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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. Prime Factorization of a Number
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Express them with a common denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

2. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
-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.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

3. Properties of the Interior and Exterior Angles of a Triangle
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Use the units to keep things straight - Snowfall inches/hours

4. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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

5. PEMDAS
Switch the numerator and denominator.
The value that appears the most often.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

6. Simplifying an Algebraic Equation
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
Cancel factors common to the numerator and denominator.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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

7. Finding the Median of a Set of Numbers
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
The value that falls in the middle of the set.
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.
-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.

8. Finding the Volume of a Cylinder
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The value that falls in the middle of the set.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
VofaC: (pie)r(2)h

9. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
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
Express them with a common denominator.
Put the equation into y=mx+b-- in which case b is the y-intercept.

10. Properties of a 30-60-90 Triangle
Plug in the given values for the unknowns and calculate according to PEMDAS.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Do whatever is necessary to both sides to isolate the variable.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

11. 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.
Two relatively prime numbers are integers that have no common factor other than 1.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

12. 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?
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
Multiply the exponents - (x^3)^4=x^3*4=x^12
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

13. Characteristics of a Square
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Use simple numbers like 1 and 2 and see what happens.
The whole number left over after division.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

14. Evaluating an Algebraic Expression
Switch the numerator and 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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.

15. Dividing Expressions with Exponents that Have a Common Base
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Two relatively prime numbers are integers that have no common factor other than 1.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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

16. Formula Used to Find Percent
Do whatever is necessary to both sides to isolate the variable.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Part=Percent x Whole
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

17. Converting From a Mixed Number to an Improper Fraction
Subtract the smallest from the largest and add 1
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the exponents - (x^3)^4=x^3*4=x^12

18. Numbers that are Relatively Prime
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Two relatively prime numbers are integers that have no common factor other than 1.
2(pie)r

19. An Important Property of a Line Tangent to a Circle
Sum: Average x Number of Terms
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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

20. Solving a Problem Involving Rates
A(2)+b(2)=c(2)
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.
Use the units to keep things straight - Snowfall inches/hours
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

21. What types of angles are formed when a transversal cross parallel lines?
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Four equal acute angles and four equal obtuse angles.

22. Dividing Fractions
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Four equal acute angles and four equal obtuse angles.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

23. General Procedure for Multiplying Polynomials
Multiply the exponents - (x^3)^4=x^3*4=x^12
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 distributive property then combine the like terms.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

24. Determining Absolute Value of a Number
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Plug in the given values for the unknowns and calculate according to PEMDAS.

25. 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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

26. 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.
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.
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

27. Multiplying Expressions with Exponents that Have a Common Base
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
-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.
Put each number in the original ratio over the sum of the numbers.

28. Multiplying Fractions
Multiply the numerators and multiply the denominators.
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.
Two relatively prime numbers are integers that have no common factor other than 1.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

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

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30. Properties of a 45-45-90 Triangle
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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

31. If the average of a - b - and 48 is 48 - what is the value of a + b?
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

32. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
-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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

33. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Part=Percent x Whole
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

34. Finding the Slope When Given an Equation of a Line
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
VofaRS=lwh
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

35. 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.
-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.
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.
Use the distributive property then combine the like terms.

36. Solving a Linear Equation
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Do whatever is necessary to both sides to isolate the variable.
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.

37. Properties of Similar Triangles
Cancel factors common to the numerator and denominator.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.

38. Definition of an Irrational Number
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

39. Finding the Surface Area of a Rectangular Solid
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)
Get the absolute value equation by itself. Solve.
Do whatever is necessary to both sides to isolate the variable.

40. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Cancel factors common to the numerator and denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

41. Calculating Negative Exponents and Radical Exponents
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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
2(pie)r
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

42. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Express them with a common denominator.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

43. Multiplying Binomials
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
FOIL: First - Outer - Inner - Last... Combine Like Terms

44. Scalene - Isosceles - and Equilateral Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Do whatever is necessary to both sides to isolate the variable.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.

45. 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.
VofaRS=lwh
(x1+x2)/2 -(y1+y2)/2
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

46. Adding and Subtracting Polynomials
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Combine like terms.
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 a Term in a Geometric Sequence
The whole number left over after division.
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.
VofaC: (pie)r(2)h
The value that appears the most often.

48. Finding the Missing Number in a Series When You are Given the Average
Plug in the given values for the unknowns and calculate according to PEMDAS.
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

49. Finding the Volume of a Rectangular Solid
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Cancel factors common to 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
VofaRS=lwh

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

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