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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. Converting From a Mixed Number to an Improper Fraction
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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
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 whole number part by the denominator - then add the numerator. Keep the same denominator.

2. If (Square Root: x-1)+5=12 - what is the value of x/2?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

3. Adding and Subtracting Roots
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Just add or subtract the coefficients in front of the radicals.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Average: Sum of the Terms/Number of the Terms

4. Solving a Proportion
2(pie)r
Cross multiply.
Average the smallest and largest number
Multiply the numerators and multiply the denominators.

5. Properties of a 30-60-90 Triangle
Sum: Average x Number of Terms
A(2)+b(2)=c(2)
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

6. Finding the Sum of the Interior Angles of a Polygon
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Plug in the given values for the unknowns and calculate according to PEMDAS.

7. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The value that falls in the middle of the set.

8. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Average: Sum of the Terms/Number of the Terms
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

9. 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?
Four equal acute angles and four equal obtuse angles.
Plug in the given values for the unknowns and calculate according to PEMDAS.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
A(2)+b(2)=c(2)

10. Finding the Area of a Triangle

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11. Finding the Distance Between Two Points on a Coordinate Graph
Plug in the given values for the unknowns and calculate according to PEMDAS.
VofaRS=lwh
Sum: Average x Number of Terms
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

12. An Important Property of a Line Tangent to a Circle
(x1+x2)/2 -(y1+y2)/2
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.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

13. Solving a Linear Equation
Subtract the smallest from the largest and add 1
Do whatever is necessary to both sides to isolate the variable.
Two relatively prime numbers are integers that have no common factor other than 1.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

14. If r#t=t(r)-r(t) - then what is 4#3?
Plug in the given values for the unknowns and calculate according to PEMDAS.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Express them with a common denominator.

15. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
Use simple numbers like 1 and 2 and see what happens.

16. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Plug in the given values for the unknowns and calculate according to PEMDAS.

17. Definition of Remainder
The whole number left over after division.
Average the smallest and largest number
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

18. 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.
Sum: Average x Number of Terms
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.
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.

19. Adding and Subtracting 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.
Combine like terms.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Sum: Average x Number of Terms

20. Evaluating an Algebraic Expression
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

21. Multiplying Monomials
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Average: Sum of the Terms/Number of the Terms
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

22. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Get the absolute value equation by itself. Solve.
Average the smallest and largest number
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

23. Definition of a Rational Number
The whole number left over after division.
Slope=change in y/change in x
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

24. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Get the absolute value equation by itself. Solve.
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 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.
-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.

25. 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?
Get the absolute value equation by itself. Solve.
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.

26. Finding the Missing Number in a Series When You are Given the Average
(x1+x2)/2 -(y1+y2)/2
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
Get the absolute value equation by itself. Solve.

27. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
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

28. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Express them with a common denominator.
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.
Combine like terms.

29. 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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to 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.
Slope=change in y/change in x

30. Knowing if an Integer is a Multiple of 2 or 4
Sum: Average x Number of 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.
Combine like terms.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

31. What types of angles are formed when a transversal cross parallel lines?
Switch the numerator and denominator.
A(2)+b(2)=c(2)
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.
Four equal acute angles and four equal obtuse angles.

32. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Combine like terms.

33. What types of angles are formed when two lines intersect?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Adjacent angles are supplementary - Vertical angles are equal
Use the formula distance=rate*time and its variations to help in this question.

34. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the distributive property then combine the like terms.
Adjacent angles are supplementary - Vertical angles are equal
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.

35. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
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.
Put each number in the original ratio over the sum of the numbers.
Use simple numbers like 1 and 2 and see what happens.

36. Multiplying Expressions with Exponents that Have a Common Base
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

37. Converting from part-to-part ratios to part-to-whole ratios
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.
Put each number in the original ratio over the sum of the numbers.
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.
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

38. Multiplying Fractions
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Multiply the numerators and multiply the denominators.
Four equal acute angles and four equal obtuse angles.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

39. Finding the LCM of Two or More Numbers

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40. Properties of a 45-45-90 Triangle
Adjacent angles are supplementary - Vertical angles are equal
Use the units to keep things straight - Snowfall inches/hours
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

41. How do you know if an integer is a multiple of 3 or 9?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
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.

42. Number of Groups - +1 Each Time
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

43. Dividing Expressions with Exponents that Have a Common Base
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

44. If the average of a - b - and 48 is 48 - what is the value of a + b?
Multiply the numerators and multiply the denominators.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
A(2)+b(2)=c(2)

45. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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
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%.
Factor out and cancel all factors the numerator and denominator have in common.

46. If 3(3x)=9(x+2) - what is the value of x?
Cancel factors common to the numerator and denominator.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.

47. Finding the Volume of a Rectangular Solid
VofaRS=lwh
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.
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.
Cross multiply.

48. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

49. Simplifying a Fraction to Lowest Terms
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
VofaRS=lwh
Factor out and cancel all factors the numerator and denominator have in common.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

50. Solving a Problem Involving Rates
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Switch the numerator and denominator.
Use the units to keep things straight - Snowfall inches/hours
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.