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. Expressing the Union and Intersection of Sets
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
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
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.


2. Multiplying Monomials
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


3. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


4. Properties of the Interior and Exterior Angles of a Triangle
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.
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 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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


5. Solving a Problem Involving Rates
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 the units to keep things straight - Snowfall inches/hours
(pie)r(squared)
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


6. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


7. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


8. If (Square Root: x-1)+5=12 - what is the value of x/2?
Multiply the numerators and multiply the denominators.
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.
Do whatever is necessary to both sides to isolate the variable.


9. Characteristics of a Square
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
The whole number left over after division.
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


10. Finding the Area of a Sector

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11. Finding the Distance Between Two Points on a Coordinate Graph
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


12. Finding the LCM of Two or More Numbers

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13. Simplifying a Fraction to Lowest Terms
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Factor out and cancel all factors the numerator and denominator have in common.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Use the formula distance=rate*time and its variations to help in this question.


14. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Average: Sum of the Terms/Number of the Terms


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

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16. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use the formula distance=rate*time and its variations to help in this question.
-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.


17. Adding and Subtracting Polynomials
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Combine like terms.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


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

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19. Definition of an Integer
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Subtract the smallest from the largest and add 1
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


20. Finding the Circumference of a Circle
Use the formula distance=rate*time and its variations to help in this question.
2(pie)r
Just add or subtract the coefficients in front of the radicals.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


21. Definition of Remainder
Use simple numbers like 1 and 2 and see what happens.
The whole number left over after division.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Combine like terms.


22. Direct Variation and Inverse Variation
A(2)+b(2)=c(2)
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
Isolate the radical expression and use the standard rules of algebra.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4


23. Finding the Sum of the Average of a Series of Numbers
The whole number left over after division.
Use the formula distance=rate*time and its variations to help in this question.
Sum: Average x Number of Terms
The value that appears the most often.


24. Characteristics of a Parallelogram
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.
2(pie)r
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Do whatever is necessary to both sides to isolate the variable.


25. Finding a Term in a Geometric Sequence
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 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.
(x1+x2)/2 -(y1+y2)/2
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


26. Formula Used to Find Percent
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Adjacent angles are supplementary - Vertical angles are equal
Isolate the radical expression and use the standard rules of algebra.
Part=Percent x Whole


27. Formula to Find Average
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Average: Sum of the Terms/Number of the Terms


28. Definition of an Irrational Number
Subtract the smallest from the largest and add 1
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Combine like terms.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


29. Multiply and Divide Positive and Negative Numbers
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Switch the numerator and denominator.
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.


30. Adding and Subtracting Monomials
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Put each number in the original ratio over the sum of the numbers.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


31. What is the Triangle Inequality Theorem?
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.
Adjacent angles are supplementary - Vertical angles are equal
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


32. Finding the Missing Number in a Series When You are Given the Average
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
2(pie)r
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.


33. Finding the Volume of a Rectangular Solid
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
x(2)-5x+6 - What factors of +6 also have a sum of -5? (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
VofaRS=lwh


34. Properties of Similar Triangles
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


35. Properties of a 45-45-90 Triangle
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


36. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
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.


37. Finding the Surface Area of a Rectangular Solid
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


38. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.


39. Scalene - Isosceles - and Equilateral Triangles
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Put each number in the original ratio over the sum of the numbers.
Subtract the smallest from the largest and add 1


40. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Average: Sum of the Terms/Number of the Terms
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


41. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


42. Adding and Subtracting Roots
Use the units to keep things straight - Snowfall inches/hours
-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.
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.
Just add or subtract the coefficients in front of the radicals.


43. What are Two Special Pythagorean Triples?

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44. Solving a Proportion
Cross multiply.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.


45. 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
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.
Four equal acute angles and four equal obtuse angles.
Average: Sum of the Terms/Number of the Terms


46. Dividing Fractions
Put each number in the original ratio over the sum of the numbers.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Plug in the given values for the unknowns and calculate according to PEMDAS.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


47. Finding the Mode of a Set of Numbers
The value that appears the most often.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
-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.
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.


48. Converting from an Improper Fraction to a Mixed Number
Use the distributive property then combine the like 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.
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.


49. If the average of a - b - and 48 is 48 - what is the value of a + b?
(x1+x2)/2 -(y1+y2)/2
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.


50. Multiplying and Dividing Roots
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The whole number left over after division.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.