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SAT Math

Subjects : 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. Properties of a 45-45-90 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.
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.
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.

2. If r#t=t(r)-r(t) - then what is 4#3?
Express them with a common denominator.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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.

3. What is the Pythagorean Theorem?
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.
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(2)+b(2)=c(2)
(pie)r(squared)

4. Finding the Domain and Range of a Function
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.
Isolate the radical expression and use the standard rules of algebra.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

5. General Procedure for Multiplying Polynomials
Use the units to keep things straight - Snowfall inches/hours
Use the distributive property then combine the like terms.
VofaRS=lwh
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

6. If 2+l6-xl=10 and x>0 - what is the value of 2x?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Get the absolute value equation by itself. Solve.
VofaC: (pie)r(2)h
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.

7. 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
Use the distributive property then combine the like terms.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.

8. Factoring the Difference of Two Squares
Combine like terms.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

9. Prime Factorization of a Number
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 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.
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

10. Finding the Sum of the Interior Angles of a Polygon
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
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.

11. Finding the Volume of a Cylinder
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
VofaC: (pie)r(2)h
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.

12. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

13. Factoring a Polynomial ('FOIL in Reverse')
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
(x1+x2)/2 -(y1+y2)/2
Sum: Average x Number of Terms
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

14. Solving a Radical Equation
Do whatever is necessary to both sides to isolate the variable.
Switch the numerator and denominator.
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.
Isolate the radical expression and use the standard rules of algebra.

15. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Get the absolute value equation by itself. Solve.

16. How do you know if an integer is a multiple of 3 or 9?
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Isolate the radical expression and use the standard rules of algebra.

17. Formula Used to Find Percent
Just add or subtract the coefficients in front of the radicals.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Part=Percent x Whole
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

18. Number of Groups - +1 Each Time
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Get the absolute value equation by itself. Solve.
Cross multiply.

19. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Subtract the smallest from the largest and add 1
Adjacent angles are supplementary - Vertical angles are equal
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

20. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Four equal acute angles and four equal obtuse angles.
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.

21. Simplifying an Algebraic Equation
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 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.
Cancel factors common to the numerator and denominator.
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

22. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
Just add or subtract the coefficients in front of the radicals.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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. 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
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Average the smallest and largest number

24. Adding and Subtracting Roots
Get the absolute value equation by itself. Solve.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Just add or subtract the coefficients in front of the radicals.
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.

25. Finding the Length of an Arc in a Circle

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26. Characteristics of a Rectangle
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-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Multiply the numerators and multiply the denominators.
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.

27. Definition of an Integer
-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.
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.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

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

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29. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Average: Sum of the Terms/Number of the Terms
Express them with a common denominator.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

30. Converting From a Mixed Number to an Improper Fraction
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

31. Multiplying Expressions with Exponents that Have a Common Base
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Do whatever is necessary to both sides to isolate the variable.

32. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Average the smallest and largest number
Use the distributive property then combine the like terms.
Put each number in the original ratio over the sum of the numbers.

33. Properties of a 30-60-90 Triangle
Sum: Average x Number of Terms
FOIL: First - Outer - Inner - Last... Combine Like Terms
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.

34. Solving a Proportion
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Factor out and cancel all factors the numerator and denominator have in common.
Cross multiply.
VofaC: (pie)r(2)h

35. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
Get the absolute value equation by itself. Solve.
The whole number left over after division.
Slope=change in y/change in x

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

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37. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
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 whole number part by the denominator - then add the numerator. Keep the same denominator.
Put each number in the original ratio over the sum of the numbers.

38. Formula to Find Average
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Average: Sum of the Terms/Number of the Terms
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.

39. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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

40. Finding the Surface Area of a Rectangular Solid
Part=Percent x Whole
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

41. Multiplying Binomials
Cross multiply.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

42. Evaluating an Algebraic Expression
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

43. Adding and Subtracting Fractions
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
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
Find a common denominator - then add or subtract the numerators.

44. Multiplying and Dividing Roots
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
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.
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.

45. Simplifying a Fraction to Lowest Terms
Multiply the numerators and multiply the denominators.
Express them with a common denominator.
Factor out and cancel all factors the numerator and denominator have in common.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

46. Direct Variation and Inverse Variation
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
Multiply the numerators and multiply the denominators.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

47. Calculating Negative Exponents and Radical Exponents
Four equal acute angles and four equal obtuse angles.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Two relatively prime numbers are integers that have no common factor other than 1.

48. Finding the Volume of a Rectangular Solid
VofaRS=lwh
Get the absolute value equation by itself. Solve.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
(pie)r(squared)

49. Finding the Slope of a Line When Given Two Points on the Line
Part=Percent x Whole
Subtract the smallest from the largest and add 1
Multiply the exponents - (x^3)^4=x^3*4=x^12
Slope=change in y/change in x

50. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Four equal acute angles and four equal obtuse angles.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.