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SAT Math

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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. How do you know if an integer is a multiple of 3 or 9?
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Isolate the radical expression and use the standard rules of algebra.
Factor out and cancel all factors the numerator and denominator have in common.

2. Finding the Distance Between Two Points on a Coordinate Graph
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

3. Definition of an Integer
Put the equation into y=mx+b-- in which case b is the y-intercept.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
(x1+x2)/2 -(y1+y2)/2

4. Solving a Proportion
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Cross multiply.
-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.
Put the equation into y=mx+b-- in which case b is the y-intercept.

5. Counting Consecutive Integers
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Sum: Average x Number of Terms
Two relatively prime numbers are integers that have no common factor other than 1.
Subtract the smallest from the largest and add 1

6. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
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.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

7. Direct Variation and Inverse Variation
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Use the formula distance=rate*time and its variations to help in this question.
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

8. Definition of a Rational Number
Cross multiply.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.

9. Knowing if an Integer is a Multiple of 5 or 10
Get the absolute value equation by itself. Solve.
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
-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.
Use simple numbers like 1 and 2 and see what happens.

10. Formula Used to Find Percent
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.
Part=Percent x Whole
Factor out and cancel all factors the numerator and denominator have in common.
-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.

11. 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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.

12. Characteristics of a Parallelogram
Use the distributive property then combine the like terms.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Get the absolute value equation by itself. Solve.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

13. Finding the Median of a Set of Numbers
Just add or subtract the coefficients in front of the radicals.
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)
The value that falls in the middle of the set.

14. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

15. Finding the Midpoint Between Two Points
Average the smallest and largest number
(x1+x2)/2 -(y1+y2)/2
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

16. Difference Between a Factor and a Multiple
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
-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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

17. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Slope=change in y/change in x
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.

18. Finding the Area of a Circle
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
(pie)r(squared)
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

19. An Important Property of a Line Tangent to a Circle
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
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.

20. Adding and Subtracting Roots
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Just add or subtract the coefficients in front of the radicals.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

21. Characteristics of a Rectangle
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 simple numbers like 1 and 2 and see what happens.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

22. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Subtract the smallest from the largest and add 1

23. Formula to Find Average
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Average: Sum of the Terms/Number of the Terms

24. Calculating the Probability that an Event will Take Place
-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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

25. Properties of the Interior and Exterior Angles of a Triangle
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.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Two relatively prime numbers are integers that have no common factor other than 1.

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

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27. Finding the Reciprocal of a Fraction
Substitute r=4 and t=3 and evaluate the exponents before subtracting the 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.
Switch the numerator and denominator.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

28. If x(2)=7x+18 - what is the positive value of x?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

29. Finding the Missing Number in a Series When You are Given the Average
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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

30. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Subtract the smallest from the largest and add 1
Multiply the numerators and multiply the denominators.
Get the absolute value equation by itself. Solve.

31. Number of Groups - +1 Each Time
Two relatively prime numbers are integers that have no common factor other than 1.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

32. Definition of an Irrational Number
-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.
Average: Sum of the Terms/Number of the 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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

33. 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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Four equal acute angles and four equal obtuse angles.
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

34. Adding and Subtracting Polynomials
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Combine like terms.
FOIL: First - Outer - Inner - Last... Combine Like Terms
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

35. Converting From a Mixed Number to an Improper Fraction
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Adjacent angles are supplementary - Vertical angles are equal
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

36. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Cancel factors common to the numerator and denominator.
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.

37. 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?
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.

38. Finding the Sum of the Average of a Series of Numbers
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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 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
Sum: Average x Number of Terms

39. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use the formula distance=rate*time and its variations to help in this question.

40. 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.
-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.
Use simple numbers like 1 and 2 and see what happens.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

41. Adding and Subtracting Monomials
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

42. Solving a Linear Equation
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Just add or subtract the coefficients in front of the radicals.
The value that appears the most often.
Do whatever is necessary to both sides to isolate the variable.

43. Raising a Power to a Power
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Multiply the exponents - (x^3)^4=x^3*4=x^12
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The value that appears the most often.

44. Multiplying Monomials
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.
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 coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Cancel factors common to the numerator and denominator.

45. 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?
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.
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.
Just add or subtract the coefficients in front of the radicals.

46. What are Two Special Pythagorean Triples?

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47. Convert From a Fraction to a Decimal - Vice Versa
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Four equal acute angles and four equal obtuse angles.
Just add or subtract the coefficients in front of the radicals.
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.

48. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
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.

49. Definition of Remainder
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
The whole number left over after division.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

50. 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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.

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