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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 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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Put each number in the original ratio over the sum of the numbers.

2. Evaluating an Algebraic Expression
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Get the absolute value equation by itself. Solve.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

3. Properties of a 45-45-90 Triangle
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
VofaC: (pie)r(2)h
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

4. What is a Function and how do you Evaluate one?
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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

5. Finding the LCM of Two or More Numbers
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Plug in the given values for the unknowns and calculate according to PEMDAS.
The value that appears the most often.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

6. Properties of a 30-60-90 Triangle
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Switch the numerator and denominator.

7. Definition of an Irrational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Use the formula distance=rate*time and its variations to help in this question.
The value that falls in the middle of the set.
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.

8. Multiplying and Dividing Roots
Four equal acute angles and four equal obtuse angles.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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 value that appears the most often.

9. 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.
Use the distributive property then combine the like terms.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

10. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
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.
-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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

11. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Plug in the given values for the unknowns and calculate according to PEMDAS.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

12. Average Rate and How Do You Find It
Do whatever is necessary to both sides to isolate the variable.
The value that appears the most often.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Just add or subtract the coefficients in front of the radicals.

13. Solving an Inequality
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Sum: Average x Number of Terms
Use the distributive property then combine the like terms.

14. Simplifying an Algebraic Equation
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Switch the numerator and denominator.
Cancel factors common to the numerator and denominator.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

15. Expressing the Union and Intersection of Sets
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
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 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.
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. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

17. Adding and Subtracting Roots
Use the distributive property then combine the like terms.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
-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.
Just add or subtract the coefficients in front of the radicals.

18. Solving a Linear Equation
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Do whatever is necessary to both sides to isolate the variable.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Subtract the smallest from the largest and add 1

19. Finding the Volume of a Rectangular Solid
VofaRS=lwh
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Slope=change in y/change in x
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.

20. Simplifying Square Roots
FOIL: First - Outer - Inner - Last... Combine Like Terms
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.

21. Solving a System of Equations
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.
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
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 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.

22. Definition of Remainder
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Factor out and cancel all factors the numerator and denominator have in common.
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 whole number left over after division.

23. Finding the Volume of a Cylinder
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
VofaC: (pie)r(2)h
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.

24. Finding the GCF of Two or More Numbers
Put each number in the original ratio over the sum of the numbers.
(x1+x2)/2 -(y1+y2)/2
Find a common denominator - then add or subtract the numerators.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

25. Finding the Length of an Arc in a Circle
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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
Just add or subtract the coefficients in front of the radicals.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

26. Dividing Expressions with Exponents that Have a Common Base
Cancel factors common to the numerator and denominator.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Part=Percent x Whole
Four equal acute angles and four equal obtuse angles.

27. 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?
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

28. Convert From a Fraction to a Decimal - Vice Versa
2(pie)r
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.

29. Finding the Circumference of a Circle
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Express them with a common denominator.
2(pie)r

30. 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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Put the equation into y=mx+b-- in which case b is the y-intercept.

31. What Does Solving In Terms of Mean?
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

32. Finding the Area of a Triangle
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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

33. Definition of an Integer
FOIL: First - Outer - Inner - Last... Combine Like Terms
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
VofaC: (pie)r(2)h
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

34. Numbers that are Relatively Prime
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Just add or subtract the coefficients in front of the radicals.
Two relatively prime numbers are integers that have no common factor other than 1.

35. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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
Slope=change in y/change in x
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

36. 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.
Two relatively prime numbers are integers that have no common factor other than 1.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.

37. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Use simple numbers like 1 and 2 and see what happens.
Just add or subtract the coefficients in front of the radicals.

38. Finding the Area of a Sector
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
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.
Find a common denominator - then add or subtract the numerators.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

39. Finding the Missing Number in a Series When You are Given the Average
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.
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.

40. Multiply and Divide Positive and Negative Numbers
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.

41. What are Two Special Pythagorean Triples?
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

42. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
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.
(pie)r(squared)
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.

43. Finding the Sum of the Interior Angles of a Polygon
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.
Part=Percent x Whole
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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

44. Finding the Area of a Circle
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
(pie)r(squared)
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

45. Converting from part-to-part ratios to part-to-whole ratios
Four equal acute angles and four equal obtuse angles.
Put each number in the original ratio over the sum of the numbers.
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
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.

46. Finding the Slope of a Line When Given Two Points on the Line
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.
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.
Do whatever is necessary to both sides to isolate the variable.
Slope=change in y/change in x

47. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
A(2)+b(2)=c(2)
FOIL: First - Outer - Inner - Last... Combine Like 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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

48. If (Square Root: x-1)+5=12 - what is the value of x/2?
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.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

49. Prime Factorization of a Number
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

50. Converting From a Mixed Number to an Improper Fraction
Use the formula distance=rate*time and its variations to help in this question.
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.
Slope=change in y/change in x

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