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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. Expressing the Union and Intersection of Sets
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.
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

2. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Do whatever is necessary to both sides to isolate the variable.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.

3. Knowing if an Integer is a Multiple of 2 or 4
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
-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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
VofaRS=lwh

4. What is the Triangle Inequality Theorem?
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.
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 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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

5. Finding the Rate of Speed
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
Use the formula distance=rate*time and its variations to help in this question.
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.
Two relatively prime numbers are integers that have no common factor other than 1.

6. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
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.
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.
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

7. 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.
The whole number left over after division.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

8. If (Square Root: x-1)+5=12 - what is the value of x/2?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

9. Difference Between a Factor and a Multiple
Use the distributive property then combine the like terms.
-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.
Adjacent angles are supplementary - Vertical angles are equal
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.

10. Definition of Remainder
The whole number left over after division.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

11. Finding the Sum of the Interior Angles of a Polygon
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

12. If 3(3x)=9(x+2) - what is the value of 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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

13. Characteristics of a Rectangle
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

14. PEMDAS
2(pie)r
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Average the smallest and largest number
Put the equation into y=mx+b-- in which case b is the y-intercept.

15. Setting Up a Ratio
Cross multiply.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

16. Dividing Fractions
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Factor out and cancel all factors the numerator and denominator have in common.

17. Prime Factorization of a Number
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

18. 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 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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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

19. What types of angles are formed when two lines intersect?
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.
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.
Adjacent angles are supplementary - Vertical angles are equal
-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.

20. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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
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.

21. Characteristics of a Square
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.

22. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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
Put the equation into y=mx+b-- in which case b is the y-intercept.

23. Multiplying Expressions with Exponents that Have a Common Base
The value that falls in the middle of the set.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
A(2)+b(2)=c(2)

24. Finding the Area of a Circle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Average: Sum of the Terms/Number of the Terms
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
(pie)r(squared)

25. Knowing if an Integer is a Multiple of 5 or 10
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.
Combine like terms.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
-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.

26. Adding and Subtracting Polynomials
Use the formula distance=rate*time and its variations to help in this question.
Combine like terms.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

27. Finding the Sum of the Average of a Series of Numbers
Cross multiply.
Sum: Average x Number of Terms
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Part=Percent x Whole

28. Formula to Find Average
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.
Switch the numerator and denominator.
Average: Sum of the Terms/Number of the Terms
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.

29. Raising a Power to a Power
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.
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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

30. Finding the Length of an Arc in a Circle

31. Comparing the values of two or more Fractions
Express them with a common denominator.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
Average the smallest and largest number

32. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Put the equation into y=mx+b-- in which case b is the y-intercept.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

33. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

34. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

35. Simplifying an Algebraic Equation
-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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.

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

37. Characteristics of a Parallelogram
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Use the units to keep things straight - Snowfall inches/hours
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

38. What are Two Special Pythagorean Triples?

39. 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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

40. Finding the Slope When Given an Equation of a Line
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Adjacent angles are supplementary - Vertical angles are equal

41. 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
Express them with a common denominator.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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%

42. Finding the Area of a Sector

43. Scalene - Isosceles - and Equilateral Triangles
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
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

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

45. Finding the Mode of a Set of Numbers
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The value that appears the most often.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

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

47. Solving a Linear Equation
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Do whatever is necessary to both sides to isolate the variable.
(x1+x2)/2 -(y1+y2)/2

48. Finding the Domain and Range of a Function
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.
Put each number in the original ratio over the sum of the numbers.
Combine like terms.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

49. Quickly Finding the Average of a Series of Evenly Spaced Numbers
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.
Average the smallest and largest number
Get the absolute value equation by itself. Solve.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

50. Solving a Proportion
Put each number in the original ratio over the sum of the numbers.
-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 smallest from the largest and add 1
Cross multiply.