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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 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.
Switch the numerator and denominator.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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. What is the Triangle Inequality Theorem?
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 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.
Factor out and cancel all factors the numerator and denominator have in common.
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

3. 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?
Just add or subtract the coefficients in front of the radicals.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
Find a common denominator - then add or subtract the numerators.

4. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Use the formula distance=rate*time and its variations to help in this question.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.

5. Calculating the Probability that an Event will Take Place
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The whole number left over after division.

6. Definition of a Rational Number
Average: Sum of the Terms/Number of the Terms
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
-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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

7. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like 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
Sum: Average x Number of Terms
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

8. If 4(x(2)-10x+25) - then what is the value of x?
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
VofaC: (pie)r(2)h
A(2)+b(2)=c(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.

9. If x(2)=7x+18 - what is the positive value of x?
A(2)+b(2)=c(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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

10. Simplifying Square Roots
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.
Use the formula distance=rate*time and its variations to help in this question.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

11. Finding the GCF of Two or More Numbers
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Average: Sum of the Terms/Number of the Terms
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

12. Expressing the Union and Intersection of Sets
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 base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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

13. Solving a Proportion
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Cross multiply.
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

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

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15. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

16. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Average the smallest and largest number
Do whatever is necessary to both sides to isolate the variable.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

17. Convert From a Fraction to a Decimal - Vice Versa
(x1+x2)/2 -(y1+y2)/2
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Combine like terms.
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.

18. Finding the Midpoint Between Two Points
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
(x1+x2)/2 -(y1+y2)/2
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.
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

19. Adding and Subtracting Roots
Use the distributive property then combine the like terms.
Isolate the radical expression and use the standard rules of algebra.
Just add or subtract the coefficients in front of the radicals.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

20. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
-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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Average: Sum of the Terms/Number of the Terms
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

21. What are Two Special Pythagorean Triples?

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22. Simplifying an Algebraic Equation
VofaRS=lwh
Find a common denominator - then add or subtract the numerators.
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.
Cancel factors common to the numerator and denominator.

23. What value of x is not in the domain of the function f(x)=x-2/x-3?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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
Do whatever is necessary to both sides to isolate the variable.

24. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
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.

25. Formula to Find Average
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
Average: Sum of the Terms/Number of the Terms
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

26. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
2(pie)r
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

27. Properties of a 45-45-90 Triangle
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.

28. Formula Used to Find Percent
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Express them with a common denominator.
Part=Percent x Whole

29. Adding and Subtracting Fractions
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Find a common denominator - then add or subtract the numerators.
Isolate the radical expression and use the standard rules of algebra.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

30. Dividing Fractions
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
FOIL: First - Outer - Inner - Last... Combine Like Terms

31. Factoring a Polynomial ('FOIL in Reverse')
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

32. Evaluating an Algebraic Expression
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

33. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Multiply the numerators and multiply the denominators.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

34. Number of Groups - +1 Each Time
-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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

35. Finding the Volume of a Rectangular Solid
VofaRS=lwh
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.
Four equal acute angles and four equal obtuse angles.
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.

36. 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.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.

37. If 3(3x)=9(x+2) - what is the value of x?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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

38. Finding the Reciprocal of a Fraction
Use the formula distance=rate*time and its variations to help in this question.
The value that appears the most often.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Switch the numerator and denominator.

39. Multiply and Divide Positive and Negative Numbers
Isolate the radical expression and use the standard rules of algebra.
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.
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

40. Prime Factorization of a Number
Get the absolute value equation by itself. Solve.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

41. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
Slope=change in y/change in x
Combine like terms.
Use the units to keep things straight - Snowfall inches/hours

42. Characteristics of a Parallelogram
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Find a common denominator - then add or subtract the numerators.
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.

43. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

44. Finding the Slope When Given an Equation of a Line
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
VofaRS=lwh

45. Finding a Term in a Geometric Sequence
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Find a common denominator - then add or subtract the numerators.

46. If r#t=t(r)-r(t) - then what is 4#3?
The whole number left over after division.
-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 a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

47. 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.
Two relatively prime numbers are integers that have no common factor other than 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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

48. Characteristics of a Rectangle
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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

49. Multiplying Monomials
The whole number left over after division.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.

50. Counting Consecutive Integers
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Switch the numerator and denominator.
Subtract the smallest from the largest and add 1