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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. Finding the Slope When Given an Equation of a Line
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

2. Simplifying an Algebraic Equation
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.
Cancel factors common to the numerator and denominator.
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
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

3. Factoring the Difference of Two Squares
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

4. General Procedure for Multiplying Polynomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

5. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
Average: Sum of the Terms/Number of the Terms
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Two relatively prime numbers are integers that have no common factor other than 1.

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

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7. What are Two Special Pythagorean Triples?

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8. 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?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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

9. Multiplying Expressions with Exponents that Have a Common Base
The value that appears the most often.
Get the absolute value equation by itself. Solve.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

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?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

11. Number of Groups - +1 Each Time
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Slope=change in y/change in x
Four equal acute angles and four equal obtuse angles.

12. Counting Consecutive Integers
Get the absolute value equation by itself. Solve.
Average: Sum of the Terms/Number of the Terms
Subtract the smallest from the largest and add 1
Probability: Number of Favorable Outcomes/Total Possible Outcomes

13. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Just add or subtract the coefficients in front of the radicals.
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

14. Finding the y-intercept When Given an Equation of a Line
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Just add or subtract the coefficients in front of the radicals.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Use the units to keep things straight - Snowfall inches/hours

15. 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.
The value that appears the most often.
Combine like terms.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

16. 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.
-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.
Switch the numerator and denominator.
Sum: Average x Number of Terms

17. Finding the Rate of Speed
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.
Use the formula distance=rate*time and its variations to help in this question.
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

18. Solving a Proportion
Cross multiply.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Average: Sum of the Terms/Number of the Terms
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.

19. Finding the Sum of the Interior Angles of a Polygon
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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

20. Characteristics of a Square
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Multiply the numerators and multiply the denominators.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

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

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22. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Average the smallest and largest number

23. If 4(x(2)-10x+25) - then what is the value of x?
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.
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.
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
Slope=change in y/change in x

24. 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.
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

25. Setting Up a Ratio
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
-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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

26. An Important Property of a Line Tangent to a Circle
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.
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.
2(pie)r
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

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

28. Convert From a Fraction to a Decimal - Vice Versa
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
-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.
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.

29. Definition of an Irrational Number
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

30. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Two relatively prime numbers are integers that have no common factor other than 1.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
A(2)+b(2)=c(2)
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.

31. Calculating the Probability that an Event will Take Place
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

32. Finding the Circumference of a Circle
2(pie)r
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

33. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
Subtract the smallest from the largest and add 1
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

34. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

35. Finding the Reciprocal of a Fraction
2(pie)r
Switch the numerator and denominator.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Multiply the numerators and multiply the denominators.

36. Definition of Remainder
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The whole number left over after division.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

37. Finding the Domain and Range of a Function
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.
Just add or subtract the coefficients in front of the radicals.
Factor out and cancel all factors the numerator and denominator have in common.

38. Finding the Surface Area of a Rectangular Solid
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 exponents - (x^3)^4=x^3*4=x^12
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

39. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Sum: Average x Number of Terms

40. Properties of Similar Triangles
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Part=Percent x Whole
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

41. Scalene - Isosceles - and Equilateral Triangles
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 value that falls in the middle of the set.
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
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.

42. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

43. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical 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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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

44. Finding the Median of a Set of Numbers
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The value that falls in the middle of the set.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

45. Multiply and Divide Positive and Negative Numbers
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Adjacent angles are supplementary - Vertical angles are equal
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

46. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
-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.
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

47. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

48. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

49. Numbers that are Relatively Prime
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Two relatively prime numbers are integers that have no common factor other than 1.
Put each number in the original ratio over the sum of the numbers.
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

50. Multiplying and Dividing Roots
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.
-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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.