SAT Math

Instructions:

• Answer 50 questions in 15 minutes.
• If you are not ready to take this test, you can study here.
• 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. Properties of Similar Triangles
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Do whatever is necessary to both sides to isolate the variable.


2. 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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.


3. How do you know if an integer is a multiple of 3 or 9?
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.
The whole number left over after division.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.


4. Prime Factorization of a Number
Cross multiply.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.


5. Finding the Slope When Given an Equation of a Line
Cross multiply.
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


6. Solving a Problem Involving Rates
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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 the units to keep things straight - Snowfall inches/hours
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.


7. Determining Absolute Value of a Number
Switch the numerator and denominator.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Part=Percent x Whole


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

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9. Direct Variation and Inverse Variation
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.
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


10. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


11. Adding and Subtracting Polynomials
Part=Percent x Whole
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 formula distance=rate*time and its variations to help in this question.
Combine like terms.


12. Adding and Subtracting Monomials
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Find a common denominator - then add or subtract the numerators.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


13. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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.
Use simple numbers like 1 and 2 and see what happens.
Multiply the exponents - (x^3)^4=x^3*4=x^12
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


14. If 4(x(2)-10x+25) - then what is the value of x?
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.


15. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.


16. Characteristics of a Square
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


17. Multiplying Monomials
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


18. Finding the Area of a Circle
(pie)r(squared)
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Put each number in the original ratio over the sum of the numbers.


19. Calculating the Probability that an Event will Take Place
Isolate the radical expression and use the standard rules of algebra.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


20. Finding the Rate of Speed
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
Use the formula distance=rate*time and its variations to help in this question.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


21. What is the Triangle Inequality Theorem?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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 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.
Use simple numbers like 1 and 2 and see what happens.


22. 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.
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


23. Finding the Distance Between Two Points on a Coordinate Graph
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
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


24. What types of angles are formed when two lines intersect?
2(pie)r
Express them with a common denominator.
Adjacent angles are supplementary - Vertical angles are equal
Average: Sum of the Terms/Number of the Terms


25. If r#t=t(r)-r(t) - then what is 4#3?
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.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


26. Finding the Length of an Arc in a Circle

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27. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Sum: Average x Number of Terms
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.
Get the absolute value equation by itself. Solve.


28. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


29. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Use the distributive property then combine the like terms.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Average the smallest and largest number
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.


30. Formula Used to Find Percent
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
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


31. Knowing if an Integer is a Multiple of 2 or 4
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Use the distributive property then combine the like terms.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
-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.


32. Finding the Area of a Sector

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33. Counting Consecutive Integers
Get the absolute value equation by itself. Solve.
Subtract the smallest from the largest and add 1
Two relatively prime numbers are integers that have no common factor other than 1.
Use the distributive property then combine the like terms.


34. Factoring a Polynomial ('FOIL in Reverse')
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
VofaRS=lwh
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


35. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


36. What are Two Special Pythagorean Triples?

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37. 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?
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.
Use simple numbers like 1 and 2 and see what happens.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


38. Finding the Circumference of a Circle
2(pie)r
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.


39. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
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.
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


40. Finding the Median of a Set 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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The value that falls in the middle of the set.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


41. Calculating Negative Exponents and Radical Exponents
(x1+x2)/2 -(y1+y2)/2
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
VofaRS=lwh


42. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Part=Percent x Whole


43. General Procedure for Multiplying Polynomials
Average the smallest and largest number
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 distributive property then combine the like terms.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


44. Comparing the values of two or more Fractions
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Express them with a common denominator.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle


45. Finding the Slope of a Line When Given Two Points on the Line
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Slope=change in y/change in x
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.


46. Adding a Positive Number to a Negative Number
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Express them with a common denominator.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


47. What Does Solving In Terms of Mean?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Do whatever is necessary to both sides to isolate the variable.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


48. Simplifying an Algebraic Equation
(x1+x2)/2 -(y1+y2)/2
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Cancel factors common to the numerator and denominator.


49. Properties of a 45-45-90 Triangle
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


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

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