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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 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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Multiply the numerators and multiply the denominators.
-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.

2. Finding the Area of a Sector

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3. Raising a Power to a Power
The value that falls in the middle of the set.
The value that appears the most often.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.

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

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5. Finding the Reciprocal of a Fraction
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Cancel factors common to the numerator and denominator.

6. Multiplying Fractions
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
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.

7. Adding and Subtracting Monomials
Switch the numerator and denominator.
VofaC: (pie)r(2)h
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

8. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
(x1+x2)/2 -(y1+y2)/2
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.
The whole number left over after division.

9. 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
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.
Find a common denominator - then add or subtract the numerators.
(pie)r(squared)

10. Characteristics of a Rectangle
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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

11. Solving a Linear Equation
Subtract the smallest from the largest and add 1
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Do whatever is necessary to both sides to isolate the variable.
Adjacent angles are supplementary - Vertical angles are equal

12. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
-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.
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.

13. Definition of Remainder
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The whole number left over after division.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
(x1+x2)/2 -(y1+y2)/2

14. Properties of a 30-60-90 Triangle
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

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

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16. Multiplying Monomials
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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 coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^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.

17. Definition of an Integer
VofaRS=lwh
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.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

18. Setting Up a Ratio
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^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.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

19. If 2+l6-xl=10 and x>0 - what is the value of 2x?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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

20. If (Square Root: x-1)+5=12 - what is the value of x/2?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

21. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
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.
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

22. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
Cross multiply.
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

23. 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?
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

24. Multiplying and Dividing Roots
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.
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use the formula distance=rate*time and its variations to help in this question.

25. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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

26. Dividing Fractions
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

27. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Part=Percent x Whole
Use simple numbers like 1 and 2 and see what happens.
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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

28. Multiply and Divide Positive and Negative Numbers
A(2)+b(2)=c(2)
The value that appears the most often.
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.
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

29. 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.
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.
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.

30. Simplifying Square Roots
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.
Just add or subtract the coefficients in front of the radicals.
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

31. Knowing if an Integer is a Multiple of 2 or 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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
VofaRS=lwh
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. An Important Property of a Line Tangent to a Circle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.

33. Finding the Area of a Circle
(pie)r(squared)
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Put each number in the original ratio over the sum of the numbers.

34. If the average of a - b - and 48 is 48 - what is the value of a + b?
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Switch the numerator and denominator.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

35. Dividing Expressions with Exponents that Have a Common Base
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Average the smallest and largest number
Average: Sum of the Terms/Number of the Terms
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

36. Finding the Surface Area of a Rectangular Solid
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

37. Difference Between a Factor and a Multiple
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Multiply the numerators and multiply the denominators.
-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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

38. Numbers that are Relatively Prime
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.
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
Get the absolute value equation by itself. Solve.

39. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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.
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
Cross multiply.

40. Comparing the values of two or more Fractions
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Express them with a common denominator.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

41. Finding the Area of a Triangle

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42. Multiplying Binomials
Multiply the numerators and multiply the denominators.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Use the units to keep things straight - Snowfall inches/hours
Two relatively prime numbers are integers that have no common factor other than 1.

43. PEMDAS
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Put the equation into y=mx+b-- in which case b is the y-intercept.

44. Finding the Circumference of a Circle
Use the distributive property then combine the like terms.
Average the smallest and largest number
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
2(pie)r

45. If x(2)=7x+18 - what is the positive value of x?
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
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

46. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Factor out and cancel all factors the numerator and denominator have in common.
Use the distributive property then combine the like terms.

47. Properties of Similar Triangles
Put each number in the original ratio over the sum of the numbers.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
VofaRS=lwh
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

48. Finding the Volume of a Cylinder
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
VofaC: (pie)r(2)h

49. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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
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.
Average the smallest and largest number
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.

50. What types of angles are formed when a transversal cross parallel lines?
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.
Four equal acute angles and four equal obtuse angles.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
A(2)+b(2)=c(2)