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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. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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%.

2. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
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
Average: Sum of the Terms/Number of the Terms
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

3. Simplifying Square Roots
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

4. Converting From a Mixed Number to an Improper Fraction
The value that falls in the middle of the set.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Sum: Average x Number of Terms
2(pie)r

5. Difference Between a Factor and a Multiple
-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.
Switch the numerator and denominator.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

6. Multiplying Expressions with Exponents that Have a Common Base
Cross multiply.
Sum: Average x Number of Terms
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

7. Adding and Subtracting Fractions
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
VofaC: (pie)r(2)h
Find a common denominator - then add or subtract the numerators.
The value that falls in the middle of the set.

8. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

9. Finding the Area of a Circle
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
(pie)r(squared)
Combine like terms.

10. If (Square Root: x-1)+5=12 - what is the value of x/2?
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.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Find a common denominator - then add or subtract the numerators.

11. Raising a Power to a Power
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

12. Finding the Slope of a Line When Given Two Points on the Line
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.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Slope=change in y/change in x

13. Finding the Distance Between Two Points on a Coordinate Graph
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Use simple numbers like 1 and 2 and see what happens.
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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

14. Evaluating an Algebraic Expression
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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

15. Definition of an Integer
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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. Finding the Domain and Range of a Function
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
FOIL: First - Outer - Inner - Last... Combine Like Terms

17. Expressing the Union and Intersection of Sets
VofaRS=lwh
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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

18. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
VofaC: (pie)r(2)h
A(2)+b(2)=c(2)
Find a common denominator - then add or subtract the numerators.

19. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
A(2)+b(2)=c(2)

20. Solving a Linear Equation
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Cancel factors common to the numerator and denominator.
Do whatever is necessary to both sides to isolate the variable.

21. Calculating Negative Exponents and Radical Exponents
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

22. Properties of the Interior and Exterior Angles of a Triangle
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 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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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. Characteristics of a Parallelogram
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Sum: Average x Number of Terms

24. Let N represent the smallest positive integer that is a multiple of 6 and 8 - but leaves a remainder of 2 when divided by 7. What is the value of N?
Average: Sum of the Terms/Number of the Terms
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Four equal acute angles and four equal obtuse angles.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

25. Dividing Fractions
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.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

26. Converting from part-to-part ratios to part-to-whole ratios
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Put each number in the original ratio over the sum of the numbers.
Factor out and cancel all factors the numerator and denominator have in common.

27. Direct Variation and Inverse Variation
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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

28. 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.
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 the formula distance=rate*time and its variations to help in this question.
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.

29. Finding the Slope When Given an Equation of a Line
Combine like terms.
(pie)r(squared)
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

30. Setting Up a Ratio
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Sum: Average x Number of Terms
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

31. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Use the distributive property then combine the like terms.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

32. Finding the Area of a Triangle

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33. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Use the distributive property then combine the like terms.
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
Average: Sum of the Terms/Number of the Terms

34. Finding the Sum of the Average of a Series of Numbers
Combine like terms.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Sum: Average x Number of Terms
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

35. What are Two Special Pythagorean Triples?

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36. Formula Used to Find Percent
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Part=Percent x Whole
Subtract the smallest from the largest and add 1

37. Average Rate and How Do You Find It
The value that appears the most often.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Multiply the exponents - (x^3)^4=x^3*4=x^12

38. Knowing if an Integer is a Multiple of 2 or 4
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
-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.
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
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.

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

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40. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

41. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Part=Percent x Whole
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

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

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43. Factoring the Difference of Two Squares
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Use the formula distance=rate*time and its variations to help in this question.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
VofaC: (pie)r(2)h

44. Comparing the values of two or more Fractions
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 variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Express them with a common denominator.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

45. Finding the Reciprocal of a Fraction
Just add or subtract the coefficients in front of the radicals.
Switch the numerator and denominator.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Get the absolute value equation by itself. Solve.

46. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

47. Finding the Volume of a Rectangular Solid
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
VofaRS=lwh
-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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

48. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Factor out and cancel all factors the numerator and denominator have in common.
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.
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

49. Increasing and Decreasing a Number by a Certain Percentage
-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.
Switch the numerator and denominator.
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

50. Definition of an Irrational Number
Two relatively prime numbers are integers that have no common factor other than 1.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.