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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. Comparing the values of two or more Fractions
-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.
Isolate the radical expression and use the standard rules of algebra.
Express them with a common denominator.
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. Finding the Volume of a Rectangular Solid
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
-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.
VofaRS=lwh
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

3. Average Rate and How Do You Find It
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.
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

4. Scalene - Isosceles - and Equilateral Triangles
Switch the numerator and denominator.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Use simple numbers like 1 and 2 and see what happens.

5. Adding and Subtracting Polynomials
Adjacent angles are supplementary - Vertical angles are equal
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Combine like terms.
Cross multiply.

6. Finding the Slope When Given an Equation of a Line
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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 the equation into the slope-intercept form: y=mx+b. The slope is m.

7. Solving a Problem Involving Rates
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
(x1+x2)/2 -(y1+y2)/2
Use the units to keep things straight - Snowfall inches/hours
The whole number left over after division.

8. Numbers that are Relatively Prime
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
-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.
Two relatively prime numbers are integers that have no common factor other than 1.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

9. Finding the Reciprocal of a Fraction
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Switch the numerator and denominator.
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

10. Solving a Proportion
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Cross multiply.
Get the absolute value equation by itself. Solve.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

11. General Procedure for Multiplying Polynomials
Use the formula distance=rate*time and its variations to help in this question.
Cancel factors common to the numerator and denominator.
Use the distributive property then combine the like terms.
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

12. Finding the Area of a Sector

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13. Multiplying Binomials
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

14. Multiplying and Dividing Roots
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

15. If 3(3x)=9(x+2) - what is the value of x?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
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.
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

16. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Multiply the exponents - (x^3)^4=x^3*4=x^12
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
-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.

17. Adding and Subtracting Fractions
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
Isolate the radical expression and use the standard rules of algebra.
Find a common denominator - then add or subtract the numerators.
The whole number left over after division.

18. 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?
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
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 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.

19. What is the Triangle Inequality Theorem?
Use the distributive property then combine the like 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.
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

20. Definition of Remainder
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The whole number left over after division.

21. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

22. Increasing and Decreasing a Number by a Certain Percentage
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
The value that appears the most often.
-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.

23. Number of Groups - +1 Each Time
Factor out and cancel all factors the numerator and denominator have in common.
-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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Average: Sum of the Terms/Number of the Terms

24. 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?
Combine like terms.
2(pie)r
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

25. Dividing Fractions
Average: Sum of the Terms/Number of the Terms
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

26. Multiplying Expressions with Exponents that Have a Common Base
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Find a common denominator - then add or subtract the numerators.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

27. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Express them with a common denominator.

28. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Four equal acute angles and four equal obtuse angles.

29. 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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
-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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

30. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Combine like terms.

31. 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.
-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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

32. If the average of a - b - and 48 is 48 - what is the value of a + b?
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
VofaRS=lwh
A(2)+b(2)=c(2)

33. Converting From a Mixed Number to an Improper Fraction
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

34. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Get the absolute value equation by itself. Solve.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

35. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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

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

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37. Solving a System of Equations
Factor out and cancel all factors the numerator and denominator have in common.
Cross multiply.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.

38. Finding the Area of a Triangle

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39. Properties of the Interior and Exterior Angles of a Triangle
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 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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.

40. Finding the Sum of the Average of a Series of 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
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

41. Setting Up a Ratio
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
(pie)r(squared)

42. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Do whatever is necessary to both sides to isolate the variable.
Use simple numbers like 1 and 2 and see what happens.
(x1+x2)/2 -(y1+y2)/2
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

43. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Cancel factors common to the numerator and denominator.

44. Finding the Missing Number in a Series When You are Given the Average
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

45. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

46. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Slope=change in y/change in x
Isolate the radical expression and use the standard rules of algebra.
Get the absolute value equation by itself. Solve.

47. Finding the Volume of a Cylinder
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
VofaC: (pie)r(2)h
Find a common denominator - then add or subtract the numerators.

48. Finding the LCM of Two or More Numbers

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49. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
The whole number left over after division.
The value that appears the most often.

50. What types of angles are formed when two lines intersect?
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Adjacent angles are supplementary - Vertical angles are equal
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Use the distributive property then combine the like terms.