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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. Simplifying an Algebraic Equation
Switch the numerator and denominator.
2(pie)r
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.
Cancel factors common to the numerator and denominator.

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

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3. Finding the Missing Number in a Series When You are Given the Average
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

4. Comparing the values of two or more Fractions
Use simple numbers like 1 and 2 and see what happens.
Express them with a common denominator.
Multiply the exponents - (x^3)^4=x^3*4=x^12
A(2)+b(2)=c(2)

5. Formula Used to Find Percent
Part=Percent x Whole
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Put each number in the original ratio over the sum of the numbers.

6. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
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.
-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. An Important Property of a Line Tangent to a Circle
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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 value that falls in the middle of the set.
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.

8. Solving a Proportion
Average: Sum of the Terms/Number of the Terms
Cross multiply.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

9. Calculating the Probability that an Event will Take Place
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Adjacent angles are supplementary - Vertical angles are equal
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

10. Finding the y-intercept When Given an Equation of a Line
Put each number in the original ratio over the sum of the numbers.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Use the units to keep things straight - Snowfall inches/hours
Put the equation into y=mx+b-- in which case b is the y-intercept.

11. Solving an Inequality
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

12. Determining Absolute Value of a Number
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.

13. Finding the Area of a Sector

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14. 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
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

15. Expressing the Union and Intersection of Sets
Four equal acute angles and four equal obtuse angles.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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

16. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.

17. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
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
Find a common denominator - then add or subtract the numerators.
VofaRS=lwh

18. Adding a Positive Number to a Negative Number
-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.
Two relatively prime numbers are integers that have no common factor other than 1.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

19. What value of x is not in the domain of the function f(x)=x-2/x-3?
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Change the division sign to a multiplication sign - invert the second fraction - and 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.
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

20. How do you know if an integer is a multiple of 3 or 9?
Adjacent angles are supplementary - Vertical angles are equal
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.
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.
-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.

21. Finding the Circumference of a Circle
Four equal acute angles and four equal obtuse angles.
VofaRS=lwh
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
2(pie)r

22. Knowing if an Integer is a Multiple of 2 or 4
The value that appears the most often.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
-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.

23. Quickly Finding the Average of a Series of Evenly Spaced Numbers
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Average the smallest and largest number
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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

24. 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.
Do whatever is necessary to both sides to isolate the variable.
-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.
Subtract the smallest from the largest and add 1

25. If 4(x(2)-10x+25) - then what is the value of 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.
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Combine like terms.

26. Convert From a Fraction to a Decimal - Vice Versa
Use simple numbers like 1 and 2 and see what happens.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Combine like terms.

27. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Sum: Average x Number of Terms
Put the equation into y=mx+b-- in which case b is the y-intercept.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

28. If x(2)=7x+18 - what is the positive value of x?
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
VofaC: (pie)r(2)h

29. Adding and Subtracting Fractions
The value that appears the most often.
Find a common denominator - then add or subtract the numerators.
(pie)r(squared)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

30. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
VofaC: (pie)r(2)h
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.
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

31. Solving a Radical Equation
Put the equation into y=mx+b-- in which case b is the y-intercept.
Isolate the radical expression and use the standard rules of algebra.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Combine like terms.

32. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use simple numbers like 1 and 2 and see what happens.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

33. Multiplying Expressions with Exponents that Have a Common Base
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

34. Finding the Sum of the Average of a Series of Numbers
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.
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
Average the smallest and largest number
Sum: Average x Number of Terms

35. Properties of a 30-60-90 Triangle
Part=Percent x Whole
-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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Plug in the given values for the unknowns and calculate according to PEMDAS.

36. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
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.
Do whatever is necessary to both sides to isolate the variable.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

37. Direct Variation and Inverse Variation
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

38. Factoring a Polynomial ('FOIL in Reverse')
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

39. What Does Solving In Terms of Mean?
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

40. Finding the GCF of Two or More Numbers
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the exponents - (x^3)^4=x^3*4=x^12
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

41. Setting Up a Ratio
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
(x1+x2)/2 -(y1+y2)/2
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

42. Dividing Expressions with Exponents that Have a Common Base
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

43. Definition of an Irrational Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Do whatever is necessary to both sides to isolate the variable.

44. Finding the Slope When Given an Equation of a Line
Just add or subtract the coefficients in front of the radicals.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

45. Adding and Subtracting Polynomials
Subtract the smallest from the largest and add 1
Combine like terms.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

46. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Factor out and cancel all factors the numerator and denominator have in common.

47. Properties of Similar Triangles
Probability: Number of Favorable Outcomes/Total Possible Outcomes
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

48. Finding the Midpoint Between Two Points
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
(x1+x2)/2 -(y1+y2)/2
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Four equal acute angles and four equal obtuse angles.

49. Solving a System of Equations
Put the equation into y=mx+b-- in which case b is the y-intercept.
(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.
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.

50. If r#t=t(r)-r(t) - then what is 4#3?
Adjacent angles are supplementary - Vertical angles are equal
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.