SAT Math

Instructions:

• Answer 50 questions in 15 minutes.
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• Match each statement with the correct term.
• Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Multiplying Monomials
Do whatever is necessary to both sides to isolate the variable.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.


2. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
The whole number left over after division.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
Adjacent angles are supplementary - Vertical angles are equal


3. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
The value that appears the most often.
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
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.


4. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Two relatively prime numbers are integers that have no common factor other than 1.
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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


5. Characteristics of a Parallelogram
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Probability: Number of Favorable Outcomes/Total Possible Outcomes


6. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Part=Percent x Whole
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


7. Dividing Expressions with Exponents that Have a Common Base
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The value that falls in the middle of the set.
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. Solving a System of Equations
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.
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.
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle


9. How do you know if an integer is a multiple of 3 or 9?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Switch the numerator and denominator.
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.


10. Prime Factorization of a 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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


11. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Get the absolute value equation by itself. Solve.


12. Converting from part-to-part ratios to part-to-whole ratios
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Isolate the radical expression and use the standard rules of algebra.
Put each number in the original ratio over the sum of the numbers.
-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.


13. Difference Between a Factor and a Multiple
Cancel factors common to the numerator and denominator.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
-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.


14. Numbers that are Relatively Prime
The whole number left over after division.
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.
Two relatively prime numbers are integers that have no common factor other than 1.
Put the equation into y=mx+b-- in which case b is the y-intercept.


15. Counting Consecutive Integers
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Part=Percent x Whole
Subtract the smallest from the largest and add 1


16. 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?
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Switch the numerator and denominator.
A(2)+b(2)=c(2)


17. Finding the Mode of a Set of Numbers
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
The value that appears the most often.


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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


19. Adding and Subtracting Polynomials
(pie)r(squared)
-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.
Combine like terms.
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.


20. Definition of a Rational Number
Get the absolute value equation by itself. Solve.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.


21. An Important Property of a Line Tangent to a Circle
Get the absolute value equation by itself. Solve.
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.
The value that falls in the middle of the set.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


22. Finding the Median of a Set of Numbers
Sum: Average x Number of Terms
-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.
The value that appears the most often.
The value that falls in the middle of the set.


23. 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.
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
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)


24. Knowing if an Integer is a Multiple of 5 or 10
-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: Average x Number of Terms
Get the absolute value equation by itself. Solve.
-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.


25. Properties of a 45-45-90 Triangle
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.


26. Finding the Area of a Sector

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27. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Cancel factors common to the numerator and denominator.
Cross multiply.
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.


28. Comparing the values of two or more Fractions
Use simple numbers like 1 and 2 and see what happens.
Multiply the numerators and multiply the denominators.
Get the absolute value equation by itself. Solve.
Express them with a common denominator.


29. Counting the Total Number of Possibilities for Several Events to Occur
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
-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.
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.


30. If x(2)=7x+18 - what is the positive value of x?
The value that falls in the middle of the set.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Probability: Number of Favorable Outcomes/Total Possible Outcomes
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


31. Adding and Subtracting Fractions
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Find a common denominator - then add or subtract the numerators.


32. Finding the Volume of a Cylinder
Sum: Average x Number of Terms
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
VofaC: (pie)r(2)h
Factor out and cancel all factors the numerator and denominator have in common.


33. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Adjacent angles are supplementary - Vertical angles are equal
Plug in the given values for the unknowns and calculate according to PEMDAS.
Subtract the smallest from the largest and add 1


34. Solving a Problem Involving Rates
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use the units to keep things straight - Snowfall inches/hours
Average: Sum of the Terms/Number of the Terms
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


35. Finding the Sum of the Average of a Series of Numbers
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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
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.
Sum: Average x Number of Terms


36. Number of Groups - +1 Each Time
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


37. Adding and Subtracting Monomials
VofaC: (pie)r(2)h
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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


38. Finding the Area of a Triangle

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39. Adding a Positive Number to a Negative 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
Cancel factors common to the numerator and denominator.
Just add or subtract the coefficients in front of the radicals.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


40. Finding a Term in a Geometric Sequence
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 formula distance=rate*time and its variations to help in this question.
VofaC: (pie)r(2)h
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.


41. Definition of an Integer
Combine like 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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


42. What are Two Special Pythagorean Triples?

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43. Finding the Circumference of a Circle
2(pie)r
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
-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.


44. Finding the Length of an Arc in a Circle

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45. Calculating Negative Exponents and Radical Exponents
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.
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
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


46. If 4(x(2)-10x+25) - then what is the value of x?
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
-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.
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.


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

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48. Finding the LCM of Two or More Numbers

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49. Finding the GCF of Two or More Numbers
Two relatively prime numbers are integers that have no common factor other than 1.
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 distributive property then combine the like terms.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


50. Direct Variation and Inverse Variation
Isolate the radical expression and use the standard rules of algebra.
Multiply the numerators and multiply the denominators.
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
-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.