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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
Cancel factors common to the numerator and denominator.
2(pie)r
VofaRS=lwh
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

2. What Does Solving In Terms of Mean?
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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
Plug in the given values for the unknowns and calculate according to PEMDAS.

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

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4. Raising a Power to a Power
-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.
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 whole number left over after division.
Multiply the exponents - (x^3)^4=x^3*4=x^12

5. Prime Factorization of a Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
FOIL: First - Outer - Inner - Last... Combine Like Terms
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.

6. PEMDAS
Plug in the given values for the unknowns and calculate according to PEMDAS.
-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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

7. Formula Used to Find Percent
Put each number in the original ratio over the sum of the numbers.
Part=Percent x Whole
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.
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.

8. Finding the Rate of Speed
Adjacent angles are supplementary - Vertical angles are equal
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.

9. Finding the Circumference of a Circle
Plug in the given values for the unknowns and calculate according to PEMDAS.
2(pie)r
Find a common denominator - then add or subtract the numerators.
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

10. 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?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Average: Sum of the Terms/Number of the Terms
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.

11. What is the Triangle Inequality Theorem?
Use the units to keep things straight - Snowfall inches/hours
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
VofaRS=lwh

12. Comparing the values of two or more Fractions
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.
Express them with a common denominator.
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.
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.

13. What are Two Special Pythagorean Triples?

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14. Solving a Problem Involving Rates
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Use the units to keep things straight - Snowfall inches/hours
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

15. Characteristics of a Rectangle
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Put each number in the original ratio over the sum of the numbers.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

16. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Average the smallest and largest number
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

17. 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?
'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)
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

18. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Cross multiply.
Use the distributive property then combine the like terms.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

19. Properties of Similar Triangles
Just add or subtract the coefficients in front of the radicals.
Part=Percent x Whole
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

20. An Important Property of a Line Tangent to a Circle
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Sum: Average x Number of Terms
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

21. Multiplying Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Multiply the numerators and multiply the denominators.
-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.
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

22. Definition of an Irrational Number
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
Switch the numerator and denominator.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

23. Converting from part-to-part ratios to part-to-whole ratios
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Put each number in the original ratio over the sum of the numbers.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

24. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Average the smallest and largest number
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 whole number left over after division.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

25. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Do whatever is necessary to both sides to isolate the variable.

26. Simplifying Square Roots
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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 the perfect squares under the radical - take their square roots - and put the result in front.
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

27. Multiply and Divide Positive and Negative Numbers
Express them with a common denominator.
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 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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

28. Finding the Slope When Given an Equation of a Line
Two relatively prime numbers are integers that have no common factor other than 1.
The value that appears the most often.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

29. Finding the y-intercept When Given an Equation of a Line
Plug in the given values for the unknowns and calculate according to PEMDAS.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Find a common denominator - then add or subtract the numerators.
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.

30. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

31. Finding the GCF of Two or More Numbers
Factor out and cancel all factors the numerator and denominator have in common.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Multiply the numerators and multiply the denominators.
VofaC: (pie)r(2)h

32. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.

33. General Procedure for Multiplying Polynomials
Use the units to keep things straight - Snowfall inches/hours
Use the distributive property then combine the like terms.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

34. 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.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

35. Number of Groups - +1 Each Time
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
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.
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

36. Finding a Term in a Geometric Sequence
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.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
-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.

37. 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.
Cancel factors common to the numerator and denominator.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Probability: Number of Favorable Outcomes/Total Possible Outcomes

38. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Average the smallest and largest 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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

39. Definition of an Integer
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Sum: Average x Number of 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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

40. Finding the Area of a Circle
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.
(pie)r(squared)
Cancel factors common to the numerator and denominator.
-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.

41. Solving a System of Equations
Use the units to keep things straight - Snowfall inches/hours
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

42. Average Rate and How Do You Find It
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

43. Increasing and Decreasing a Number by a Certain Percentage
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
-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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

44. Solving a Radical Equation
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Isolate the radical expression and use the standard rules of algebra.
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

45. What types of angles are formed when a transversal cross parallel lines?
(pie)r(squared)
2(pie)r
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Four equal acute angles and four equal obtuse angles.

46. Adding and Subtracting Monomials
-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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Multiply the exponents - (x^3)^4=x^3*4=x^12
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. What is a Function and how do you Evaluate one?

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48. Numbers that are Relatively Prime
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Two relatively prime numbers are integers that have no common factor other than 1.
Average the smallest and largest number

49. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Use simple numbers like 1 and 2 and see what happens.
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.
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

50. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
Express them with a common denominator.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2