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SAT Math

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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. 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.
Slope=change in y/change in x
VofaRS=lwh
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

2. What is the Pythagorean Theorem?
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
A(2)+b(2)=c(2)

3. Finding the Area of a Circle
Find a common denominator - then add or subtract the numerators.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
(pie)r(squared)

4. 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
Use the formula distance=rate*time and its variations to help in this question.
2(pie)r
-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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

5. Dividing Fractions
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

6. Adding a Positive Number to a Negative Number
Subtract the smallest from the largest and add 1
-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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.

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

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8. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Use simple numbers like 1 and 2 and see what happens.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

9. Multiplying and Dividing Roots
Put each number in the original ratio over the sum of the numbers.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
-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.
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.

10. Characteristics of a Rectangle
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.
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 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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

11. Convert From a Fraction to a Decimal - Vice Versa
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
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.
The value that falls in the middle of the set.
Put the equation into y=mx+b-- in which case b is the y-intercept.

12. Scalene - Isosceles - and Equilateral Triangles
(x1+x2)/2 -(y1+y2)/2
Sum: Average x Number of Terms
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.
Average the smallest and largest number

13. If 2+l6-xl=10 and x>0 - what is the value of 2x?
-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.
Get the absolute value equation by itself. Solve.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

14. 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.
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

15. Adding and Subtracting Roots
Two relatively prime numbers are integers that have no common factor other than 1.
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 base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Just add or subtract the coefficients in front of the radicals.

16. Calculating Negative Exponents and Radical Exponents
-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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

17. 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?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

18. Solving a Problem Involving Rates
Adjacent angles are supplementary - Vertical angles are equal
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
Switch the numerator and denominator.

19. Finding the Median of a Set of Numbers
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
The value that falls in the middle of the set.

20. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Four equal acute angles and four equal obtuse angles.
Cross multiply.

21. Finding the Area of a Sector

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22. What is the Triangle Inequality Theorem?
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.
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
Combine like terms.
-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.

23. Solving a Radical Equation
Just add or subtract the coefficients in front of the radicals.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Isolate the radical expression and use the standard rules of algebra.

24. Properties of a 45-45-90 Triangle
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Sum: Average x Number of Terms

25. Finding the GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Factor out and cancel all factors the numerator and denominator have in common.

26. Finding the Rate of Speed
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.
Factor out and cancel all factors the numerator and denominator have in common.
Use the formula distance=rate*time and its variations to help in this question.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

27. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

28. How do you know if an integer is a multiple of 3 or 9?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
(x1+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

29. If 4(x(2)-10x+25) - then what is the value of x?
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.
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.
Subtract the smallest from the largest and add 1
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. Simplifying an Algebraic Equation
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Cancel factors common to the numerator and denominator.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Get the absolute value equation by itself. Solve.

31. 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?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Part=Percent x Whole
(x1+x2)/2 -(y1+y2)/2

32. Properties of the Interior and Exterior Angles of a Triangle
(pie)r(squared)
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 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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

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

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34. Determining Absolute Value of a Number
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Switch the numerator and denominator.

35. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
The value that falls in the middle of the set.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

36. PEMDAS
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.
Put each number in the original ratio over the sum of the numbers.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
FOIL: First - Outer - Inner - Last... Combine Like Terms

37. Multiply and Divide Positive and Negative Numbers
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

38. Characteristics of a Square
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
2(pie)r
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

39. Finding a Term in a Geometric Sequence
Combine like terms.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

40. If (Square Root: x-1)+5=12 - what is the value of x/2?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

41. 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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

42. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
2(pie)r
Part=Percent x Whole
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

43. Finding the Volume of a Rectangular Solid
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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
VofaRS=lwh
Use the formula distance=rate*time and its variations to help in this question.

44. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.

45. Converting from an Improper Fraction to a Mixed Number
The whole number left over after division.
Find a common denominator - then add or subtract the numerators.
Factor out and cancel all factors the numerator and denominator have in common.
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.

46. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

47. Multiplying Monomials
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^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 the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

48. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
Use the distributive property then combine the like terms.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

49. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

50. What types of angles are formed when two lines intersect?
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Adjacent angles are supplementary - Vertical angles are equal
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

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