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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. An Important Property of a Line Tangent to 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.
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.
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.
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

2. Properties of the Interior and Exterior Angles of a Triangle
Cancel factors common to 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.
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.
The value that falls in the middle of the set.

3. Convert From a Fraction to a Decimal - Vice Versa
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
-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.
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.
(x1+x2)/2 -(y1+y2)/2

4. Finding the Area of a Sector

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5. Multiplying Expressions with Exponents that Have a Common Base
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Slope=change in y/change in x
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

6. Raising a Power to a Power
Just add or subtract the coefficients in front of the radicals.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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

7. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Four equal acute angles and four equal obtuse angles.
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.
The value that appears the most often.

8. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

9. Direct Variation and Inverse Variation
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the numerators and multiply the denominators.

10. What types of angles are formed when a transversal cross parallel lines?
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Four equal acute angles and four equal obtuse angles.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

11. Adding and Subtracting Polynomials
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
The value that falls in the middle of the set.
Combine like terms.
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.

12. If the average of a - b - and 48 is 48 - what is the value of a + b?
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Isolate the radical expression and use the standard rules of algebra.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

13. Formula Used to Find Percent
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 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Part=Percent x Whole

14. Finding the Mode of a Set of Numbers
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The value that appears the most often.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

15. Solving a Proportion
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 value that falls in the middle of the set.
Cross multiply.
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.

16. Definition of a Rational Number
Switch the numerator and denominator.
VofaRS=lwh
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The whole number left over after division.

17. 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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

18. Numbers that are Relatively Prime
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.
Isolate the radical expression and use the standard rules of algebra.
Slope=change in y/change in x
Two relatively prime numbers are integers that have no common factor other than 1.

19. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
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.
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.
2(pie)r

20. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Express them with a common denominator.
Isolate the radical expression and use the standard rules of algebra.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.

21. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
(pie)r(squared)
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
Slope=change in y/change in x

22. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.

23. 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?
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Subtract the smallest from the largest and add 1
Probability: Number of Favorable Outcomes/Total Possible Outcomes

24. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
2(pie)r
Two relatively prime numbers are integers that have no common factor other than 1.
Use simple numbers like 1 and 2 and see what happens.
-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.

25. Simplifying a Fraction to Lowest Terms
Use the distributive property then combine the like terms.
Sum: Average x Number of Terms
Factor out and cancel all factors the numerator and denominator have in common.
Put each number in the original ratio over the sum of the numbers.

26. 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?
Cross multiply.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
The whole number left over after division.

27. Difference Between a Factor and a Multiple
(x1+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.
Factor out and cancel all factors the numerator and denominator have in common.
Do whatever is necessary to both sides to isolate the variable.

28. If 3(3x)=9(x+2) - what is the value of x?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Find a common denominator - then add or subtract the numerators.

29. 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.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

30. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

31. Finding the Missing Number in a Series When You are Given the Average
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 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.
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.
2(pie)r

32. Converting from part-to-part ratios to part-to-whole ratios
Slope=change in y/change in x
Adjacent angles are supplementary - Vertical angles are equal
Put each number in the original ratio over the sum of the numbers.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

33. Finding the y-intercept When Given an Equation of a Line
Cancel factors common to the numerator and denominator.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.

34. What are Two Special Pythagorean Triples?

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35. Properties of a 45-45-90 Triangle
The value that falls in the middle of the set.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

36. Scalene - Isosceles - and Equilateral Triangles
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 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.
The value that appears the most often.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

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

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38. Finding the Midpoint Between Two Points
-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.
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 - 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.
(x1+x2)/2 -(y1+y2)/2

39. Finding the Sum of the Interior Angles of a Polygon
Put each number in the original ratio over the sum of the numbers.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

40. Evaluating an Algebraic Expression
Find a common denominator - then add or subtract the numerators.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

41. Expressing the Union and Intersection of Sets
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Get the absolute value equation by itself. Solve.
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

42. Finding the Area of a Circle
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
(pie)r(squared)

43. Average Rate and How Do You Find It
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.
Just add or subtract the coefficients in front of the radicals.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

44. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
The value that falls in the middle of the set.
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

45. Finding the LCM of Two or More Numbers

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46. Finding the Domain and Range of a Function
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.
The value that appears the most often.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Express them with a common denominator.

47. Finding the Volume of a Rectangular Solid
VofaRS=lwh
Multiply the exponents - (x^3)^4=x^3*4=x^12
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

48. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
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.
Slope=change in y/change in x
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.

49. Dividing Expressions with Exponents that Have a Common Base
Use the distributive property then combine the like terms.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Put the equation into y=mx+b-- in which case b is the y-intercept.

50. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
-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.