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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. Definition of an Irrational Number
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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 smallest from the largest and add 1

2. Finding the Circumference of a Circle
2(pie)r
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Just add or subtract the coefficients in front of the radicals.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

3. Setting Up a Ratio
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 pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
VofaRS=lwh
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

4. Finding a Term in a Geometric Sequence
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
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.
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

5. Identifying Which Number of a Fraction is the Part and Which Number is the Whole
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.

6. Direct Variation and Inverse Variation
Adjacent angles are supplementary - Vertical angles are equal
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
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.

7. Dividing Expressions with Exponents that Have a Common Base
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The whole number left over after division.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply the numerators and multiply the denominators.

8. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
-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.

9. Convert From a Fraction to a Decimal - Vice Versa
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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
Use simple numbers like 1 and 2 and see what happens.

10. Formula Used to Find Percent
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.
Part=Percent x Whole
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

11. Finding the Midpoint Between Two Points
Get the absolute value equation by itself. Solve.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
(x1+x2)/2 -(y1+y2)/2
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

12. Finding the Area of a Triangle
Slope=change in y/change in x
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 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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

13. Comparing the values of two or more Fractions
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Express them with a common denominator.

14. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
The whole number left over after division.

15. If x(2)=7x+18 - what is the positive value of x?
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.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the 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.

16. Finding the Sum of the Average of a Series of Numbers
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Sum: Average x Number of Terms
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Use the units to keep things straight - Snowfall inches/hours

17. 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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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

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

19. Solving a System of Equations
FOIL: First - Outer - Inner - Last... Combine Like Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

20. Knowing if an Integer is a Multiple of 5 or 10
Use simple numbers like 1 and 2 and see what happens.
-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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.

21. Number of Groups - +1 Each Time
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
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 Reciprocal of a Fraction
Two relatively prime numbers are integers that have no common factor other than 1.
Do whatever is necessary to both sides to isolate the variable.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Switch the numerator and denominator.

23. 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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Subtract the smallest from the largest and add 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.

24. Dividing Fractions
-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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

25. Multiplying and Dividing Roots
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
Subtract the smallest from the largest and add 1
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.

26. Increasing and Decreasing a Number by a Certain Percentage
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Just add or subtract the coefficients in front of the radicals.
-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.

27. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Combine like 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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

28. Finding the Sum of the Interior Angles of a Polygon
-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.
Just add or subtract the coefficients in front of the radicals.
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

29. Finding the GCF of Two or More Numbers
VofaC: (pie)r(2)h
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.
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

30. Finding the y-intercept When Given an Equation of a Line
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 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.

31. Multiplying Monomials
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 the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.

32. Calculating the Probability that an Event will Take Place
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
(x1+x2)/2 -(y1+y2)/2

33. Adding and Subtracting Polynomials
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
Combine like 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.
Do whatever is necessary to both sides to isolate the variable.

34. 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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

35. Knowing if an Integer is a Multiple of 2 or 4
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
A(2)+b(2)=c(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.

36. Characteristics of a Parallelogram
FOIL: First - Outer - Inner - Last... Combine Like Terms
Multiply the exponents - (x^3)^4=x^3*4=x^12
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

37. Finding the Mode of a Set of Numbers
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
Subtract the smallest from the largest and add 1
The value that appears the most often.
-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.

38. Calculating Negative Exponents and Radical Exponents
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
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The value that appears the most often.

39. Finding the Median of a Set of Numbers
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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
The value that falls in the middle of the set.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

40. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
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.
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.
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.

41. General Procedure for Multiplying Polynomials
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

42. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
-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.
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
Slope=change in y/change in x

43. How do you know if an integer is a multiple of 3 or 9?
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.
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.
2(pie)r
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

44. Adding and Subtracting Monomials
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Average the smallest and largest number

45. Finding the Area of a Sector
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

46. Converting From a Mixed Number to an Improper Fraction
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
FOIL: First - Outer - Inner - Last... Combine Like Terms

47. What is the positive difference between the answers to the equation 35+x(2)=12x?
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

48. Expressing the Union and Intersection of Sets
Use simple numbers like 1 and 2 and see what happens.
Average: Sum of the Terms/Number of the Terms
Four equal acute angles and four equal obtuse angles.
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

49. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Use simple numbers like 1 and 2 and see what happens.

50. Factoring the Difference of Two Squares
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 the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

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