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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. Counting the Total Number of Possibilities for Several Events to Occur
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.
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
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
2(pie)r

2. Characteristics of a Square
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
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.

3. Finding the y-intercept When Given an Equation of a Line
Adjacent angles are supplementary - Vertical angles are equal
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

4. If 3(3x)=9(x+2) - what is the value of x?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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 units to keep things straight - Snowfall inches/hours
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.

5. Finding the LCM of Two or More Numbers

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6. 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?
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.
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

7. Finding the Length of an Arc in a Circle

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8. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
Express them with a common denominator.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
-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.

9. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Combine like terms.
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
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
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.

10. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
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.
Part=Percent x Whole

11. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

12. Solving a Proportion
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
Cross multiply.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

13. Definition of an Irrational Number
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
VofaRS=lwh
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

14. Solving a System of Equations
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Do whatever is necessary to both sides to isolate the variable.
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.
Just add or subtract the coefficients in front of the radicals.

15. If r#t=t(r)-r(t) - then what is 4#3?
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.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

16. Multiplying Monomials
Cross multiply.
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

17. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Switch the numerator and denominator.
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.
Two relatively prime numbers are integers that have no common factor other than 1.

18. What Does Solving In Terms of Mean?
Combine like terms.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

19. Finding the Area of a Triangle

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20. If x(2)=7x+18 - what is the positive value of 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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

21. Properties of Similar Triangles
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

22. Expressing the Union and Intersection of Sets
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
Adjacent angles are supplementary - Vertical angles are equal
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

23. Increasing and Decreasing a Number by a Certain Percentage
-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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
Subtract the smallest from the largest and add 1

24. Multiplying Expressions with Exponents that Have a Common Base
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

25. Solving an Inequality
-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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

26. Calculating the Probability that an Event will Take Place
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Put the equation into y=mx+b-- in which case b is the y-intercept.

27. Finding the Mode of a Set of Numbers
-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.
Do whatever is necessary to both sides to isolate the variable.
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

28. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
(pie)r(squared)
VofaC: (pie)r(2)h
Average the smallest and largest number
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

29. Properties of the Interior and Exterior Angles of a Triangle
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.
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.
2(pie)r

30. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
The value that appears the most often.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

31. Finding the Missing Number in a Series When You are Given the Average
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.
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Multiply the numerators and multiply the denominators.

32. 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.
-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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

33. Solving a Problem Involving Rates
The value that appears the most often.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.

34. What value of x is not in the domain of the function f(x)=x-2/x-3?
Use simple numbers like 1 and 2 and see what happens.
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 and cancel all factors the numerator and denominator have in common.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

35. General Procedure for Multiplying Polynomials
Slope=change in y/change in x
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Use the distributive property then combine the like terms.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

36. Definition of Remainder
The whole number left over after division.
Cancel factors common to the numerator and denominator.
Use simple numbers like 1 and 2 and see what happens.
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

37. An Important Property of a Line Tangent to a Circle
Put the equation into y=mx+b-- in which case b is the y-intercept.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The value that falls in the middle of the set.
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.

38. What is the Pythagorean Theorem?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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
Part=Percent x Whole
A(2)+b(2)=c(2)

39. Dividing Expressions with Exponents that Have a Common Base
Use simple numbers like 1 and 2 and see what happens.
The value that falls in the middle of the set.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

40. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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 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.

41. Finding the Volume of a Rectangular Solid
Get the absolute value equation by itself. Solve.
Switch the numerator and denominator.
VofaRS=lwh
Average: Sum of the Terms/Number of the Terms

42. Characteristics of a Parallelogram
Put the equation into y=mx+b-- in which case b is the y-intercept.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Sum: Average x Number of Terms
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

43. Setting Up a Ratio
Factor out and cancel all factors the numerator and denominator have in common.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Switch the numerator and denominator.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

44. Factoring the Difference of Two Squares
Part=Percent x Whole
Use the units to keep things straight - Snowfall inches/hours
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

45. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use simple numbers like 1 and 2 and see what happens.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

46. Converting From a Mixed Number to an Improper Fraction
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
Two relatively prime numbers are integers that have no common factor other than 1.
Use the distributive property then combine the like terms.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

47. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Average: Sum of the Terms/Number of the Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.

48. What is the Triangle Inequality Theorem?
Four equal acute angles and four equal obtuse angles.
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.
A(2)+b(2)=c(2)
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. Simplifying a Fraction to Lowest Terms
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Factor out and cancel all factors the numerator and denominator 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.
VofaC: (pie)r(2)h

50. Finding the Distance Between Two Points on a Coordinate Graph
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Average: Sum of the Terms/Number of the Terms
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.