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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. If r#t=t(r)-r(t) - then what is 4#3?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

2. Average Rate and How Do You Find It
Put each number in the original ratio over the sum of the numbers.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.

3. Finding the Midpoint Between Two Points
Switch the numerator and denominator.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use the units to keep things straight - Snowfall inches/hours
(x1+x2)/2 -(y1+y2)/2

4. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Get the absolute value equation by itself. Solve.
The value that falls in the middle of the set.
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

5. 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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

6. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Plug in the given values for the unknowns and calculate according to PEMDAS.
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
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

7. Solving a System of Equations
Use the units to keep things straight - Snowfall inches/hours
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.
Multiply the numerators and multiply the denominators.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

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

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9. 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
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.
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.
-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.

10. Adding a Positive Number to a Negative Number
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.
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

11. Definition of an Integer
A(2)+b(2)=c(2)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

12. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Part=Percent x Whole
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

13. Finding the Area of a Triangle

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14. What Does Solving In Terms of Mean?
(x1+x2)/2 -(y1+y2)/2
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

15. 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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The value that falls in the middle of the set.
Just add or subtract the coefficients in front of the radicals.

16. Finding the Mode of a Set of Numbers
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.
Just add or subtract the coefficients in front of the radicals.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

17. Knowing if an Integer is a Multiple of 2 or 4
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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.
Slope=change in y/change in x
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.

18. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Multiply the exponents - (x^3)^4=x^3*4=x^12
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
VofaC: (pie)r(2)h

19. What types of angles are formed when two lines intersect?
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.
A(2)+b(2)=c(2)
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Adjacent angles are supplementary - Vertical angles are equal

20. Formula to Find Average
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: Sum of the Terms/Number of the Terms
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Combine like terms.

21. If x(2)=7x+18 - what is the positive value of x?
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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.

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

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23. Finding the Volume of a Cylinder
Put each number in the original ratio over the sum of the numbers.
VofaC: (pie)r(2)h
Cross multiply.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

24. Finding the Domain and Range of a Function
Use the formula distance=rate*time and its variations to help in this question.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.

25. Solving a Proportion
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Slope=change in y/change in x
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.
Cross multiply.

26. Multiplying and Dividing Roots
(pie)r(squared)
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

27. Characteristics of a Rectangle
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Sum: Average x Number of Terms
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

28. 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.
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.
Use simple numbers like 1 and 2 and see what happens.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

29. 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
VofaC: (pie)r(2)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
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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

30. Simplifying a Fraction to Lowest Terms
Cross multiply.
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.
Factor out and cancel all factors the numerator and denominator have in common.
Just add or subtract the coefficients in front of the radicals.

31. Prime Factorization of a Number
Express them with a common denominator.
'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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

32. An Important Property of a Line Tangent to a Circle
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.
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
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
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.

33. Converting From a Mixed Number to an Improper Fraction
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

34. Adding and Subtracting Fractions
Plug in the given values for the unknowns and calculate according to PEMDAS.
Find a common denominator - then add or subtract the numerators.
Adjacent angles are supplementary - Vertical angles are equal
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

35. Finding the Area of a Sector

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36. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Use the units to keep things straight - Snowfall inches/hours
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Put each number in the original ratio over the sum of the numbers.
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. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

38. Factoring a Polynomial ('FOIL in Reverse')
Multiply the numerators and multiply the denominators.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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

39. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
2(pie)r
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 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.

40. 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.
-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.
Switch the numerator and denominator.
Get the absolute value equation by itself. Solve.

41. 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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
-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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

42. 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
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
(x1+x2)/2 -(y1+y2)/2
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

43. Converting from an Improper Fraction to a Mixed Number
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12

44. Setting Up a Ratio
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
VofaC: (pie)r(2)h

45. Factoring the Difference of Two Squares
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Slope=change in y/change in x
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

46. What is the greatest of three consecutive odd integers where the sum of the third and twice the first is equal to nine more than twice the second?
Cancel factors common to the numerator and denominator.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.

47. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
Sum: Average x Number of Terms
The whole number left over after division.
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.

48. Determining Absolute Value of a Number
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

49. Convert From a Fraction to a Decimal - Vice Versa
-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.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.

50. Dividing Expressions with Exponents that Have a Common Base
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Four equal acute angles and four equal obtuse angles.
Use the units to keep things straight - Snowfall inches/hours
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

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