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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. Multiplying Fractions
Multiply the numerators and multiply the denominators.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
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.

2. What are Two Special Pythagorean Triples?

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3. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
Switch the numerator and denominator.
Four equal acute angles and four equal obtuse angles.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

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

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5. Solving a Proportion
Cross multiply.
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.
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

6. Adding and Subtracting Polynomials
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Combine like terms.

7. Setting Up a Ratio
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
-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.
Use the units to keep things straight - Snowfall inches/hours

8. Finding the Sum of the Average of a Series of Numbers
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Sum: Average x Number of Terms

9. Adding a Positive Number to a Negative Number
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.

10. Definition of Remainder
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.
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 whole number left over after division.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

11. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Subtract the smallest from the largest and add 1
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.
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 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.

12. Finding the Volume of a Cylinder
Use the formula distance=rate*time and its variations to help in this question.
VofaC: (pie)r(2)h
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.

13. Finding the Slope When Given an Equation of a Line
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

14. Determining Absolute Value of a Number
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.
Cancel factors common to the numerator and denominator.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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

15. Finding the Volume of a Rectangular Solid
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
VofaRS=lwh

16. PEMDAS
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Average the smallest and largest number

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

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18. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
-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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Part=Percent x Whole

19. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
Express them with a common denominator.

20. Finding the Midpoint Between Two Points
Express them with a common denominator.
(x1+x2)/2 -(y1+y2)/2
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

21. Formula Used to Find Percent
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Part=Percent x Whole
(x1+x2)/2 -(y1+y2)/2

22. Counting Consecutive Integers
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
Slope=change in y/change in x
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

23. Solving an Inequality
Average the smallest and largest number
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Factor out and cancel all factors the numerator and denominator have in common.

24. 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?
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
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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.

25. Multiplying Expressions with Exponents that Have a Common Base
Get the absolute value equation by itself. Solve.
2(pie)r
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

26. Solving a System of Equations
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)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.

27. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
Use the formula distance=rate*time and its variations to help in this question.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

28. Converting from part-to-part ratios to part-to-whole ratios
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Put each number in the original ratio over the sum of the numbers.

29. Factoring a Polynomial ('FOIL in Reverse')
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
VofaC: (pie)r(2)h
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

30. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Do whatever is necessary to both sides to isolate the variable.
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.
Four equal acute angles and four equal obtuse angles.

31. Properties of the Interior and Exterior Angles of a Triangle
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
(x1+x2)/2 -(y1+y2)/2
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

32. What types of angles are formed when two lines intersect?
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.
Two relatively prime numbers are integers that have no common factor other than 1.
Adjacent angles are supplementary - Vertical angles are equal
2(pie)r

33. Finding the Domain and Range of a Function
Cancel factors common to the numerator and denominator.
(x1+x2)/2 -(y1+y2)/2
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

34. Difference Between a Factor and a Multiple
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

35. Direct Variation and Inverse Variation
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.
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
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

36. Multiplying and Dividing Roots
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%
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Two relatively prime numbers are integers that have no common factor other than 1.

37. Raising a Power to a Power
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply the exponents - (x^3)^4=x^3*4=x^12
Combine like terms.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

38. 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
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
-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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

39. What Does Solving In Terms of Mean?
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

40. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
Put each number in the original ratio over the sum of the numbers.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

41. What is the Triangle Inequality Theorem?
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
Just add or subtract the coefficients in front of the radicals.
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.
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

42. 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?
Use the units to keep things straight - Snowfall inches/hours
Put each number in the original ratio over the sum of the numbers.
Average: Sum of the Terms/Number of the Terms
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

43. 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?
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.
Slope=change in y/change in x
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

44. 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.
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.
Express them with a common denominator.
Use the formula distance=rate*time and its variations to help in this question.

45. If x(2)=7x+18 - what is the positive value of x?
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
The value that appears the most often.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

46. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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
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

47. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Isolate the radical expression and use the standard rules of algebra.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

48. Evaluating an Algebraic Expression
VofaC: (pie)r(2)h
Switch the numerator and denominator.
Plug in the given values for the unknowns and calculate according to PEMDAS.
The value that falls in the middle of the set.

49. Multiplying Monomials
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.
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 A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

50. Formula to Find Average
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
Part=Percent x Whole
Average: Sum of the Terms/Number of the 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.