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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. 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?
Adjacent angles are supplementary - Vertical angles are equal
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
2(pie)r

2. Number of Groups - +1 Each Time
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
VofaC: (pie)r(2)h
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

3. What Does Solving In Terms of Mean?
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.

4. Setting Up a Ratio
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
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 the numerators and multiply the denominators.

5. Solving a Linear Equation
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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
Do whatever is necessary to both sides to isolate the variable.

6. 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?
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
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
Express them with a common denominator.

7. Difference Between a Factor and a Multiple
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Combine like terms.
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
-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. Raising a Power to a Power
Get the absolute value equation by itself. Solve.
-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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

9. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
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.
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.

10. Finding the Missing Number in a Series When You are Given the Average
Switch the numerator and denominator.
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.
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.
Sum: Average x Number of Terms

11. Finding the Sum of the Average of a Series of Numbers
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
(x1+x2)/2 -(y1+y2)/2
VofaC: (pie)r(2)h
Sum: Average x Number of Terms

12. What types of angles are formed when two lines intersect?
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use the distributive property then combine the like terms.
Adjacent angles are supplementary - Vertical angles are equal
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

13. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

14. Finding the Reciprocal of a Fraction
Multiply the numerators and multiply the denominators.
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
Switch the numerator and denominator.
-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.

15. Properties of a 30-60-90 Triangle
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

16. Finding the Median of a Set of Numbers
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
The value that falls in the middle of the set.
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

17. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
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
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

18. 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.
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.
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
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.

19. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.

20. Characteristics of a Parallelogram
(x1+x2)/2 -(y1+y2)/2
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

21. What is the Triangle Inequality Theorem?
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
-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.

22. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Combine like terms.

23. 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.
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 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 the smallest and largest number

24. Properties of the Interior and Exterior Angles of a Triangle
Use the units to keep things straight - Snowfall inches/hours
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

25. Dividing Fractions
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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. Determining Absolute Value of a Number
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Sum: Average x Number of Terms

27. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Sum: Average x Number of 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
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.

28. Numbers that are Relatively Prime
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
Two relatively prime numbers are integers that have no common factor other than 1.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
2(pie)r

29. Definition of Remainder
The whole number left over after division.
Find a common denominator - then add or subtract the numerators.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-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.

30. Definition of a Rational Number
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
-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.
Combine like terms.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

31. Finding the GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
The value that falls in the middle of the set.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

32. Evaluating an Algebraic Expression
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.
Factor out and cancel all factors the numerator and denominator have in common.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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

33. Finding the Area of a Triangle

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34. Dividing Expressions with Exponents that Have a Common Base
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

35. Finding the Rate of Speed
Four equal acute angles and four equal obtuse angles.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

36. Finding the Volume of a Rectangular Solid
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
VofaRS=lwh
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

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

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38. PEMDAS
-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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.

39. Finding the Slope When Given an Equation of a Line
Use the units to keep things straight - Snowfall inches/hours
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

40. 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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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
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.

41. Finding the Mode of a Set of Numbers
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The value that appears the most often.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

42. Finding the Circumference of a Circle
Subtract the smallest from the largest and add 1
The value that falls in the middle of the set.
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.
2(pie)r

43. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to 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.

44. If 4(x(2)-10x+25) - then what is the value of x?
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.
Part=Percent x Whole
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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

45. Multiplying Monomials
-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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The value that appears the most often.

46. Formula to Find Average
Multiply the numerators and multiply the denominators.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Average: Sum of the Terms/Number of the Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.

47. Prime Factorization of a Number
Switch the numerator and denominator.
Average the smallest and largest number
Subtract the smallest from the largest and add 1
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

48. 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
Express them with a common denominator.
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.
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

49. If (Square Root: x-1)+5=12 - what is the value of x/2?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

50. Solving a Radical Equation
Two relatively prime numbers are integers that have no common factor other than 1.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Isolate the radical expression and use the standard rules of algebra.
Adjacent angles are supplementary - Vertical angles are equal