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. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
Do whatever is necessary to both sides to isolate the variable.
-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.


2. Number of Groups - +1 Each Time
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.
Switch the numerator and denominator.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Plug in the given values for the unknowns and calculate according to PEMDAS.


3. Calculating Negative Exponents and Radical Exponents
Part=Percent x Whole
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Slope=change in y/change in x
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


4. Comparing the values of two or more Fractions
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
VofaRS=lwh
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Express them with a common denominator.


5. 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
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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Two relatively prime numbers are integers that have no common factor other than 1.


6. Finding the Mode of a Set of Numbers
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
The value that appears the most often.
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.


7. Characteristics of a Square
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


8. Knowing if an Integer is a Multiple of 5 or 10
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
The value that falls in the middle of the set.
-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.
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.


9. Simplifying an Algebraic Equation
Use simple numbers like 1 and 2 and see what happens.
Cancel factors common to the numerator and denominator.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.


10. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

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11. Properties of the Interior and Exterior Angles of a Triangle
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.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


12. Solving a Proportion
Cross multiply.
Put each number in the original ratio over the sum of the numbers.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.


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

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

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15. Solving a Radical Equation
Sum: Average x Number of Terms
Isolate the radical expression and use the standard rules of algebra.
Cross multiply.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


16. General Procedure for Multiplying Polynomials
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.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use the distributive property then combine the like terms.


17. Multiplying and Dividing Roots
Cancel factors common to the numerator and denominator.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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 the slope-intercept form: y=mx+b. The slope is m.


18. Scalene - Isosceles - and Equilateral Triangles
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
-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.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


19. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
Put the equation into y=mx+b-- in which case b is the y-intercept.
Switch the numerator and denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


20. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Express them with a common denominator.
Factor out and cancel all factors the numerator and denominator have in common.


21. Finding the Reciprocal of a Fraction
A(2)+b(2)=c(2)
Switch the numerator and denominator.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.


22. Solving an Inequality
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
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.


23. Adding and Subtracting Polynomials
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Combine like terms.
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.


24. Direct Variation and Inverse Variation
Sum: Average x Number of Terms
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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


25. 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
Plug in the given values for the unknowns and calculate according to PEMDAS.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


26. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12


27. Calculating the Probability that an Event will Take Place
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


28. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
A(2)+b(2)=c(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.


29. Simplifying a Fraction to Lowest 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.
Factor out and cancel all factors the numerator and denominator have in common.
Cross multiply.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


30. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Slope=change in y/change in x
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


31. Finding the LCM of Two or More Numbers

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32. Properties of Similar Triangles
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


33. What value of x is not in the domain of the function f(x)=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.
Use simple numbers like 1 and 2 and see what happens.
(pie)r(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


34. 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.
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.
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.
(pie)r(squared)


35. Finding the Area of a Triangle

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36. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Combine like terms.
Get the absolute value equation by itself. Solve.
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


37. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The whole number left over after division.
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
Subtract the smallest from the largest and add 1


38. 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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Find a common denominator - then add or subtract the numerators.


39. Finding the Sum of the Interior Angles of a Polygon
Plug in the given values for the unknowns and calculate according to PEMDAS.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
(x1+x2)/2 -(y1+y2)/2
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


40. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Use the distributive property then combine the like terms.
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


41. Prime Factorization of a Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Put each number in the original ratio over the sum of the numbers.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.


42. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
-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.


43. Multiplying Fractions
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.
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 the numerators and multiply the denominators.


44. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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 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.


45. If r#t=t(r)-r(t) - then what is 4#3?
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
A(2)+b(2)=c(2)
Isolate the radical expression and use the standard rules of algebra.


46. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Use the formula distance=rate*time and its variations to help in this question.


47. Dividing Expressions with Exponents that Have a Common Base
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
-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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


48. Formula Used to Find Percent
Part=Percent x Whole
-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.
Sum: Average x Number of Terms
Cross multiply.


49. What is the Pythagorean Theorem?
Put the equation into y=mx+b-- in which case b is the y-intercept.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
A(2)+b(2)=c(2)
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


50. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
VofaC: (pie)r(2)h
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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