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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. Increasing and Decreasing a Number by a Certain Percentage
-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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Find a common denominator - then add or subtract the numerators.

2. 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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

3. Finding a Term in a Geometric Sequence
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.
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
Isolate the radical expression and use the standard rules of algebra.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

4. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
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.
Get the absolute value equation by itself. 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.

5. Comparing the values of two or more Fractions
Express them with a common denominator.
Adjacent angles are supplementary - Vertical angles are equal
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^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.

6. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Combine like terms.
Use the formula distance=rate*time and its variations to help in this question.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

7. If x(2)=7x+18 - what is the positive value of x?
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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

8. Finding the Surface Area of a Rectangular Solid
The whole number left over after division.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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 units to keep things straight - Snowfall inches/hours

9. Finding the Area of a Sector

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

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11. Number of Groups - +1 Each 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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Get the absolute value equation by itself. Solve.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

12. Finding the Mode of a Set of Numbers
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The value that appears the most often.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

13. Finding the Sum of the Average of a Series of Numbers
The value that appears the most often.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Sum: Average x Number of Terms

14. Definition of 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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
The whole number left over after division.
Use the formula distance=rate*time and its variations to help in this question.

15. Finding the Distance Between Two Points on a Coordinate Graph
Two relatively prime numbers are integers that have no common factor other than 1.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Put the equation into y=mx+b-- in which case b is the y-intercept.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

16. Adding and Subtracting Roots
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
Use the distributive property then combine the like terms.
Just add or subtract the coefficients in front of the radicals.

17. Counting Consecutive Integers
-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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Subtract the smallest from the largest and add 1

18. Simplifying Square Roots
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.

19. What Does Solving In Terms of Mean?
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Slope=change in y/change in x

20. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use simple numbers like 1 and 2 and see what happens.

21. Adding and Subtracting Monomials
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Put the equation into y=mx+b-- in which case b is the y-intercept.
Cancel factors common to the numerator and denominator.

22. What is the Pythagorean Theorem?
-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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
A(2)+b(2)=c(2)
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.

23. Properties of Similar Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
(x1+x2)/2 -(y1+y2)/2
A(2)+b(2)=c(2)

24. Raising a Power to a Power
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
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.

25. Knowing if an Integer is a Multiple of 2 or 4
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.
-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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
-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.

26. If the average of a - b - and 48 is 48 - what is the value of a + b?
Sum: Average x Number of Terms
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.
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

27. Scalene - Isosceles - and Equilateral Triangles
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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
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.
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.

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

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29. Average Rate and How Do You Find It
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.

30. Expressing the Union and Intersection of Sets
Adjacent angles are supplementary - Vertical angles are equal
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 distance=rate*time and its variations to help in this question.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

31. Multiplying and Dividing Roots
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.
Just add or subtract the coefficients in front of the radicals.
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.

32. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.

33. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Four equal acute angles and four equal obtuse angles.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
A(2)+b(2)=c(2)

34. Dividing Expressions with Exponents that Have a Common Base
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

35. What are Two Special Pythagorean Triples?

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36. Definition of an Irrational Number
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.
A(2)+b(2)=c(2)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

37. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Plug in the given values for the unknowns and calculate according to PEMDAS.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Two relatively prime numbers are integers that have no common factor other than 1.
Average the smallest and largest number

38. 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.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

39. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Use the distributive property then combine the like terms.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Express them with a common denominator.

40. Adding and Subtracting Fractions
Use the units to keep things straight - Snowfall inches/hours
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Find a common denominator - then add or subtract the numerators.

41. Properties of the Interior and Exterior Angles of a Triangle
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
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 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 formula distance=rate*time and its variations to help in this question.

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
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.
Get the absolute value equation by itself. Solve.
FOIL: First - Outer - Inner - Last... Combine Like Terms

43. Adding and Subtracting Polynomials
Combine like terms.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^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.
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.

44. Solving a System of Equations
Average: Sum of the Terms/Number of the Terms
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.
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.

45. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Adjacent angles are supplementary - Vertical angles are equal
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

46. Multiplying Monomials
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Express them with a common denominator.

47. Converting from part-to-part ratios to part-to-whole ratios
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.
Put each number in the original ratio over the sum of the numbers.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

48. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
(x1+x2)/2 -(y1+y2)/2
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

49. Multiplying Expressions with Exponents that Have a Common Base
Put each number in the original ratio over the sum of the numbers.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.

50. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Isolate the radical expression and use the standard rules of algebra.
VofaC: (pie)r(2)h
Put the equation into the slope-intercept form: y=mx+b. The slope is m.