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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. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Sum: Average x Number of Terms
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

2. Finding the Area of a Triangle
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
A(2)+b(2)=c(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.

3. An Important Property of a Line Tangent to a Circle
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Switch the numerator and denominator.
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.

4. Properties of a 45-45-90 Triangle
-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 one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
VofaRS=lwh
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

5. Converting from part-to-part ratios to part-to-whole ratios
Two relatively prime numbers are integers that have no common factor other than 1.
A(2)+b(2)=c(2)
Find a common denominator - then add or subtract the numerators.
Put each number in the original ratio over the sum of the numbers.

6. 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?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Two relatively prime numbers are integers that have no common factor other than 1.
Sum: Average x Number of 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.

7. Multiplying Binomials
The value that falls in the middle of the set.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Cross multiply.

8. Raising a Power to a Power
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.
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12

9. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Subtract the smallest from the largest and add 1
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

10. Knowing if an Integer is a Multiple of 2 or 4
-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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

11. Properties of a 30-60-90 Triangle
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.

12. Multiplying 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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

13. Finding the Area of a Sector
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
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
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
VofaC: (pie)r(2)h

14. Formula to Find Average
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Average: Sum of the Terms/Number of the Terms

15. Adding and Subtracting Roots
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.
Just add or subtract the coefficients in front of the radicals.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Cross multiply.

16. What are Two Special Pythagorean Triples?
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
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms

17. Finding the LCM of Two or More Numbers
Multiply the numerators and multiply the denominators.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

18. Finding the Area of a Circle
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
(pie)r(squared)
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.

19. Finding the Missing Number in a Series When You are Given the Average
(x1+x2)/2 -(y1+y2)/2
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

20. If 4(x(2)-10x+25) - then what is the value of x?
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
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.
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.

21. Counting the Total Number of Possibilities for Several Events to Occur
Part=Percent x Whole
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.
Adjacent angles are supplementary - Vertical angles are equal
Do whatever is necessary to both sides to isolate the variable.

22. What is the Triangle Inequality Theorem?
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Switch the numerator and denominator.
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.

23. Finding the Volume of a Rectangular Solid
VofaRS=lwh
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.
Switch the numerator and denominator.
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.

24. Converting from an Improper Fraction to a Mixed Number
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
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.
Adjacent angles are supplementary - Vertical angles are equal

25. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

26. Finding the Length of an Arc in a Circle
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
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

27. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Four equal acute angles and four equal obtuse angles.
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.
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

28. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.

29. What Does Solving In Terms of Mean?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Cancel factors common to the numerator and denominator.

30. Converting From a Mixed Number to an Improper Fraction
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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 the units to keep things straight - Snowfall inches/hours

31. Multiplying and Dividing Roots
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
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.
Switch the numerator and denominator.

32. What types of angles are formed when a transversal cross parallel lines?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Get the absolute value equation by itself. Solve.
Four equal acute angles and four equal obtuse angles.
Multiply the numerators and multiply the denominators.

33. Numbers that are Relatively Prime
Adjacent angles are supplementary - Vertical angles are equal
Four equal acute angles and four equal obtuse angles.
Two relatively prime numbers are integers that have no common factor other than 1.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

34. Dividing Expressions with Exponents that Have a Common Base
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.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

35. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-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.
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.
Average the smallest and largest number

36. Finding the Midpoint Between Two Points
The value that falls in the middle of the set.
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.
(x1+x2)/2 -(y1+y2)/2
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

37. Evaluating an Algebraic Expression
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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 base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Plug in the given values for the unknowns and calculate according to PEMDAS.

38. Finding the Volume of a Cylinder
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
VofaC: (pie)r(2)h

39. Solving a Proportion
A(2)+b(2)=c(2)
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Cross multiply.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

40. How do you know if an integer is a multiple of 3 or 9?
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.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.

41. Formula Used to Find Percent
Part=Percent x Whole
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

42. Determining Absolute Value of a Number
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Cross multiply.
Adjacent angles are supplementary - Vertical angles are equal

43. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
A(2)+b(2)=c(2)
Put each number in the original ratio over the sum of the numbers.
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.
Find a common denominator - then add or subtract the numerators.

44. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Express them with a common denominator.

45. Identifying Which Number of a Fraction is the Part and Which Number is the Whole
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Sum: Average x Number of Terms
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

46. Direct Variation and Inverse Variation
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.
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
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.
Do whatever is necessary to both sides to isolate the variable.

47. Finding the Mode of a Set of Numbers
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The value that appears the most often.
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.

48. Prime Factorization of a Number
The whole number left over after division.
Sum: Average x Number of Terms
Express them with a common denominator.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

49. If x varies directly with y - and the value of x is 12 when y is 11 - what is the value of y when x is 66?
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
2(pie)r
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

50. Finding the Sum of the Average of a Series of Numbers
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
Sum: Average x Number of Terms
-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.
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.

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