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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. 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.
A(2)+b(2)=c(2)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

2. Knowing if an Integer is a Multiple of 2 or 4
-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.
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 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

3. Difference Between a Factor and a Multiple
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
-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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

4. Simplifying a Fraction to Lowest Terms
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Sum: Average x Number of Terms

5. Finding the Area of a Triangle

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6. Characteristics of a Rectangle
Adjacent angles are supplementary - Vertical angles are equal
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

7. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
-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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

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.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

9. Finding the Missing Number in a Series When You are Given the Average
Use the units to keep things straight - Snowfall inches/hours
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
(x1+x2)/2 -(y1+y2)/2
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.

10. Definition of Remainder
Combine like terms.
A(2)+b(2)=c(2)
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
The whole number left over after division.

11. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
FOIL: First - Outer - Inner - Last... Combine Like Terms
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

12. Dividing Expressions with Exponents that Have a Common Base
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
-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.
Adjacent angles are supplementary - Vertical angles are equal

13. Converting From a Mixed Number to an Improper Fraction
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Average the smallest and largest number

14. Finding the Area of a Circle
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
A(2)+b(2)=c(2)
VofaC: (pie)r(2)h
(pie)r(squared)

15. 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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.

16. Multiply and Divide Positive and Negative Numbers
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
The whole number left over after division.
Use the units to keep things straight - Snowfall inches/hours
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

17. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
-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.
VofaRS=lwh
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.
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.

18. Simplifying an Algebraic Equation
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
FOIL: First - Outer - Inner - Last... Combine Like Terms
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Cancel factors common to the numerator and denominator.

19. Number of Groups - +1 Each Time
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
-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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

20. Finding the Sum of the Interior Angles of a Polygon
Do whatever is necessary to both sides to isolate the variable.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.

21. How do you know if an integer is a multiple of 3 or 9?
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.
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
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.

22. Numbers that are Relatively Prime
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Two relatively prime numbers are integers that have no common factor other than 1.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

23. If x(2)=7x+18 - what is the positive value of x?
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

24. Converting from an Improper Fraction to a Mixed Number
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.
VofaC: (pie)r(2)h
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.

25. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Find a common denominator - then add or subtract the numerators.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

26. Finding the Mode of a Set of Numbers
Plug in the given values for the unknowns and calculate according to PEMDAS.
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 value that appears the most often.
Put the equation into y=mx+b-- in which case b is the y-intercept.

27. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

28. Finding the Slope of a Line When Given Two Points on the Line
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
Slope=change in y/change in x
Factor out and cancel all factors the numerator and denominator have in common.
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.

29. If 2+l6-xl=10 and x>0 - what is the value of 2x?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Direct Variation- y=kx - where k is constant. As x gets larger - y gets larger. If the number of units of B were to double - the number of units of A would double - Inverse Variation- xy=k - where k is a constant. As x gets larger - y gets smaller. A
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Get the absolute value equation by itself. Solve.

30. Setting Up a Ratio
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.
Do whatever is necessary to both sides to isolate the variable.
Express them with a common denominator.

31. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Get the absolute value equation by itself. Solve.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.

32. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

33. Evaluating an Algebraic Expression
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

34. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
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.
Do whatever is necessary to both sides to isolate the variable.
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.

35. 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
(x1+x2)/2 -(y1+y2)/2
Average: Sum of the Terms/Number of the Terms
Average the smallest and largest number

36. If 4(x(2)-10x+25) - then what is the value of x?
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

37. Expressing the Union and Intersection of Sets
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 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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

38. Definition of an Irrational Number
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.

39. Finding the Length of an Arc in a Circle

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40. Finding a Term in a Geometric Sequence
VofaRS=lwh
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

41. Properties of a 30-60-90 Triangle
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

42. Finding the Sum of the Average of a Series of Numbers
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
VofaC: (pie)r(2)h
Sum: Average x Number of Terms

43. Converting from part-to-part ratios to part-to-whole ratios
(x1+x2)/2 -(y1+y2)/2
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
Put each number in the original ratio over the sum of the numbers.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

44. Characteristics of a Square
Isolate the radical expression and use the standard rules of algebra.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

45. Counting the Total Number of Possibilities for Several Events to Occur
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the formula distance=rate*time and its variations to help in this question.
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.
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

46. Formula to Find Average
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.
Average: Sum of the Terms/Number of the Terms
Use the formula distance=rate*time and its variations to help in this question.

47. Finding the LCM of Two or More Numbers

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48. Solving a Linear Equation
Combine like terms.
Do whatever is necessary to both sides to isolate the variable.
Subtract the smallest from the largest and add 1
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

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

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50. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
(pie)r(squared)
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.