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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. What is the Triangle Inequality Theorem?
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

2. Increasing and Decreasing a Number by a Certain Percentage
-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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
(x1+x2)/2 -(y1+y2)/2

3. Scalene - Isosceles - and Equilateral Triangles
Use the formula distance=rate*time and its variations to help in this question.
Multiply the whole number part by the denominator - then add the numerator. Keep the same 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.
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

4. Finding the GCF of Two or More Numbers
Use the formula distance=rate*time and its variations to help in this question.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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 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.

5. Formula to Find Average
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Average: Sum of the Terms/Number of the Terms
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

6. 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.
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.

7. Difference Between a Factor and a Multiple
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
-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.

8. Properties of a 45-45-90 Triangle
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Plug in the given values for the unknowns and calculate according to PEMDAS.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Cancel factors common to the numerator and denominator.

9. Finding the Length of an Arc in a Circle

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10. Comparing the values of two or more Fractions
Express them with a common denominator.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Combine like terms.
Two relatively prime numbers are integers that have no common factor other than 1.

11. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Cancel factors common to the numerator and denominator.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

12. 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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the units to keep things straight - Snowfall inches/hours

13. Finding the Rate of Speed
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
-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 formula distance=rate*time and its variations to help in this question.
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.

14. Raising a Power to a Power
The value that appears the most often.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use the units to keep things straight - Snowfall inches/hours

15. Finding the LCM of Two or More Numbers

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16. If the average of a - b - and 48 is 48 - what is the value of a + b?
Four equal acute angles and four equal obtuse angles.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Multiply the numerators and multiply the denominators.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

17. Properties of a 30-60-90 Triangle
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
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.

18. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

19. What is the Pythagorean Theorem?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
A(2)+b(2)=c(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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

20. Definition of a Rational Number
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

21. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
-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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

22. Solving a Proportion
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.
Cross multiply.
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

23. 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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

24. Solving an Inequality
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Adjacent angles are supplementary - Vertical angles are equal
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

25. Finding the Volume of a Rectangular Solid
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
VofaRS=lwh
Part=Percent x Whole

26. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
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 units to keep things straight - Snowfall inches/hours

27. Factoring a Polynomial ('FOIL in Reverse')
Find a common denominator - then add or subtract the numerators.
Adjacent angles are supplementary - Vertical angles are equal
A(2)+b(2)=c(2)
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

28. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
FOIL: First - Outer - Inner - Last... Combine Like Terms

29. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

30. Finding the Slope of a Line When Given Two Points on the Line
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Average the smallest and largest number
Slope=change in y/change in x
Switch the numerator and denominator.

31. 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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Use simple numbers like 1 and 2 and see what happens.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

32. Definition of Remainder
The whole number left over after division.
(x1+x2)/2 -(y1+y2)/2
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

33. If 4(x(2)-10x+25) - then what is the value of x?
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Use the formula distance=rate*time and its variations to help in this question.

34. Finding the Area of a Sector

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35. General Procedure for Multiplying Polynomials
VofaC: (pie)r(2)h
Use the units to keep things straight - Snowfall inches/hours
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Use the distributive property then combine the like terms.

36. Converting From a Mixed Number to an Improper Fraction
(x1+x2)/2 -(y1+y2)/2
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

37. Evaluating an Algebraic Expression
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
VofaRS=lwh

38. If r#t=t(r)-r(t) - then what is 4#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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Find a common denominator - then add or subtract the numerators.

39. Definition of an Integer
Multiply the numerators and multiply the denominators.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

40. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
A(2)+b(2)=c(2)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

41. Setting Up a Ratio
Get the absolute value equation by itself. Solve.
The value that appears the most often.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Multiply the exponents - (x^3)^4=x^3*4=x^12

42. Adding a Positive Number to a Negative Number
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

43. Multiplying and Dividing Roots
Two relatively prime numbers are integers that have no common factor other than 1.
VofaC: (pie)r(2)h
Factor out and cancel all factors the numerator and denominator have in common.
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.

44. Finding the Volume of a Cylinder
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
VofaC: (pie)r(2)h
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

45. Multiply and Divide Positive and Negative Numbers
Cancel factors common to the numerator and denominator.
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.
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

46. If 3(3x)=9(x+2) - what is the value of x?
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

47. Finding the Domain and Range of a Function
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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.

48. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
Put each number in the original ratio over the sum of the numbers.
The whole number left over after division.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

49. 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?
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.
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Cancel factors common to the numerator and denominator.

50. Calculating Negative Exponents and Radical Exponents
Cancel factors common to the numerator and denominator.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.