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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. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Do whatever is necessary to both sides to isolate the variable.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

2. What are Two Special Pythagorean Triples?

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3. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.

4. Properties of Similar Triangles
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Put each number in the original ratio over the sum of the numbers.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

5. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
A(2)+b(2)=c(2)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.

6. Finding the Median of a Set of Numbers
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.
The value that falls in the middle of the set.
VofaRS=lwh

7. If 3(3x)=9(x+2) - what is the value of x?
(pie)r(squared)
Use the distributive property then combine the like terms.
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
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

8. Counting Consecutive Integers
Probability: Number of Favorable Outcomes/Total Possible Outcomes
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Subtract the smallest from the largest and add 1
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

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

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10. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
A(2)+b(2)=c(2)
Part=Percent x Whole
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

11. How do you know if an integer is a multiple of 3 or 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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Slope=change in y/change in x
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.

12. Definition of an Irrational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Just add or subtract the coefficients in front of the radicals.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Use the formula distance=rate*time and its variations to help in this question.

13. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Combine like terms.
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.
Put each number in the original ratio over the sum of the numbers.
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.

14. Formula Used to Find Percent
Part=Percent x Whole
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use simple numbers like 1 and 2 and see what happens.

15. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Sum: Average x Number of Terms
(pie)r(squared)
Do whatever is necessary to both sides to isolate the variable.

16. Finding the Volume of a Rectangular Solid
VofaRS=lwh
Probability: Number of Favorable Outcomes/Total Possible Outcomes
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
The whole number left over after division.

17. Converting From a Mixed Number to an Improper Fraction
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Combine like terms.

18. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

19. Finding the Area of a Sector

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20. Converting from part-to-part ratios to part-to-whole ratios
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.
Put each number in the original ratio over the sum of the numbers.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

21. Finding the Mode of a Set of Numbers
Part=Percent x Whole
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.
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.

22. 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
Get the absolute value equation by itself. Solve.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

23. If 4(x(2)-10x+25) - then what is the value of x?
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.
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 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.
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.

24. Formula to Find Average
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.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Average: Sum of the Terms/Number of the Terms

25. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Average the smallest and largest number
Four equal acute angles and four equal obtuse angles.

26. Raising a Power to a Power
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Multiply the numerators and multiply the denominators.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Combine like terms.

27. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
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.
Multiply the numerators and multiply the denominators.

28. 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
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
Do whatever is necessary to both sides to isolate the variable.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

29. What is the Pythagorean Theorem?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Use the distributive property then combine the like terms.
2(pie)r
A(2)+b(2)=c(2)

30. Definition of Remainder
The whole number left over after division.
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.
A(2)+b(2)=c(2)
Combine like terms.

31. Finding the Volume of a Cylinder
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
VofaC: (pie)r(2)h
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.

32. Dividing Fractions
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

33. 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.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

34. Solving a Linear Equation
Multiply the numerators and multiply the denominators.
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
Do whatever is necessary to both sides to isolate the variable.
Slope=change in y/change in x

35. Average Rate and How Do You Find It
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

36. Convert From a Fraction to a Decimal - Vice Versa
Isolate the radical expression and use the standard rules of algebra.
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

37. Definition of a Rational Number
Put each number in the original ratio over the sum of the numbers.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

38. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Part=Percent x Whole
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
-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.

39. Finding a Term in a Geometric Sequence
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Part=Percent x Whole
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.

40. Properties of a 30-60-90 Triangle
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Sum: Average x Number of 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

41. Adding and Subtracting Roots
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.
Just add or subtract the coefficients in front of the radicals.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
-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.

42. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Express them with a common denominator.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.

43. 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?
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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

44. An Important Property of a Line Tangent to a Circle
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
A(2)+b(2)=c(2)

45. Factoring the Difference of Two Squares
FOIL: First - Outer - Inner - Last... Combine Like Terms
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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 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.

46. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Express them with a common denominator.
Sum: Average x Number of Terms
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

47. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

48. 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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
A(2)+b(2)=c(2)

49. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 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.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
VofaRS=lwh

50. Dividing Expressions with Exponents that Have a Common Base
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.
Express them with a common denominator.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5