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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. Multiplying Fractions
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Multiply the numerators and multiply the denominators.

2. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
2(pie)r

3. Finding the Mode of a Set of Numbers
The value that appears the most often.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Cancel factors common to the numerator and denominator.

4. If the average of a - b - and 48 is 48 - what is the value of a + b?
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 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.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

5. Evaluating an Algebraic Expression
Use simple numbers like 1 and 2 and see what happens.
Isolate the radical expression and use the standard rules of algebra.
Average the smallest and largest number
Plug in the given values for the unknowns and calculate according to PEMDAS.

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

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7. What are Two Special Pythagorean Triples?

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8. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
Sum: Average x Number of Terms
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

9. Quickly Finding the Average of a Series of Evenly Spaced Numbers
FOIL: First - Outer - Inner - Last... Combine Like Terms
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Average the smallest and largest number

10. Adding and Subtracting Fractions
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 formula distance=rate*time and its variations to help in this question.
Find a common denominator - then add or subtract the numerators.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

11. Determining Absolute Value of a Number
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.

12. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
(pie)r(squared)
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

13. If r#t=t(r)-r(t) - then what is 4#3?
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.
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.
Part=Percent x Whole
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

14. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

15. Properties of the Interior and Exterior Angles of a Triangle
Just add or subtract the coefficients in front of the radicals.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
VofaC: (pie)r(2)h

16. If 4(x(2)-10x+25) - then what is the value of x?
Cancel factors common to the numerator and denominator.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

17. An Important Property of a Line Tangent to a Circle
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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 whole number left over after division.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

18. Finding the Missing Number in a Series When You are Given the Average
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

19. Definition of a Rational Number
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
-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.
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

20. Factoring the Difference of Two Squares
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.
The value that appears the most often.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

21. Convert From a Fraction to a Decimal - Vice Versa
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime 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.
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.

22. Finding the Volume of a Rectangular Solid
VofaRS=lwh
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 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
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

23. Counting the Total Number of Possibilities for Several Events to Occur
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

24. Converting from an Improper Fraction to a Mixed Number
Use the formula distance=rate*time and its variations to help in this question.
Sum: Average x Number of Terms
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.
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.

25. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
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.

26. Adding and Subtracting Polynomials
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Combine like terms.
Average the smallest and largest number
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

27. Raising a Power to a Power
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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 exponents - (x^3)^4=x^3*4=x^12

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?
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)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. Finding the Reciprocal of a Fraction
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Use the units to keep things straight - Snowfall inches/hours
Switch the numerator and denominator.
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

30. Finding the Median of a Set of Numbers
Switch the numerator and denominator.
Factor out and cancel all factors the numerator and denominator have in common.
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.
The value that falls in the middle of the set.

31. Simplifying an Algebraic Equation
Isolate the radical expression and use the standard rules of algebra.
Cancel factors common to the numerator and denominator.
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.
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.

32. Definition of an Integer
Slope=change in y/change in x
Use the formula distance=rate*time and its variations to help in this question.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

33. Multiplying Binomials
Sum: Average x Number of Terms
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.
Factor out and cancel all factors the numerator and denominator have in common.
FOIL: First - Outer - Inner - Last... Combine Like Terms

34. Average Rate and How Do You Find It
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.
Part=Percent x Whole
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Adjacent angles are supplementary - Vertical angles are equal

35. Finding the LCM of Two or More Numbers

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36. Finding the Area of a Circle
(pie)r(squared)
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
A(2)+b(2)=c(2)
Express them with a common denominator.

37. Finding the Rate of Speed
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use the formula distance=rate*time and its variations to help in this question.
Plug in the given values for the unknowns and calculate according to PEMDAS.

38. Solving a Problem Involving Rates
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
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use the units to keep things straight - Snowfall inches/hours

39. Formula Used to Find Percent
The value that appears the most often.
Part=Percent x Whole
Average the smallest and largest number
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.

40. Setting Up a Ratio
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 the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Cross multiply.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

41. What types of angles are formed when two lines intersect?
Combine like terms.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Adjacent angles are supplementary - Vertical angles are equal
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

42. 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.
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.
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.
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.

43. Counting Consecutive Integers
Do whatever is necessary to both sides to isolate the variable.
-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.
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
Subtract the smallest from the largest and add 1

44. Finding the Domain and Range of a Function
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.
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.
-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.
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.

45. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
A(2)+b(2)=c(2)
Two relatively prime numbers are integers that have no common factor other than 1.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

46. If (Square Root: x-1)+5=12 - what is the value of x/2?
Subtract the smallest from the largest and add 1
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

47. Characteristics of a Parallelogram
-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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
-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.
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.

48. Calculating Negative Exponents and Radical Exponents
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Subtract the smallest from the largest and add 1
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
VofaRS=lwh

49. Finding the Sum of the Average of a Series of Numbers
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Sum: Average x Number of Terms

50. Finding the Volume of a Cylinder
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.
Switch the numerator and denominator.
VofaC: (pie)r(2)h
Use simple numbers like 1 and 2 and see what happens.