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SAT Math

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Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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1. Adding and Subtracting Roots
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.
Just add or subtract the coefficients in front of the radicals.
VofaRS=lwh
-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.

2. Finding the Missing Number in a Series When You are Given the Average
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
(pie)r(squared)
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

3. 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
Put the equation into y=mx+b-- in which case b is the y-intercept.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.

4. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

5. What types of angles are formed when a transversal cross parallel lines?
The value that appears the most often.
(pie)r(squared)
Four equal acute angles and four equal obtuse angles.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

6. Characteristics of a Rectangle
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 each number in the original ratio over the sum of the numbers.
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)

7. Solving a Radical Equation
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Isolate the radical expression and use the standard rules of algebra.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Don't be confused by all the variables. Recall that (x-y)(x+y)=x(2)-y(2). Then - x(2)-y(2)=5*7=35. x(2)+1-y(2)=x(2)-y(2)+1=35+1=36.

8. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

9. 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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Get the absolute value equation by itself. Solve.

10. Evaluating an Algebraic Expression
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Plug in the given values for the unknowns and calculate according to PEMDAS.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

11. Adding and Subtracting Polynomials
Put the equation into y=mx+b-- in which case b is the y-intercept.
Multiply the numerators and multiply the denominators.
Combine like terms.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

12. Adding and Subtracting Fractions
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Cancel factors common to the numerator and denominator.
Find a common denominator - then add or subtract the numerators.
Factor out and cancel all factors the numerator and denominator have in common.

13. If r#t=t(r)-r(t) - then what is 4#3?
The value that falls in the middle of the set.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Cancel factors common to the numerator and denominator.
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

14. Dividing Fractions
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Adjacent angles are supplementary - Vertical angles are equal
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

15. Multiplying Binomials
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Use the distributive property then combine the like terms.

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

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17. An Important Property of a Line Tangent to a Circle
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.
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.
Two relatively prime numbers are integers that have no common factor other than 1.
Plug in the given values for the unknowns and calculate according to PEMDAS.

18. 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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.

19. Finding the Slope of a Line When Given Two Points on the Line
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Slope=change in y/change in x
Find a common denominator - then add or subtract the numerators.

20. Finding the Rate of Speed
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.
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
Slope=change in y/change in x
Use the formula distance=rate*time and its variations to help in this question.

21. Simplifying an Algebraic Equation
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Part=Percent x Whole
Cancel factors common to the numerator and denominator.
Multiply the numerators and multiply the denominators.

22. Finding the Volume of a Rectangular Solid
Average: Sum of the Terms/Number of the Terms
The value that falls in the middle of the set.
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

23. Number of Groups - +1 Each Time
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

24. Knowing if an Integer is a Multiple of 2 or 4
-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 and cancel all factors the numerator and denominator have in common.
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

25. Knowing if an Integer is a Multiple of 5 or 10
-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.
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.
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.
Two relatively prime numbers are integers that have no common factor other than 1.

26. Counting Consecutive Integers
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Use the formula distance=rate*time and its variations to help in this question.
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

27. Finding the LCM of Two or More Numbers

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28. What are Two Special Pythagorean Triples?

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29. Convert From a Fraction to a Decimal - Vice Versa
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Use simple numbers like 1 and 2 and see what happens.

30. 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.
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
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.

31. Finding a Term in a Geometric Sequence
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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 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.
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. 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?
Put each number in the original ratio over the sum of the numbers.
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.
Subtract the smallest from the largest and add 1
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.

33. Difference Between a Factor and a Multiple
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

34. Finding the Area of a Triangle

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35. General Procedure for Multiplying Polynomials
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
Use the distributive property then combine the like terms.
(x1+x2)/2 -(y1+y2)/2

36. Formula Used to Find Percent
Part=Percent x Whole
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Four equal acute angles and four equal obtuse angles.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

37. Properties of the Interior and Exterior Angles of a Triangle
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

38. Counting the Total Number of Possibilities for Several Events to Occur
-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.
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.
Cross multiply.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

39. Solving a Problem Involving Rates
Subtract the smallest from the largest and add 1
Use the units to keep things straight - Snowfall inches/hours
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

40. Adding a Positive Number to a Negative Number
-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.
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
-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. Calculating Negative Exponents and Radical Exponents
Use simple numbers like 1 and 2 and see what happens.
Four equal acute angles and four equal obtuse angles.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The whole number left over after division.

42. Finding the Sum of the Average of a Series of Numbers
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Combine like terms.
Sum: Average x Number of Terms

43. Factoring the Difference of Two Squares
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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

44. Direct Variation and Inverse Variation
Express them with a common 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.
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
Two relatively prime numbers are integers that have no common factor other than 1.

45. 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
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
Switch the numerator and denominator.
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

46. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Express them with a common denominator.

47. 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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
VofaC: (pie)r(2)h
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

48. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Isolate the radical expression and use the standard rules of algebra.
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

49. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
2(pie)r
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

50. What value of x is not in the domain of the function f(x)=x-2/x-3?
Cancel factors common to the numerator and denominator.
(x1+x2)/2 -(y1+y2)/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
Part=Percent x Whole

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