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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?
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

2. Solving an Inequality
Put the equation into y=mx+b-- in which case b is the y-intercept.
Sum: Average x Number of Terms
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Slope=change in y/change in x

3. 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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Four equal acute angles and four equal obtuse angles.

4. Formula Used to Find Percent
Part=Percent x Whole
Put each number in the original ratio over the sum of the numbers.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Slope=change in y/change in x

5. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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.
Average: Sum of the Terms/Number of the Terms
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

6. Knowing if an Integer is a Multiple of 2 or 4
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.
(x1+x2)/2 -(y1+y2)/2
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.
-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.

7. Converting from part-to-part ratios to part-to-whole ratios
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
The value that appears the most often.
Put each number in the original ratio over the sum of the numbers.
Average the smallest and largest number

8. Properties of a 30-60-90 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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

9. 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)
Use simple numbers like 1 and 2 and see what happens.
Find a common denominator - then add or subtract the numerators.
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

10. Solving a System of Equations
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms

11. Evaluating an Algebraic Expression
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
(x1+x2)/2 -(y1+y2)/2
Plug in the given values for the unknowns and calculate according to PEMDAS.
Subtract the smallest from the largest and add 1

12. Finding the Rate of Speed
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The value that appears the most often.
Average the smallest and largest number
Use the formula distance=rate*time and its variations to help in this question.

13. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Do whatever is necessary to both sides to isolate the variable.
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.

14. Definition of an Integer
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.

15. 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?
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.
Just add or subtract the coefficients in front of the radicals.
-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.
Put the equation into y=mx+b-- in which case b is the y-intercept.

16. Difference Between a Factor and a Multiple
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-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 distributive property then combine the like terms.

17. Adding and Subtracting Polynomials
Combine like terms.
Average the smallest and largest number
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

18. Finding the Sum of the Average of a Series of Numbers
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Sum: Average x Number of 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.

19. 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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

20. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

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21. Multiplying Monomials
Isolate the radical expression and use the standard rules of algebra.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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

22. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
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.
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

23. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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 number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

24. 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
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Find a common denominator - then add or subtract the numerators.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

25. Finding the Area of a Sector

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

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27. Multiplying Fractions
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 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.
Multiply the numerators and multiply the denominators.

28. Finding the Length of an Arc in a Circle

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29. If 2+l6-xl=10 and x>0 - what is the value of 2x?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Get the absolute value equation by itself. Solve.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Part=Percent x Whole

30. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Cross multiply.

31. How do you know if an integer is a multiple of 3 or 9?
A(2)+b(2)=c(2)
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.
Factor out and cancel all factors the numerator and denominator have in common.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

32. Factoring a Polynomial ('FOIL in Reverse')
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
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%.
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.

33. Adding and Subtracting Roots
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Just add or subtract the coefficients in front of the radicals.
Adjacent angles are supplementary - Vertical angles are equal
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.

34. Properties of Similar Triangles
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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 base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

35. If 3(3x)=9(x+2) - what is the value of x?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
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
Use the formula distance=rate*time and its variations to help in this question.

36. Direct Variation and Inverse Variation
-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.
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

37. Properties of the Interior and Exterior Angles of a Triangle
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 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.
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.
Sum: Average x Number of Terms

38. 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
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.
Use simple numbers like 1 and 2 and see what happens.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

39. 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.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

40. Definition of Remainder
The whole number left over after division.
Combine like terms.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
-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.

41. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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
Combine like terms.

42. Finding the Sum of the Interior Angles of a Polygon
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
-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.
-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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

43. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
2(pie)r
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. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
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.
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.
Switch the numerator and denominator.

45. Comparing the values of two or more Fractions
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Express them with a common denominator.

46. Multiplying Binomials
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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

47. What types of angles are formed when a transversal cross parallel lines?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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
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.

48. An Important Property of a Line Tangent to a Circle
Average: Sum of the Terms/Number of the Terms
Just add or subtract the coefficients in front of the radicals.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.

49. Dividing Expressions with Exponents that Have a Common Base
Slope=change in y/change in x
Combine like terms.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use simple numbers like 1 and 2 and see what happens.

50. Multiplying Expressions with Exponents that Have a Common Base
Express them with a common 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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7