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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. Adding and Subtracting Roots
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
-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.
Just add or subtract the coefficients in front of the radicals.
Do whatever is necessary to both sides to isolate the variable.

2. General Procedure for Multiplying Polynomials
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Use the distributive property then combine the 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.

3. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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
Put each number in the original ratio over the sum of the numbers.

4. 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?
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Subtract the smallest from the largest and add 1
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

5. An Important Property of a Line Tangent to a Circle
Adjacent angles are supplementary - Vertical angles are equal
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
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.

6. Finding the Midpoint Between Two Points
Adjacent angles are supplementary - Vertical angles are equal
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
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

7. Finding the Area of a Sector

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8. Finding the Circumference 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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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

9. Adding and Subtracting Monomials
Use the distributive property then combine the like terms.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.

10. Properties of a 30-60-90 Triangle
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.
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
The whole number left over after division.

11. Finding the Surface Area of a Rectangular Solid
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

12. Formula Used to Find Percent
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Part=Percent x Whole
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use the formula distance=rate*time and its variations to help in this question.

13. Finding the Area of a Circle
(pie)r(squared)
Do whatever is necessary to both sides to isolate the variable.
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
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

14. 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.
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

15. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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

16. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

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

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18. Finding the Missing Number in a Series When You are Given the Average
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Average the smallest and largest number
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.

19. Expressing the Union and Intersection of Sets
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.
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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

20. Characteristics of a Square
Find a common denominator - then add or subtract the numerators.
Just add or subtract the coefficients in front of the radicals.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

21. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Adjacent angles are supplementary - Vertical angles are equal
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.

22. Definition of an Integer
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

23. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Part=Percent x Whole
Get the absolute value equation by itself. Solve.

24. Counting Consecutive Integers
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Subtract the smallest from the largest and add 1

25. Evaluating an Algebraic Expression
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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

26. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
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.
Sum: Average x Number of Terms
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.

27. 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
Do whatever is necessary to both sides to isolate the variable.
(pie)r(squared)
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

28. 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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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 find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

29. Increasing and Decreasing a Number by a Certain Percentage
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
-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.
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 find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

30. Factoring a Polynomial ('FOIL in Reverse')
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)
-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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

31. Difference Between a Factor and a Multiple
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
-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.
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 numerators and multiply the denominators.

32. Finding a Term in a Geometric Sequence
Four equal acute angles and four equal obtuse angles.
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.
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.
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.

33. Finding the Domain and Range of a Function
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.
Express them with a common denominator.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put each number in the original ratio over the sum of the numbers.

34. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
Average the smallest and largest number

35. Converting From a Mixed Number to an Improper Fraction
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 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

36. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Use simple numbers like 1 and 2 and see what happens.
Part=Percent x Whole

37. Determining Absolute Value of a Number
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

38. Finding the Rate of Speed
VofaRS=lwh
Use the formula distance=rate*time and its variations to help in this question.
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.
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.

39. If 3(3x)=9(x+2) - what is the value of x?
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
(pie)r(squared)
A(2)+b(2)=c(2)

40. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Adjacent angles are supplementary - Vertical angles are equal
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

41. Finding the Volume of a Rectangular Solid
VofaRS=lwh
FOIL: First - Outer - Inner - Last... Combine Like Terms
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

42. Properties of a 45-45-90 Triangle
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
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)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
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.

43. Solving a System of Equations
The value that appears the most often.
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.
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
Do whatever is necessary to both sides to isolate the variable.

44. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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 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.
A(2)+b(2)=c(2)

45. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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.
-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.
2(pie)r

46. Numbers that are Relatively Prime
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Two relatively prime numbers are integers that have no common factor other than 1.

47. 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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Average: Sum of the Terms/Number of the Terms
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.

48. Solving a Problem Involving Rates
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 units to keep things straight - Snowfall inches/hours
-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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

49. Number of Groups - +1 Each Time
Two relatively prime numbers are integers that have no common factor other than 1.
The value that appears the most often.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

50. Finding the Sum of the Interior Angles of a Polygon
Combine like terms.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.