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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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1. Finding the Domain and Range of a Function
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.
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.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

2. Multiply and Divide Positive and Negative Numbers
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.
Use the units to keep things straight - Snowfall inches/hours
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
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

3. Comparing the values of two or more Fractions
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Express them with a common denominator.
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.
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.

4. 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?
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.
Combine like terms.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.

5. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Find a common denominator - then add or subtract the numerators.
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 simple numbers like 1 and 2 and see what happens.
The value that appears the most often.

6. Knowing if an Integer is a Multiple of 5 or 10
Two relatively prime numbers are integers that have no common factor other than 1.
-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.
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms

7. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

8. If 4(x(2)-10x+25) - then what is the value of x?
Factor out and cancel all factors the numerator and denominator 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.
Use simple numbers like 1 and 2 and see what happens.
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.

9. Multiplying Monomials
Find a common denominator - then add or subtract the numerators.
Use the units to keep things straight - Snowfall inches/hours
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The value that falls in the middle of the set.

10. 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.
Use the units to keep things straight - Snowfall inches/hours
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.

11. Definition of an Integer
Plug in the given values for the unknowns and calculate according to PEMDAS.
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
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

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

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13. 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.
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.
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.

14. Finding the Sum of the Average of a Series of Numbers
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.
Sum: Average x Number of Terms
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.
Slope=change in y/change in x

15. What is the Triangle Inequality Theorem?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
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.
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.

16. Properties of the Interior and Exterior Angles of a Triangle
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
-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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.

17. Simplifying Square Roots
Probability: Number of Favorable Outcomes/Total Possible Outcomes
-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.
Find a common denominator - then add or subtract the numerators.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

18. Solving a System of Equations
Use simple numbers like 1 and 2 and see what happens.
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.
Adjacent angles are supplementary - Vertical angles are equal
-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.

19. What types of angles are formed when two lines intersect?
Express them with a common denominator.
Adjacent angles are supplementary - Vertical angles are equal
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Multiply the exponents - (x^3)^4=x^3*4=x^12

20. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
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
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

21. Properties of a 30-60-90 Triangle
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
FOIL: First - Outer - Inner - Last... Combine Like Terms

22. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The whole number left over after division.
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

23. Finding a Term in a Geometric Sequence
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
Do whatever is necessary to both sides to isolate the variable.
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.

24. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

25. 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?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Do whatever is necessary to both sides to isolate the variable.
Adjacent angles are supplementary - Vertical angles are equal
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

26. If 3(3x)=9(x+2) - what is the value of x?
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

27. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
Part=Percent x Whole
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.

28. Adding and Subtracting Roots
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Just add or subtract the coefficients in front of the radicals.

29. Solving a Proportion
Cross multiply.
The value that falls in the middle of the set.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
-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.

30. Multiplying Fractions
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 numerators and multiply the denominators.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Slope=change in y/change in x

31. Direct Variation and Inverse Variation
Average: Sum of the Terms/Number of the Terms
VofaC: (pie)r(2)h
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
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.

32. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
Part=Percent x Whole
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^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.

33. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Use the distributive property then combine the like terms.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

34. Characteristics of a Parallelogram
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.

35. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Use the units to keep things straight - Snowfall inches/hours
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.

36. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

37. Convert From a Fraction to a Decimal - Vice Versa
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
A(2)+b(2)=c(2)
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.
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

38. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Use the units to keep things straight - Snowfall inches/hours
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

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

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40. Counting the Total Number of Possibilities for Several Events to Occur
Isolate the radical expression and use the standard rules of algebra.
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.
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

41. 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%.
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.
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
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.

42. Finding the Slope of a Line When Given Two Points on the Line
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
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Slope=change in y/change in x

43. Adding and Subtracting Polynomials
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.
Combine like terms.
Put each number in the original ratio over the sum of the numbers.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

44. 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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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
Do whatever is necessary to both sides to isolate the variable.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

45. Scalene - Isosceles - and Equilateral Triangles
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

46. If the average of a - b - and 48 is 48 - what is the value of a + b?
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

47. If (Square Root: x-1)+5=12 - what is the value of x/2?
Use the formula distance=rate*time and its variations to help in this question.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Switch the numerator and denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

48. Solving a Radical Equation
-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.
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.
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.

49. An Important Property of a Line Tangent to a Circle
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 equation into y=mx+b-- in which case b is the y-intercept.
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.
Factor out and cancel all factors the numerator and denominator have in common.

50. Finding the Area of a Triangle

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