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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 4(x(2)-10x+25) - then what is the value of x?
Use the distributive property then combine the like terms.
Subtract the smallest from the largest and add 1
Part=Percent x Whole
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. 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
Use the formula distance=rate*time and its variations to help in this question.
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.
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.

3. Finding the Reciprocal of a Fraction
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Get the absolute value equation by itself. Solve.
Switch the numerator and denominator.

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

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5. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

6. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

7. Finding the Domain and Range of a Function
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.
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 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
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.

8. What is the Triangle Inequality Theorem?
-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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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 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.

9. 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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

10. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
-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.
-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.
Average the smallest and largest number

11. General Procedure for Multiplying Polynomials
Do whatever is necessary to both sides to isolate the variable.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Use the distributive property then combine the like terms.
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.

12. 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
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
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.

13. Solving a Radical Equation
Cancel factors common to the numerator and denominator.
Isolate the radical expression and use the standard rules of algebra.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Probability: Number of Favorable Outcomes/Total Possible Outcomes

14. 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.
VofaRS=lwh
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
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

15. Increasing and Decreasing a Number by a Certain Percentage
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
-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.

16. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

17. Properties of a 30-60-90 Triangle
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.
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 the whole number part by the denominator - then add the numerator. Keep the same denominator.

18. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Switch the numerator and denominator.

19. Finding the Rate of Speed
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.
Use the formula distance=rate*time and its variations to help in this question.
Factor out and cancel all factors the numerator and denominator have in common.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

20. Formula Used to Find Percent
Factor out and cancel all factors the numerator and denominator have in common.
Part=Percent x Whole
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

21. Dividing Expressions with Exponents that Have a Common Base
-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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

22. Solving an Inequality
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

23. Finding the Sum of the Interior Angles of a Polygon
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Use simple numbers like 1 and 2 and see what happens.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

24. Multiplying Monomials
Use the units to keep things straight - Snowfall inches/hours
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Adjacent angles are supplementary - Vertical angles are equal
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

25. Adding and Subtracting Polynomials
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Combine like terms.

26. Multiply and Divide Positive and Negative Numbers
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
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.
Isolate the radical expression and use the standard rules of algebra.
Use simple numbers like 1 and 2 and see what happens.

27. 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.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

28. Convert From a Fraction to a Decimal - Vice Versa
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.
Just add or subtract the coefficients in front of the radicals.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

29. 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
Combine like terms.
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

30. Multiplying Fractions
Multiply the numerators and multiply the denominators.
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 distributive property then combine the like terms.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

31. Finding the Circumference of a Circle
2(pie)r
The value that falls in the middle of the set.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

32. Simplifying an Algebraic Equation
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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
Cancel factors common to the numerator and denominator.
Get the absolute value equation by itself. Solve.

33. Calculating Negative Exponents and Radical Exponents
Adjacent angles are supplementary - Vertical angles are equal
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.

34. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Sum: Average x Number of Terms
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Average: Sum of the Terms/Number of the Terms

35. Adding and Subtracting Monomials
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

36. Finding the Missing Number in a Series When You are Given the Average
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
Factor out and cancel all factors the numerator and denominator have in common.
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.

37. Finding the Volume of a Rectangular Solid
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
VofaRS=lwh
Find a common denominator - then add or subtract the numerators.
(pie)r(squared)

38. 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.
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

39. Finding the Median of a Set of Numbers
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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 value that falls in the middle of the set.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

40. Formula to Find Average
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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 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.
Average: Sum of the Terms/Number of the Terms

41. Difference Between a Factor and a Multiple
(pie)r(squared)
-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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Cross multiply.

42. Knowing if an Integer is a Multiple of 2 or 4
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
-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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Use simple numbers like 1 and 2 and see what happens.

43. Finding the LCM of Two or More Numbers

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44. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
-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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

45. Multiplying Binomials
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
FOIL: First - Outer - Inner - Last... Combine Like Terms
-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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

46. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Use simple numbers like 1 and 2 and see what happens.
Adjacent angles are supplementary - Vertical angles are equal
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.

47. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
The value that appears the most often.
Part=Percent x Whole
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.
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.

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

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49. Dividing Fractions
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

50. Numbers that are Relatively Prime
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Two relatively prime numbers are integers that have no common factor other than 1.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Adjacent angles are supplementary - Vertical angles are equal