circle

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7. Finding the GCF of Two or More Numbers
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Get the absolute value equation by itself. Solve.

8. Scalene - Isosceles - and Equilateral Triangles
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Put each number in the original ratio over the sum of the numbers.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

9. Determining Absolute Value of a Number
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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 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.

10. Properties of the Interior and Exterior Angles of a Triangle
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Slope=change in y/change in x
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

11. Difference Between a Factor and a Multiple
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.
-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.
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.
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.

12. Definition of Remainder
The whole number left over after division.
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
Cancel factors common to the numerator and denominator.
Get the absolute value equation by itself. Solve.

13. If the average of a - b - and 48 is 48 - what is the value of a + b?
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
-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.
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.

14. Prime Factorization of a Number
Sum: Average x Number of Terms
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
FOIL: First - Outer - Inner - Last... Combine Like 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.

15. Expressing the Union and Intersection of Sets
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Two relatively prime numbers are integers that have no common factor other than 1.
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

16. What is the Triangle Inequality Theorem?
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
Do whatever is necessary to both sides to isolate the variable.
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.

17. Converting from part-to-part ratios to part-to-whole ratios
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Put each number in the original ratio over the sum of the numbers.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Combine like terms.

18. Comparing the values of two or more Fractions
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Express them with a common denominator.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Average the smallest and largest number

19. 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.
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Plug in the given values for the unknowns and calculate according to PEMDAS.

20. 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.
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.
VofaC: (pie)r(2)h
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

21. Solving a Radical Equation
Switch the numerator and denominator.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Isolate the radical expression and use the standard rules of algebra.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

22. Adding and Subtracting Monomials
Average the smallest and largest number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

23. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Use simple numbers like 1 and 2 and see what happens.
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.

24. Finding the Area of a Triangle

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25. Quickly Finding the Average of a Series of Evenly Spaced Numbers
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 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Average the smallest and largest number

26. If r#t=t(r)-r(t) - then what is 4#3?
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

27. Finding the Midpoint Between Two Points
VofaC: (pie)r(2)h
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
(x1+x2)/2 -(y1+y2)/2
FOIL: First - Outer - Inner - Last... Combine Like Terms

28. 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?
FOIL: First - Outer - Inner - Last... Combine Like Terms
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
VofaRS=lwh
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

29. Numbers that are Relatively Prime
Part=Percent x Whole
Slope=change in y/change in x
Put each number in the original ratio over the sum of the numbers.
Two relatively prime numbers are integers that have no common factor other than 1.

30. Finding a Term in a Geometric Sequence
Combine like terms.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

31. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Just add or subtract the coefficients in front of the radicals.
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.
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

32. Adding a Positive Number to a Negative Number
Average: Sum of the Terms/Number of the Terms
FOIL: First - Outer - Inner - Last... Combine Like Terms
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

33. Finding the Volume of a Cylinder
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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
VofaC: (pie)r(2)h

34. Properties of Similar Triangles
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.
Use the distributive property then combine the like terms.
Put the equation into y=mx+b-- in which case b is the y-intercept.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

35. If 4(x(2)-10x+25) - then what is the value of x?
Part=Percent x Whole
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
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.

36. Factoring a Polynomial ('FOIL in Reverse')
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 whole number part by the denominator - then add the numerator. Keep the same denominator.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

37. How do you know if an integer is a multiple of 3 or 9?
The whole number left over after division.
Just add or subtract the coefficients in front of the radicals.
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.

38. Finding the Median of a Set of Numbers
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
VofaRS=lwh
The value that falls in the middle of the set.
-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.

39. Solving a System of Equations
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Express them with a common denominator.
Factor out and cancel all factors the numerator and denominator have in common.
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. Setting Up a Ratio
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
-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.
Four equal acute angles and four equal obtuse angles.
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.

41. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

42. PEMDAS
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
(x1+x2)/2 -(y1+y2)/2
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Combine like terms.

43. Increasing and Decreasing a Number by a Certain Percentage
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.

44. Formula Used to Find Percent
Slope=change in y/change in x
Part=Percent x Whole
(pie)r(squared)
Put each number in the original ratio over the sum of the numbers.

45. Properties of a 45-45-90 Triangle
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

46. 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
Use simple numbers like 1 and 2 and see what happens.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Factor out and cancel all factors the numerator and denominator have in common.
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.

47. Factoring the Difference of Two Squares
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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

48. Solving a Problem Involving Rates
Slope=change in y/change in x
Use simple numbers like 1 and 2 and see what happens.
Use the units to keep things straight - Snowfall inches/hours
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

49. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Use the distributive property then combine the like terms.
Multiply the exponents - (x^3)^4=x^3*4=x^12

50. If 3(3x)=9(x+2) - what is the value of x?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Multiply the numerators and multiply the denominators.
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