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 Length of an Arc in a Circle

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2. Formula to Find Average
A(2)+b(2)=c(2)
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
(x1+x2)/2 -(y1+y2)/2
Average: Sum of the Terms/Number of the Terms


3. PEMDAS
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
VofaRS=lwh
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Multiply the exponents - (x^3)^4=x^3*4=x^12


4. Difference Between a Factor and a Multiple
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Combine like terms.
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.


5. Scalene - Isosceles - and Equilateral Triangles
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


6. Finding the Surface Area of a Rectangular Solid
Adjacent angles are supplementary - Vertical angles are equal
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.


7. Factoring the Difference of Two Squares
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Plug in the given values for the unknowns and calculate according to PEMDAS.
(pie)r(squared)
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


8. If r#t=t(r)-r(t) - then what is 4#3?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Combine like terms.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


9. 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%
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Use the distributive property then combine the like terms.


10. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


11. Finding the Area of a Sector

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12. Comparing the values of two or more Fractions
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
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
Express them with a common denominator.
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.


13. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


14. Finding the Missing Number in a Series When You are Given the Average
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.
Average the smallest and largest number
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


15. Counting Consecutive Integers
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


16. Characteristics of a Square
Plug in the given values for the unknowns and calculate according to PEMDAS.
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
Isolate the radical expression and use the standard rules of algebra.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


17. Average Rate and How Do You Find It
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


18. What Does Solving In Terms of Mean?
Four equal acute angles and four equal obtuse angles.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.


19. Finding the Median of a Set of Numbers
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The value that falls in the middle of the set.
-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.
-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.


20. Finding the Circumference of a Circle
Express them with a common denominator.
2(pie)r
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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


21. General Procedure for Multiplying Polynomials
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
Use the distributive property then combine the like terms.
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.
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


22. 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.
Switch the numerator and denominator.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


23. Finding the GCF of Two or More Numbers
Put each number in the original ratio over the sum of the numbers.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Switch the numerator and denominator.


24. Multiplying Expressions with Exponents that Have a Common Base
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


25. Finding the Reciprocal of a Fraction
The whole number left over after division.
Switch the numerator and denominator.
Slope=change in y/change in x
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


26. Solving a Problem Involving Rates
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Use the units to keep things straight - Snowfall inches/hours
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


27. Definition of Remainder
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 whole number left over after division.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.


28. Converting from part-to-part ratios to part-to-whole ratios
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
Put each number in the original ratio over the sum of the numbers.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


29. Characteristics of a Parallelogram
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.


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

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31. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle


32. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.


33. Finding the Midpoint Between Two Points
Adjacent angles are supplementary - Vertical angles are equal
(x1+x2)/2 -(y1+y2)/2
Part=Percent x Whole
Sum: Average x Number of Terms


34. Finding the Domain and Range of a Function
The value that appears the most often.
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.
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.


35. Definition of a Rational 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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
-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.


36. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Get the absolute value equation by itself. Solve.


37. What is the Pythagorean Theorem?
Average: Sum of the Terms/Number of the Terms
(x1+x2)/2 -(y1+y2)/2
FOIL: First - Outer - Inner - Last... Combine Like Terms
A(2)+b(2)=c(2)


38. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
-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.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


39. How do you know if an integer is a multiple of 3 or 9?
Use the distributive property then combine the like terms.
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 appears the most often.
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.


40. Finding the y-intercept When Given an Equation of a Line
-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 y=mx+b-- in which case b is the y-intercept.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Get the absolute value equation by itself. Solve.


41. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Get the absolute value equation by itself. Solve.


42. Finding the Slope of a Line When Given Two Points on the Line
Combine like terms.
Slope=change in y/change in x
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


43. Finding the Area of a Triangle

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44. What are Two Special Pythagorean Triples?

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45. Setting Up a Ratio
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.
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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


46. Solving a Radical Equation
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Switch the numerator and denominator.
Isolate the radical expression and use the standard rules of algebra.
Use the distributive property then combine the like terms.


47. Finding the Mode of a Set of Numbers
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The value that appears the most often.
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.


48. Properties of Similar Triangles
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.


49. Dividing Fractions
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.


50. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Isolate the radical expression and use the standard rules of algebra.