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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 Sum of the Interior Angles of a Polygon
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
Multiply the numerators and multiply the denominators.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

2. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply the exponents - (x^3)^4=x^3*4=x^12

3. If the average of a - b - and 48 is 48 - what is the value of a + b?
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use simple numbers like 1 and 2 and see what happens.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

4. Finding the Area of a Triangle

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5. Expressing the Union and Intersection of Sets
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Two relatively prime numbers are integers that have no common factor other than 1.
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

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

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7. Knowing if an Integer is a Multiple of 2 or 4
Find a common denominator - then add or subtract the numerators.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
-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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

8. Finding the GCF of Two or More Numbers
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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

9. Solving a System of Equations
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.
Switch the numerator and denominator.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

10. If 4(x(2)-10x+25) - then what is the value of x?
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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 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.

11. Definition of an Integer
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

12. Finding the Length of an Arc in a Circle

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13. What are Two Special Pythagorean Triples?

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14. Direct Variation and Inverse Variation
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.
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.
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

15. Finding the Median of a Set of Numbers
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.
Put each number in the original ratio over the sum of the numbers.
The value that falls in the middle of the set.
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

16. Solving a Linear Equation
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Do whatever is necessary to both sides to isolate the variable.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

17. Quickly Finding the Average of a Series of Evenly Spaced Numbers
-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.
-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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Average the smallest and largest number

18. Finding the Mode of a Set of Numbers
The whole number left over after division.
Plug in the given values for the unknowns and calculate according to PEMDAS.
The value that appears the most often.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

19. Dividing Expressions with Exponents that Have a Common Base
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.
Express them with a common denominator.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

20. Average Rate and How Do You Find It
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
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
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

21. Finding the Sum of the Average of a Series of Numbers
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.
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.
Sum: Average x Number of Terms
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

22. Dividing Fractions
Subtract the smallest from the largest and add 1
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

23. Calculating Negative Exponents and Radical Exponents
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Sum: Average x Number of Terms
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

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?
FOIL: First - Outer - Inner - Last... Combine Like Terms
-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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

25. What types of angles are formed when two lines intersect?
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.
Adjacent angles are supplementary - Vertical angles are equal
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

26. If (Square Root: x-1)+5=12 - what is the value of x/2?
The value that appears the most often.
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

27. 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.
Average: Sum of the Terms/Number of the Terms
Sum: Average x Number of Terms
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

28. Scalene - Isosceles - and Equilateral Triangles
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

29. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Cancel factors common to the numerator and denominator.
Four equal acute angles and four equal obtuse angles.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

30. Comparing the values of two or more Fractions
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Express them with a common denominator.

31. Difference Between a Factor and a Multiple
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
-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.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

32. Multiplying Monomials
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 coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^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.

33. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Get the absolute value equation by itself. Solve.
Just add or subtract the coefficients in front of the radicals.

34. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

35. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

36. Solving a Radical Equation
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Isolate the radical expression and use the standard rules of algebra.

37. Evaluating an Algebraic Expression
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

38. 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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

39. What is the Pythagorean Theorem?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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
A(2)+b(2)=c(2)

40. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

41. Adding and Subtracting Monomials
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
Cross multiply.
Subtract the smallest from the largest and add 1
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

42. Knowing if an Integer is a Multiple of 5 or 10
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.
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
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.

43. Adding a Positive Number to a Negative Number
Multiply the exponents - (x^3)^4=x^3*4=x^12
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

44. Converting From a Mixed Number to an Improper Fraction
Slope=change in y/change in x
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
(x1+x2)/2 -(y1+y2)/2

45. Characteristics of a Parallelogram
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

46. Converting from an Improper Fraction to a Mixed Number
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
(x1+x2)/2 -(y1+y2)/2
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

47. Adding and Subtracting Fractions
Average the smallest and largest number
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Combine like terms.
Find a common denominator - then add or subtract the numerators.

48. What value of x is not in the domain of the function f(x)=x-2/x-3?
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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

49. If r#t=t(r)-r(t) - then what is 4#3?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
The value that appears the most often.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

50. Solving a Proportion
Cross multiply.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Switch the numerator and denominator.
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.