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SAT Math

Subjects : sat, math

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Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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1. If 2+l6-xl=10 and x>0 - what is the value of 2x?
-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.
Get the absolute value equation by itself. Solve.
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.

2. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

3. What is a Function and how do you Evaluate one?

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4. Number of Groups - +1 Each Time
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

5. Finding the Length of an Arc in a Circle

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6. Finding the Midpoint Between Two Points
FOIL: First - Outer - Inner - Last... Combine Like Terms
Multiply the numerators and multiply the denominators.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
(x1+x2)/2 -(y1+y2)/2

7. Solving a System of Equations
(pie)r(squared)
Use the formula distance=rate*time and its variations to help in this question.
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.
Find a common denominator - then add or subtract the numerators.

8. Characteristics of a Square
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

9. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-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.
Cross multiply.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

10. Properties of a 45-45-90 Triangle
-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.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Adjacent angles are supplementary - Vertical angles are equal

11. Finding the Missing Number in a Series When You are Given the Average
VofaC: (pie)r(2)h
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

12. General Procedure for Multiplying Polynomials
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Subtract the smallest from the largest and add 1
Factor out and cancel all factors the numerator and denominator have in common.
Use the distributive property then combine the like terms.

13. What is the Triangle Inequality Theorem?
Sum: Average x Number of Terms
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
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.

14. Multiply and Divide Positive and Negative Numbers
2(pie)r
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.
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

15. Determining Absolute Value of a Number
Express them with a common denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

16. Simplifying an Algebraic Equation
VofaC: (pie)r(2)h
Cancel factors common to the numerator and denominator.
-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 distributive property then combine the like terms.

17. Quickly Finding the Average of a Series of Evenly Spaced Numbers
(pie)r(squared)
Cross multiply.
Average the smallest and largest number
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

18. Calculating Negative Exponents and Radical Exponents
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.

19. Evaluating an Algebraic Expression
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

20. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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
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.
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.
Use simple numbers like 1 and 2 and see what happens.

21. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Multiply the exponents - (x^3)^4=x^3*4=x^12
Just add or subtract the coefficients in front of the radicals.

22. Calculating the Probability that an Event will Take Place
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Part=Percent x Whole
2(pie)r
Probability: Number of Favorable Outcomes/Total Possible Outcomes

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

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24. Factoring a Polynomial ('FOIL in Reverse')
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

25. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Use simple numbers like 1 and 2 and see what happens.
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

26. Adding a Positive Number to a Negative Number
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
VofaRS=lwh
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

27. What types of angles are formed when two lines intersect?
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
Adjacent angles are supplementary - Vertical angles are equal

28. Finding the Rate of Speed
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.
Get the absolute value equation by itself. Solve.
Four equal acute angles and four equal obtuse angles.
Use the formula distance=rate*time and its variations to help in this question.

29. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Do whatever is necessary to both sides to isolate the variable.
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.

30. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Isolate the radical expression and use the standard rules of algebra.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

31. Counting the Total Number of Possibilities for Several Events to Occur
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.
Combine like terms.
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
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

32. Adding and Subtracting Polynomials
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Combine like terms.

33. If 4(x(2)-10x+25) - then what is the value of x?
VofaC: (pie)r(2)h
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
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.

34. Multiplying Monomials
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.
Use the units to keep things straight - Snowfall inches/hours
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^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

35. Finding the Distance Between Two Points on a Coordinate Graph
A(2)+b(2)=c(2)
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

36. What is the Pythagorean Theorem?
VofaRS=lwh
A(2)+b(2)=c(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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

37. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
-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 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

38. Finding the Slope When Given an Equation of a Line
Do whatever is necessary to both sides to isolate the variable.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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

39. Raising a Power to a Power
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Multiply the exponents - (x^3)^4=x^3*4=x^12
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

40. Scalene - Isosceles - and Equilateral Triangles
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

41. If r#t=t(r)-r(t) - then what is 4#3?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Cancel factors common to the numerator and denominator.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

42. Adding and Subtracting Monomials
The value that appears the most often.
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

43. What Does Solving In Terms of Mean?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Multiply the numerators and multiply the denominators.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

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

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45. Prime Factorization of a Number
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

46. Finding the Mode of a Set of Numbers
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.
-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.
Switch the numerator and denominator.
The value that appears the most often.

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?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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
(x1+x2)/2 -(y1+y2)/2
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

48. How do you know if an integer is a multiple of 3 or 9?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
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.

49. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
-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.
Switch the numerator and denominator.
Use the formula distance=rate*time and its variations to help in this question.
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

50. Definition of Remainder
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Adjacent angles are supplementary - Vertical angles are equal
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.
The whole number left over after division.

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