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 Volume of a Cylinder
VofaC: (pie)r(2)h
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


2. 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?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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
Use the formula distance=rate*time and its variations to help in this question.


3. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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
Adjacent angles are supplementary - Vertical angles are equal


4. Finding the Rate of Speed
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
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
Use the formula distance=rate*time and its variations to help in this question.


5. Dividing Fractions
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


6. Properties of a 30-60-90 Triangle
Express them with a common denominator.
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 y=mx+b-- in which case b is the y-intercept.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


7. 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.
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
VofaC: (pie)r(2)h


8. Raising a Power to a Power
Cancel factors common to the numerator and denominator.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Put each number in the original ratio over the sum of the numbers.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


9. Definition of an Irrational Number
Two relatively prime numbers are integers that have no common factor other than 1.
(x1+x2)/2 -(y1+y2)/2
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.


10. Solving a Proportion
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
The value that falls in the middle of the set.
Cross multiply.
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.


11. Finding the Reciprocal of a Fraction
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 of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
Switch the numerator and denominator.


12. Finding the Sum of the Average of a Series of Numbers
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.
Slope=change in y/change in x
Sum: Average x Number of 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.


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

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14. 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.
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.
-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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


15. Finding the Domain and Range of a Function
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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


16. Number of Groups - +1 Each Time
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


17. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Multiply the numerators and multiply the denominators.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


18. Formula Used to Find Percent
2(pie)r
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.
Part=Percent x Whole
Cancel factors common to the numerator and denominator.


19. Numbers that are Relatively Prime
-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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Two relatively prime numbers are integers that have no common factor other than 1.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


20. How do you know if an integer is a multiple of 3 or 9?
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.
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.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


21. Finding the Length of an Arc in a Circle

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22. Calculating the Probability that an Event will Take Place
Do whatever is necessary to both sides to isolate the variable.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.


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

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24. Adding a Positive Number to a Negative Number
(x1+x2)/2 -(y1+y2)/2
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


25. 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%
Isolate the radical expression and use the standard rules of algebra.
Average the smallest and largest number
The whole number left over after division.


26. Difference Between a Factor and a Multiple
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.
-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 value that falls in the middle of the set.


27. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
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.
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-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


28. 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
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle


29. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Slope=change in y/change in 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.


30. If 3(3x)=9(x+2) - what is the value of x?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Just add or subtract the coefficients in front of the radicals.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Subtract the smallest from the largest and add 1


31. Solving a Linear Equation
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Do whatever is necessary to both sides to isolate the variable.
-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.
Express them with a common denominator.


32. Adding and Subtracting Monomials
Plug in the given values for the unknowns and calculate according to PEMDAS.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Use the formula distance=rate*time and its variations to help in this question.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


33. Simplifying Square Roots
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Get the absolute value equation by itself. Solve.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


34. Knowing if an Integer is a Multiple of 5 or 10
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.
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.
-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.
VofaC: (pie)r(2)h


35. Finding the Area of a Sector

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36. 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?
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


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

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38. Finding the Missing Number in a Series When You are Given the Average
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Put each number in the original ratio over the sum of the numbers.


39. Convert From a Fraction to a Decimal - Vice Versa
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Express them with a common denominator.


40. If r#t=t(r)-r(t) - then what is 4#3?
Put the equation into y=mx+b-- in which case b is the y-intercept.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Switch the numerator and denominator.


41. Direct Variation and Inverse Variation
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


42. Dividing Expressions with Exponents that Have a Common Base
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


43. Finding the Median of a Set of Numbers
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.
Four equal acute angles and four equal obtuse angles.
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.


44. Prime Factorization of a Number
Cross multiply.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Multiply the numerators and multiply the denominators.
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


45. What value of x is not in the domain of the function f(x)=x-2/x-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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
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


46. 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
Subtract the smallest from the largest and add 1
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


47. Finding the Sum of the Interior Angles of a Polygon
Sum: Average x Number of Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


48. Scalene - Isosceles - and Equilateral Triangles
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
Use the distributive property then combine the like terms.
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.


49. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Use the formula distance=rate*time and its variations to help in this question.


50. Solving a System of Equations
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.
Use simple numbers like 1 and 2 and see what happens.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.