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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. Factoring the Difference of Two Squares
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.
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
2(pie)r

2. Finding the Slope of a Line When Given Two Points on the Line
Switch the numerator and denominator.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Slope=change in y/change in x

3. Properties of Similar Triangles
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

4. Adding and Subtracting Polynomials
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.
Isolate the radical expression and use the standard rules of algebra.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Combine like terms.

5. Scalene - Isosceles - and Equilateral Triangles
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
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.

6. If the average of a - b - and 48 is 48 - what is the value of a + b?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

7. 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?
-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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Use the formula distance=rate*time and its variations to help in this question.

8. Finding the GCF of Two or More Numbers
Sum: Average x Number of Terms
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Slope=change in y/change in x
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

9. Calculating Negative Exponents and Radical Exponents
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.

10. Properties of the Interior and Exterior Angles of a Triangle
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.
Put each number in the original ratio over the sum of the numbers.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

11. Raising a Power to a Power
-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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply the exponents - (x^3)^4=x^3*4=x^12

12. What is the Triangle Inequality Theorem?
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
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.

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

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14. Formula to Find Average
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Average: Sum of the Terms/Number of the Terms
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.

15. Characteristics of a Rectangle
-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.
Use simple numbers like 1 and 2 and see what happens.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

16. Solving a System of Equations
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
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
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.

17. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Factor out and cancel all factors the numerator and denominator 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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.

18. Prime Factorization of a Number
Average: Sum of the Terms/Number of the Terms
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Express them with a common denominator.

19. What types of angles are formed when a transversal cross parallel lines?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Four equal acute angles and four equal obtuse angles.
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.

20. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
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 formula distance=rate*time and its variations to help in this question.
-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.

21. Finding the y-intercept When Given an Equation of a Line
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
Put each number in the original ratio over the sum of the numbers.
Put the equation into y=mx+b-- in which case b is the y-intercept.

22. Evaluating an Algebraic Expression
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

23. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.
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.

24. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Factor out and cancel all factors the numerator and denominator have in common.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use simple numbers like 1 and 2 and see what happens.
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.

25. Converting from an Improper Fraction to a Mixed Number
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.
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
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms

26. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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 formula distance=rate*time and its variations to help in this question.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

27. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
Use the formula distance=rate*time and its variations to help in this question.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

28. Finding the Volume of a Cylinder
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
VofaC: (pie)r(2)h
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.
Part=Percent x Whole

29. Finding the Volume of a Rectangular Solid
Four equal acute angles and four equal obtuse angles.
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.
VofaC: (pie)r(2)h
VofaRS=lwh

30. Properties of a 45-45-90 Triangle
Multiply the exponents - (x^3)^4=x^3*4=x^12
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.

31. Converting from part-to-part ratios to part-to-whole ratios
Slope=change in y/change in x
Just add or subtract the coefficients in front of the radicals.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Put each number in the original ratio over the sum of the numbers.

32. PEMDAS
Put the equation into y=mx+b-- in which case b is the y-intercept.
Average: Sum of the Terms/Number of the Terms
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

33. Expressing the Union and Intersection of Sets
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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

34. Definition of Remainder
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
The whole number left over after division.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

35. 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?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Do whatever is necessary to both sides to isolate the variable.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

36. Counting the Total Number of Possibilities for Several Events to Occur
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.
-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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
2(pie)r

37. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
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.
Do whatever is necessary to both sides to isolate the variable.

38. Comparing the values of two or more Fractions
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Isolate the radical expression and use the standard rules of algebra.
The value that falls in the middle of the set.
Express them with a common denominator.

39. Knowing if an Integer is a Multiple of 5 or 10
Subtract the smallest from the largest and add 1
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
-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.
Two relatively prime numbers are integers that have no common factor other than 1.

40. If 4(x(2)-10x+25) - then what is the value of x?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

41. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Combine like terms.

42. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Sum: Average x Number of Terms
Cross multiply.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

43. If x(2)=7x+18 - what is the positive value of x?
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Isolate the radical expression and use the standard rules of algebra.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

44. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

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45. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Cancel factors common to the numerator and denominator.
Multiply the numerators and multiply the denominators.
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

46. Formula Used to Find Percent
Multiply the numerators and multiply the denominators.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Part=Percent x Whole

47. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Slope=change in y/change in x
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Factor out and cancel all factors the numerator and denominator have in common.

48. Finding the Surface Area of a Rectangular Solid
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

49. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-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.
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

50. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%