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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. If 3(3x)=9(x+2) - what is the value of x?
Two relatively prime numbers are integers that have no common factor other than 1.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
-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.

2. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
-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.
The whole number left over after division.
Get the absolute value equation by itself. Solve.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

3. If r#t=t(r)-r(t) - then what is 4#3?
The value that falls in the middle of the set.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

4. Properties of Similar Triangles
-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 number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

5. Simplifying an Algebraic Equation
Average the smallest and largest number
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
Cancel factors common to the numerator and denominator.
Two relatively prime numbers are integers that have no common factor other than 1.

6. Simplifying a Fraction to Lowest Terms
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Factor out and cancel all factors the numerator and denominator have in common.
(x1+x2)/2 -(y1+y2)/2

7. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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
Four equal acute angles and four equal obtuse angles.
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

8. Finding the LCM of Two or More Numbers

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9. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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
Put the equation into y=mx+b-- in which case b is the y-intercept.
Get the absolute value equation by itself. Solve.

10. Finding the Volume of a Cylinder
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
Isolate the radical expression and use the standard rules of algebra.
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.
VofaC: (pie)r(2)h

11. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Sum: Average x Number of Terms
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

12. Multiply and Divide Positive and Negative Numbers
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
Switch the numerator and denominator.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.

13. Multiplying and Dividing Roots
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)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.

14. Comparing the values of two or more Fractions
Express them with a common denominator.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

15. Characteristics of a Parallelogram
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

16. Dividing Expressions with Exponents that Have a Common Base
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Four equal acute angles and four equal obtuse angles.
The value that appears the most often.

17. Characteristics of a Square
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Factor out and cancel all factors the numerator and denominator have in common.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

18. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
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
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
Isolate the radical expression and use the standard rules of algebra.

19. Finding the Distance Between Two Points on a Coordinate Graph
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
-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 the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

20. Finding the Circumference of a Circle
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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

21. What Does Solving In Terms of Mean?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use simple numbers like 1 and 2 and see what happens.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

22. Factoring the Difference of Two Squares
Isolate the radical expression and use the standard rules of algebra.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

23. Converting from part-to-part ratios to part-to-whole ratios
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
Four equal acute angles and four equal obtuse angles.
Cancel factors common to the numerator and denominator.
Put each number in the original ratio over the sum of the numbers.

24. Prime Factorization of a Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Part=Percent x Whole
Combine like terms.
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.

25. How do you know if an integer is a multiple of 3 or 9?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Sum: Average x Number of Terms
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.

26. Scalene - Isosceles - and Equilateral Triangles
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.
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.
Just add or subtract the coefficients in front of the radicals.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

27. 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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Combine like terms.

28. Calculating the Probability that an Event will Take Place
VofaRS=lwh
Probability: Number of Favorable Outcomes/Total Possible Outcomes
VofaC: (pie)r(2)h
Part=Percent x Whole

29. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The whole number left over after division.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the units to keep things straight - Snowfall inches/hours

30. Finding the Slope When Given an Equation of a Line
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

31. PEMDAS
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
An integer is divisible by 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.
2(pie)r
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

32. Finding the Missing Number in a Series When You are Given the Average
Use simple numbers like 1 and 2 and see what happens.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.

33. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Slope=change in y/change in x
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
-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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

34. Quickly Finding the Average of a Series of Evenly Spaced Numbers
-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.
Sum: Average x Number of Terms
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Average the smallest and largest number

35. Finding a Term in a Geometric Sequence
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Use the distributive property then combine the like terms.

36. If x(2)=7x+18 - what is the positive value of x?
Part=Percent x Whole
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Just add or subtract the coefficients in front of the radicals.

37. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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 number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

38. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The value that falls in the middle of the set.
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.

39. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

40. Direct Variation and Inverse Variation
Cross multiply.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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

41. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Average the smallest and largest number
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

42. Finding the Area of a Triangle

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43. Converting from an Improper Fraction to a Mixed Number
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

44. 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?
Cross multiply.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
(pie)r(squared)

45. Setting Up a Ratio
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
The whole number left over after division.
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.

46. 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?
Plug in the given values for the unknowns and calculate according to PEMDAS.
Adjacent angles are supplementary - Vertical angles are equal
Use simple numbers like 1 and 2 and see what happens.
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.

47. Properties of a 45-45-90 Triangle
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

48. Counting the Total Number of Possibilities for Several Events to Occur
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Use the units to keep things straight - Snowfall inches/hours
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. Definition of Remainder
A(2)+b(2)=c(2)
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.
The whole number left over after division.
The value that falls in the middle of the set.

50. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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
Adjacent angles are supplementary - Vertical angles are equal
A(2)+b(2)=c(2)