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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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Sum: Average x Number of Terms
Multiply the numerators and multiply the denominators.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

2. Properties of the Interior and Exterior Angles of a Triangle
Average: Sum of the Terms/Number of the Terms
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.

3. Sale Price of a Jacket Marked Down 30% Each Week for 3 Weeks - What % of the Original Price is the Cost of the Jacket After the 3 Week Sale Period
Factor out and cancel all factors the numerator and denominator have in common.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.

4. What are Two Special Pythagorean Triples?

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5. Finding the Area of a Sector

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

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7. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Combine like terms.
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 equal acute angles and four equal obtuse angles.
Multiply the numerators and multiply the denominators.

8. How do you know if an integer is a multiple of 3 or 9?
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
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.

9. 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
Sum: Average x Number of Terms
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.

10. 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
Use simple numbers like 1 and 2 and see what happens.
Use the formula distance=rate*time and its variations to help in this question.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

11. If 3(3x)=9(x+2) - what is the value of x?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Plug in the given values for the unknowns and calculate according to PEMDAS.

12. Characteristics of a Square
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
-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.

13. 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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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 solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

14. Finding the Midpoint Between Two Points
FOIL: First - Outer - Inner - Last... Combine Like Terms
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
(x1+x2)/2 -(y1+y2)/2

15. General Procedure for Multiplying Polynomials
Sum: Average x Number of Terms
Use the distributive property then combine the like terms.
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
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.

16. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
2(pie)r
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

17. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Average the smallest and largest number

18. Formula Used to Find Percent
(pie)r(squared)
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use the distributive property then combine the like terms.
Part=Percent x Whole

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

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20. Finding the Sum of the Interior Angles of a Polygon
Four equal acute angles and four equal obtuse angles.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.

21. 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
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
FOIL: First - Outer - Inner - Last... Combine Like Terms

22. Finding the Mode of a Set of Numbers
The value that appears the most often.
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 the whole number part by the denominator - then add the numerator. Keep the same denominator.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

23. Finding a Term in a Geometric Sequence
A(2)+b(2)=c(2)
Average the smallest and largest number
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.
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

24. Factoring the Difference of Two Squares
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
(pie)r(squared)
VofaC: (pie)r(2)h
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

25. Finding the y-intercept When Given an Equation of a Line
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

26. Adding and Subtracting Polynomials
Combine like terms.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

27. Formula to Find Average
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.
Put each number in the original ratio over the sum of the numbers.
Average: Sum of the Terms/Number of the Terms
(x1+x2)/2 -(y1+y2)/2

28. Finding the Volume of a Rectangular Solid
Find a common denominator - then add or subtract the numerators.
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.
VofaRS=lwh
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

29. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Two relatively prime numbers are integers that have no common factor other than 1.
Cross multiply.

30. Let N represent the smallest positive integer that is a multiple of 6 and 8 - but leaves a remainder of 2 when divided by 7. What is the value of N?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Isolate the radical expression and use the standard rules of algebra.
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.

31. What value of x is not in the domain of the function f(x)=x-2/x-3?
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.
Average the smallest and largest number
(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

32. Properties of a 45-45-90 Triangle
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
Find a common denominator - then add or subtract the numerators.

33. Scalene - Isosceles - and Equilateral Triangles
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.
Express them with a common denominator.
2(pie)r
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.

34. Multiplying 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.
Use simple numbers like 1 and 2 and see what happens.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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

35. Finding the Slope When Given an Equation of a Line
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

36. An Important Property of a Line Tangent to a Circle
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.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.

37. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

38. If 2+l6-xl=10 and x>0 - what is the value of 2x?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Get the absolute value equation by itself. Solve.
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

39. If the average of a - b - and 48 is 48 - what is the value of a + b?
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

40. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
VofaC: (pie)r(2)h
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

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.
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 the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Subtract the smallest from the largest and add 1

42. Multiplying Fractions
VofaRS=lwh
Multiply the numerators and multiply the denominators.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

43. What types of angles are formed when a transversal cross parallel lines?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
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.
Four equal acute angles and four equal obtuse angles.

44. Expressing the Union and Intersection of Sets
Part=Percent x Whole
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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
Put the equation into y=mx+b-- in which case b is the y-intercept.

45. If x(2)=7x+18 - what is the positive value of x?
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
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

46. Number of Groups - +1 Each Time
Isolate the radical expression and use the standard rules of algebra.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Probability: Number of Favorable Outcomes/Total Possible Outcomes

47. Factoring a Polynomial ('FOIL in Reverse')
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.
Cancel factors common to the numerator and denominator.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

48. Multiplying and Dividing 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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
FOIL: First - Outer - Inner - Last... Combine Like Terms

49. 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%.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

50. Finding the Surface Area of a Rectangular Solid
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)
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

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