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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. Numbers that are Relatively Prime
Sum: Average x Number of Terms
Cross multiply.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Two relatively prime numbers are integers that have no common factor other than 1.

2. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
-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.
Use simple numbers like 1 and 2 and see what happens.

3. Properties of Similar Triangles
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
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.
2(pie)r
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

4. Factoring a Polynomial ('FOIL in Reverse')
Cancel factors common to the numerator and denominator.
Get the absolute value equation by itself. Solve.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

5. Adding and Subtracting Monomials
Do whatever is necessary to both sides to isolate the variable.
A(2)+b(2)=c(2)
VofaRS=lwh
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

6. Finding the y-intercept When Given an Equation of a Line
Isolate the radical expression and use the standard rules of algebra.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.

7. Multiplying Fractions
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Multiply the numerators and multiply the denominators.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

8. 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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.

9. Determining Absolute Value of a Number
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
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.

10. Direct Variation and Inverse Variation
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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. Solving an Inequality
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Put the equation into y=mx+b-- in which case b is the y-intercept.
The whole number left over after division.

12. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
Find a common denominator - then add or subtract the numerators.

13. If the average of a - b - and 48 is 48 - what is the value of a + b?
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

14. Setting Up a Ratio
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
Switch the numerator and denominator.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

15. Adding and Subtracting Polynomials
Combine like terms.
-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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

16. What is the Pythagorean Theorem?
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
A(2)+b(2)=c(2)
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

17. Adding and Subtracting Roots
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
(x1+x2)/2 -(y1+y2)/2
Just add or subtract the coefficients in front of the radicals.
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

18. 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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

19. 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.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Multiply the exponents - (x^3)^4=x^3*4=x^12

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.
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.
-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 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

21. Calculating the Probability that an Event will Take Place
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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

22. Scalene - Isosceles - and Equilateral Triangles
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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 whole number left over after division.

23. What are Two Special Pythagorean Triples?

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24. 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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

25. Dividing Fractions
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Do whatever is necessary to both sides to isolate the variable.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
VofaC: (pie)r(2)h

26. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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
Two relatively prime numbers are integers that have no common factor other than 1.

27. Finding the Sum of the Average of a Series of Numbers
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
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
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.

28. If r#t=t(r)-r(t) - then what is 4#3?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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
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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

29. 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?
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.
The value that falls in the middle of the set.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

30. Finding the Domain and Range of a Function
VofaC: (pie)r(2)h
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^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.

31. If 2+l6-xl=10 and x>0 - what is the value of 2x?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Get the absolute value equation by itself. Solve.
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.
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.

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

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33. Finding the Missing Number in a Series When You are Given the Average
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

34. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Plug in the given values for the unknowns and calculate according to PEMDAS.
Average the smallest and largest number

35. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Isolate the radical expression and use the standard rules of algebra.
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

36. Increasing and Decreasing a Number by a Certain Percentage
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)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.
-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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

37. Finding the Circumference of a Circle
Combine like terms.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Do whatever is necessary to both sides to isolate the variable.
2(pie)r

38. Adding a Positive Number to a Negative Number
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
2(pie)r

39. Finding the Area of a Circle
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
(pie)r(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.

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

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41. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

42. Definition of Remainder
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
VofaC: (pie)r(2)h
-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.
The whole number left over after division.

43. Solving a Linear Equation
Multiply the numerators and multiply the denominators.
Use the units to keep things straight - Snowfall inches/hours
Do whatever is necessary to both sides to isolate the variable.
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

44. 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
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.
VofaC: (pie)r(2)h
Use the units to keep things straight - Snowfall inches/hours

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

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46. Expressing the Union and Intersection of Sets
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

47. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.

48. Finding the Slope When Given an Equation of a Line
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Four equal acute angles and four equal obtuse angles.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
A(2)+b(2)=c(2)

49. Counting Consecutive Integers
Substitute r=4 and t=3 and evaluate the exponents before subtracting 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.
Subtract the smallest from the largest and add 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.

50. Properties of a 30-60-90 Triangle
Average the smallest and largest number
The value that appears the most often.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Combine like terms.