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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. Finding the Sum of the Interior Angles of a Polygon
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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

2. Finding a Term in a Geometric Sequence
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Cross multiply.
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. Properties of a 30-60-90 Triangle
Isolate the radical expression and use the standard rules of algebra.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
The value that appears the most often.
Put the equation into y=mx+b-- in which case b is the y-intercept.

4. Multiplying and Dividing Roots
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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.
(x1+x2)/2 -(y1+y2)/2
VofaC: (pie)r(2)h

5. Finding the Slope When Given an Equation of a Line
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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

6. Finding the Slope of a Line When Given Two Points on the Line
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.
Slope=change in y/change in x
Sum: Average x Number of Terms
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

7. Characteristics of a Rectangle
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

8. Dividing Fractions
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

9. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Just add or subtract the coefficients in front of the radicals.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.

10. Characteristics of a Square
Average: Sum of the Terms/Number of the Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.
The whole number left over after division.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

11. Multiplying Expressions with Exponents that Have a Common Base
Put each number in the original ratio over the sum of the numbers.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

12. Finding the Mode of a Set of Numbers
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 appears the most often.
Do whatever is necessary to both sides to isolate the variable.
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.

13. If 3(3x)=9(x+2) - what is the value of x?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Subtract the smallest from the largest and add 1
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

14. If 4(x(2)-10x+25) - then what is the value of x?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
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
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.

15. 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?
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12

16. Finding the Volume of a Cylinder
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use the units to keep things straight - Snowfall inches/hours
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.
VofaC: (pie)r(2)h

17. Evaluating an Algebraic Expression
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
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.
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.

18. Adding and Subtracting Polynomials
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
Combine like terms.
(x1+x2)/2 -(y1+y2)/2

19. 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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Cross multiply.
(x1+x2)/2 -(y1+y2)/2

20. Convert From a Fraction to a Decimal - Vice Versa
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.

21. Finding the y-intercept When Given an Equation of a Line
Just add or subtract the coefficients in front of the radicals.
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Use simple numbers like 1 and 2 and see what happens.
Put the equation into y=mx+b-- in which case b is the y-intercept.

22. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
(pie)r(squared)
The value that appears the most often.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

23. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Express them with a common denominator.
Cancel factors common to the numerator and denominator.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

24. What are Two Special Pythagorean Triples?

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25. Formula to Find Average
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Average: Sum of the Terms/Number of the 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.
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.

26. An Important Property of a Line Tangent to a Circle
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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 value that falls in the middle of the set.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

27. Adding a Positive Number to a Negative Number
Use the formula distance=rate*time and its variations to help in this question.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Sum: Average x Number of Terms
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

28. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Four equal acute angles and four equal obtuse angles.
Use simple numbers like 1 and 2 and see what happens.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

29. Calculating Negative Exponents and Radical Exponents
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

30. Finding the Reciprocal of a Fraction
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.
-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.
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

31. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Put the equation into y=mx+b-- in which case b is the y-intercept.

32. Prime Factorization of a Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Use the formula distance=rate*time and its variations to help in this question.
Put each number in the original ratio over the sum of the numbers.

33. Increasing and Decreasing a Number by a Certain Percentage
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
-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.

34. Converting from part-to-part ratios to part-to-whole ratios
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
FOIL: First - Outer - Inner - Last... Combine Like Terms
Put each number in the original ratio over the sum of the numbers.

35. Finding the Median of a Set of Numbers
Multiply the exponents - (x^3)^4=x^3*4=x^12
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
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. What types of angles are formed when a transversal cross parallel lines?
2(pie)r
Four equal acute angles and four equal obtuse angles.
Part=Percent x Whole
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

37. Finding the Sum of the Average of a Series of Numbers
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Average: Sum of the Terms/Number of the Terms
Cross multiply.
Sum: Average x Number of Terms

38. Number of Groups - +1 Each Time
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
VofaC: (pie)r(2)h
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.

39. Numbers that are Relatively Prime
Express them with a common denominator.
Two relatively prime numbers are integers that have no common factor other than 1.
Adjacent angles are supplementary - Vertical angles are equal
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

40. Comparing the values of two or more Fractions
Express them with a common denominator.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

41. Properties of the Interior and Exterior Angles of a Triangle
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
The whole number left over after division.

42. Knowing if an Integer is a Multiple of 5 or 10
Find a common denominator - then add or subtract the numerators.
-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.
Subtract the smallest from the largest and add 1
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

43. Definition of an Irrational Number
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Express them with a common denominator.
Adjacent angles are supplementary - Vertical angles are equal
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

44. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Find a common denominator - then add or subtract the numerators.
Average the smallest and largest 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.
Get the absolute value equation by itself. Solve.

45. Raising a Power to a Power
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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
The value that appears the most often.

46. Factoring the Difference of Two Squares
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Multiply the exponents - (x^3)^4=x^3*4=x^12
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

47. Finding the Midpoint Between Two Points
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
(x1+x2)/2 -(y1+y2)/2
Average: Sum of the Terms/Number of the 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.

48. What is the Triangle Inequality Theorem?
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
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.

49. Finding the Area of a Triangle

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50. Solving a Linear Equation
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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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.