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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. What are Two Special Pythagorean Triples?

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2. Dividing Expressions with Exponents that Have a Common Base
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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

3. Comparing the values of two or more Fractions
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.
Express them with a common denominator.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

4. What types of angles are formed when two lines intersect?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Adjacent angles are supplementary - Vertical angles are equal
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.

5. What Does Solving In Terms of Mean?
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Isolate the radical expression and use the standard rules of algebra.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

6. Determining Absolute Value of a Number
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
VofaC: (pie)r(2)h
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

7. Solving a System of Equations
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
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

8. Definition of an Integer
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.
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.
Combine like terms.

9. Finding the Length of an Arc in a Circle

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10. General Procedure for Multiplying Polynomials
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Use the distributive property then combine the like terms.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

11. 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.
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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

12. Properties of a 45-45-90 Triangle
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Sum: Average x Number of Terms
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

13. What types of angles are formed when a transversal cross parallel lines?
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Subtract the smallest from the largest and add 1
Four equal acute angles and four equal obtuse angles.
Adjacent angles are supplementary - Vertical angles are equal

14. Factoring the Difference of Two Squares
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

15. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

16. Converting from an Improper Fraction to a Mixed Number
-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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Get the absolute value equation by itself. Solve.
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.

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

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18. What is the Pythagorean Theorem?
Factor out and cancel all factors the numerator and denominator have in common.
-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.
A(2)+b(2)=c(2)
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

19. 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
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.
Cancel factors common to the numerator and denominator.
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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

20. Calculating Negative Exponents and Radical Exponents
Use simple numbers like 1 and 2 and see what happens.
Four equal acute angles and four equal obtuse angles.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
(pie)r(squared)

21. Factoring a Polynomial ('FOIL in Reverse')
Slope=change in y/change in x
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

22. If the average of a - b - and 48 is 48 - what is the value of a + b?
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
-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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

23. Finding the y-intercept When Given an Equation of a Line
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.

24. What value of x is not in the domain of the function f(x)=x-2/x-3?
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.
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Put each number in the original ratio over the sum of the numbers.
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

25. 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.
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.
Isolate the radical expression and use the standard rules of algebra.
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.

26. Difference Between a Factor and a Multiple
-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.
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.
Put each number in the original ratio over the sum of the numbers.
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.

27. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
The value that appears the most often.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

28. Properties of the Interior and Exterior Angles of a Triangle
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use the distributive property then combine the like terms.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

29. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
Adjacent angles are supplementary - Vertical angles are equal

30. PEMDAS
Get the absolute value equation by itself. Solve.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Adjacent angles are supplementary - Vertical angles are equal
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

31. Numbers that are Relatively Prime
A(2)+b(2)=c(2)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Two relatively prime numbers are integers that have no common factor other than 1.

32. If x varies directly with y - and the value of x is 12 when y is 11 - what is the value of y when x is 66?
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
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
VofaRS=lwh

33. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
-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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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

34. Counting the Total Number of Possibilities for Several Events to Occur
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
-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.
Average the smallest and largest number

35. What is the Triangle Inequality Theorem?
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.
Average the smallest and largest number
Combine like terms.
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.

36. An Important Property of a Line Tangent to a Circle
Cross multiply.
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 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.
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.

37. Finding the Reciprocal of a Fraction
Combine like terms.
VofaC: (pie)r(2)h
Switch the numerator and denominator.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

38. Multiplying Fractions
Multiply the numerators and multiply the denominators.
Do whatever is necessary to both sides to isolate the variable.
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.
Subtract the smallest from the largest and add 1

39. If x(2)=7x+18 - what is the positive value of x?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Isolate the radical expression and use the standard rules of algebra.

40. Formula to Find Average
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Average: Sum of the Terms/Number of the Terms
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

41. Finding the Domain and Range of a Function
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
Factor out and cancel all factors the numerator and denominator have in common.
-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.

42. Finding the Volume of a Rectangular Solid
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
VofaRS=lwh
-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.
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.

43. Raising a Power to a Power
Combine like terms.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Multiply the exponents - (x^3)^4=x^3*4=x^12

44. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
Two relatively prime numbers are integers that have no common factor other than 1.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

45. Definition of an Irrational Number
Multiply the numerators and multiply the denominators.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Do whatever is necessary to both sides to isolate the variable.

46. Definition of Remainder
Switch the numerator and denominator.
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 whole number part by the denominator - then add the numerator. Keep the same denominator.
The whole number left over after division.

47. Solving a Radical Equation
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.
Isolate the radical expression and use the standard rules of algebra.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

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

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49. If r#t=t(r)-r(t) - then what is 4#3?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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 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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

50. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
-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.