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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. Adding and Subtracting Fractions
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Subtract the smallest from the largest and add 1
Multiply the exponents - (x^3)^4=x^3*4=x^12
Find a common denominator - then add or subtract the numerators.

2. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

3. Solving a Problem Involving Rates
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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 units to keep things straight - Snowfall inches/hours
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

4. Factoring the Difference of Two Squares
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 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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

5. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
Four equal acute angles and four equal obtuse angles.
Subtract the smallest from the largest and add 1
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

6. Solving a Radical Equation
Put each number in the original ratio over the sum of the numbers.
Isolate the radical expression and use the standard rules of algebra.
Find a common denominator - then add or subtract the numerators.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

7. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
-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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
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

8. If r#t=t(r)-r(t) - then what is 4#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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Put each number in the original ratio over the sum of the numbers.
Just add or subtract the coefficients in front of the radicals.

9. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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.
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.
Use simple numbers like 1 and 2 and see what happens.
Use the distributive property then combine the like terms.

10. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

11. Comparing the values of two or more Fractions
Express them with a common denominator.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
2(pie)r
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

12. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
-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.
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.

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

14. What Does Solving In Terms of Mean?
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.
Sum: Average x Number of 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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

15. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
Just add or subtract the coefficients in front of the radicals.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

16. Knowing if an Integer is a Multiple of 5 or 10
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
-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.

17. Finding the Volume of a Rectangular Solid
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Switch the numerator and denominator.
VofaRS=lwh
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

18. Multiplying and Dividing Roots
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.
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

19. If (Square Root: x-1)+5=12 - what is the value of x/2?
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.
(pie)r(squared)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

20. Finding the Sum of the Interior Angles of a Polygon
Use the distributive property then combine the like terms.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
FOIL: First - Outer - Inner - Last... Combine Like Terms

21. What are Two Special Pythagorean Triples?

22. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Slope=change in y/change in x
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

23. Prime Factorization of a Number
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

24. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
-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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.

25. Formula to Find Average
Get the absolute value equation by itself. Solve.
Average: Sum of the Terms/Number of the Terms
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

26. General Procedure for Multiplying Polynomials
-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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Use the distributive property then combine the like terms.

27. If 4(x(2)-10x+25) - then what is the value of x?
The whole number left over after division.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
(x1+x2)/2 -(y1+y2)/2
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.

28. Properties of a 30-60-90 Triangle
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.
Use simple numbers like 1 and 2 and see what happens.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

29. 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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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
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.

30. What is the Triangle Inequality Theorem?
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.
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 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 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

31. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

32. Calculating the Probability that an Event will Take Place
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
A(2)+b(2)=c(2)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Plug in the given values for the unknowns and calculate according to PEMDAS.

33. Definition of an Integer
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
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
-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. Adding and Subtracting Roots
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
Just add or subtract the coefficients in front of the radicals.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.

35. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

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

37. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
(x1+x2)/2 -(y1+y2)/2
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

38. 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?
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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
FOIL: First - Outer - Inner - Last... Combine Like Terms
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

39. Finding the Median of a Set of Numbers
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
The value that falls in the middle of the set.

40. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Get the absolute value equation by itself. Solve.

41. Formula Used to Find Percent
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
Part=Percent x Whole
Sum: Average x Number of Terms
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

42. Convert From a Fraction to a Decimal - Vice Versa
Find a common denominator - then add or subtract the numerators.
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.
Switch the numerator and denominator.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

43. An Important Property of a Line Tangent to a Circle
Adjacent angles are supplementary - Vertical angles are equal
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

44. Definition of an Irrational Number
(x1+x2)/2 -(y1+y2)/2
Express them with a common denominator.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

45. 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
Use the units to keep things straight - Snowfall inches/hours
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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

46. Characteristics of a Square
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

47. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

48. Multiplying Fractions
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Multiply the numerators and multiply the denominators.

49. Finding the Reciprocal of a Fraction
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Switch the numerator and denominator.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

50. Finding the Domain and Range of a Function
VofaRS=lwh
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.
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.
A(2)+b(2)=c(2)