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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 y-intercept When Given an Equation of a Line
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
Part=Percent x Whole
Put the equation into y=mx+b-- in which case b is the y-intercept.

2. What is the Triangle Inequality Theorem?
(pie)r(squared)
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.
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

3. Converting From a Mixed Number to an Improper Fraction
Cross multiply.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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

4. Multiplying Fractions
Multiply the numerators and multiply the denominators.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
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

5. Simplifying an Algebraic Equation
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Multiply the exponents - (x^3)^4=x^3*4=x^12
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Cancel factors common to the numerator and denominator.

6. Characteristics of a Parallelogram
Slope=change in y/change in x
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
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

7. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
FOIL: First - Outer - Inner - Last... Combine Like Terms

8. Expressing the Union and Intersection of Sets
Express them with a common denominator.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
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

9. Raising a Power to a Power
Factor out and cancel all factors the numerator and denominator have in common.
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.
Subtract the smallest from the largest and add 1
Multiply the exponents - (x^3)^4=x^3*4=x^12

10. Finding the Sum of the Average of a Series of Numbers
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Just add or subtract the coefficients in front of the radicals.
Factor out and cancel all factors the numerator and denominator have in common.
Sum: Average x Number of Terms

11. 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
Isolate the radical expression and use the standard rules of algebra.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

12. 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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Plug in the given values for the unknowns and calculate according to PEMDAS.

13. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Average the smallest and largest number
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.

14. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 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.
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.
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.

15. Dividing Expressions with Exponents that Have a Common Base
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Adjacent angles are supplementary - Vertical angles are equal
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

16. Finding the Area of a Triangle

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17. Evaluating an Algebraic Expression
Just add or subtract the coefficients in front of the radicals.
The value that appears the most often.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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

18. Definition of an Integer
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Isolate the radical expression and use the standard rules of algebra.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Put each number in the original ratio over the sum of the numbers.

19. Solving an Inequality
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Adjacent angles are supplementary - Vertical angles are equal
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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

20. Formula Used to Find Percent
Part=Percent x Whole
A(2)+b(2)=c(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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

21. Numbers that are Relatively Prime
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.
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.
Two relatively prime numbers are integers that have no common factor other than 1.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

22. Convert From a Fraction to a Decimal - Vice Versa
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.

23. Definition of a Rational Number
The whole number left over after division.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

24. Direct Variation and Inverse Variation
VofaC: (pie)r(2)h
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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

25. Dividing Fractions
Plug in the given values for the unknowns and calculate according to PEMDAS.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Part=Percent x Whole
Multiply the exponents - (x^3)^4=x^3*4=x^12

26. Finding the Surface Area of a Rectangular Solid
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Sum: Average x Number of Terms

27. Comparing the values of two or more Fractions
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 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.
Express them with a common denominator.
Part=Percent x Whole

28. Finding the Median of a Set of 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.
The value that falls in the middle of the set.
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

29. Finding the Rate of Speed
Use the formula distance=rate*time and its variations to help in this question.
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
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.
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

30. Multiplying Monomials
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

31. Increasing and Decreasing a Number by a Certain Percentage
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
-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.
Use the distributive property then combine the like terms.
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

32. Properties of a 45-45-90 Triangle
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

33. What types of angles are formed when a transversal cross parallel lines?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Four equal acute angles and four equal obtuse angles.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.

34. If r#t=t(r)-r(t) - then what is 4#3?
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.
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.
A(2)+b(2)=c(2)

35. Solving a System of Equations
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

36. Average Rate and How Do You Find It
Four equal acute angles and four equal obtuse angles.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Average the smallest and largest number
Multiply the exponents - (x^3)^4=x^3*4=x^12

37. Solving a Linear Equation
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Do whatever is necessary to both sides to isolate the variable.

38. 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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
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.

39. What is the positive difference between the answers to the equation 35+x(2)=12x?

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40. Finding the Circumference of a Circle
Four equal acute angles and four equal obtuse angles.
2(pie)r
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Find a common denominator - then add or subtract the numerators.

41. Finding the Reciprocal of a Fraction
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.
Switch the numerator and denominator.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

42. Determining Absolute Value of a Number
Express them with a common denominator.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Slope=change in y/change in x

43. Multiplying and Dividing Roots
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

44. 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?
Multiply the numerators and multiply the denominators.
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.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

45. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Use simple numbers like 1 and 2 and see what happens.
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.
Express them with a common denominator.

46. General Procedure for Multiplying Polynomials
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Adjacent angles are supplementary - Vertical angles are equal
Use the distributive property then combine the like terms.

47. 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
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.

48. Finding the Midpoint Between Two Points
Put the equation into y=mx+b-- in which case b is the y-intercept.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
(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

49. Multiply and Divide Positive and Negative Numbers
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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
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 simple numbers like 1 and 2 and see what happens.

50. Prime Factorization of a Number
2(pie)r
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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 the slope-intercept form: y=mx+b. The slope is m.