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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. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Use the formula distance=rate*time and its variations to help in this question.
Average the smallest and largest number
(x1+x2)/2 -(y1+y2)/2
Plug in the given values for the unknowns and calculate according to PEMDAS.

2. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
Plug in the given values for the unknowns and calculate according to PEMDAS.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.

3. What types of angles are formed when a transversal cross parallel lines?
Use the units to keep things straight - Snowfall inches/hours
(pie)r(squared)
2(pie)r
Four equal acute angles and four equal obtuse angles.

4. 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
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.

5. 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
Adjacent angles are supplementary - Vertical angles are equal
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-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.

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

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7. General Procedure for Multiplying Polynomials
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use the distributive property then combine the like terms.

8. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
-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.
VofaC: (pie)r(2)h
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

9. Definition of Remainder
The whole number left over after division.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
VofaRS=lwh
Two relatively prime numbers are integers that have no common factor other than 1.

10. Properties of the Interior and Exterior Angles of a Triangle
-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.
Use simple numbers like 1 and 2 and see what happens.
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.
Slope=change in y/change in x

11. Average Rate and How Do You Find It
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Sum: Average x Number of Terms
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. Finding the GCF of Two or More Numbers
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
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.
Find a common denominator - then add or subtract the numerators.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

13. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
A(2)+b(2)=c(2)

14. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
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.
Do whatever is necessary to both sides to isolate the variable.

15. Convert From a Fraction to a Decimal - Vice Versa
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.
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
Combine like terms.

16. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Factor out and cancel all factors the numerator and denominator have in common.
Get the absolute value equation by itself. Solve.

17. What value of x is not in the domain of the function f(x)=x-2/x-3?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Two relatively prime numbers are integers that have no common factor other than 1.
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

18. Converting from an Improper Fraction to a Mixed Number
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
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.

19. Solving a Linear Equation
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
Do whatever is necessary to both sides to isolate the variable.
Four equal acute angles and four equal obtuse angles.
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.

20. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
Find a common denominator - then add or subtract the numerators.
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.
Subtract the smallest from the largest and add 1

21. 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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Multiply the numerators and multiply the denominators.
Factor out and cancel all factors the numerator and denominator have in common.

22. Properties of a 30-60-90 Triangle
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
(pie)r(squared)

23. 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
Express them with a common denominator.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

24. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The whole number left over after division.

25. Expressing the Union and Intersection of Sets
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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
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

26. Properties of Similar Triangles
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use the distributive property then combine the like terms.

27. Difference Between a Factor and a Multiple
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
-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.
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
(x1+x2)/2 -(y1+y2)/2

28. Finding the Area of a Sector

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29. Solving an Inequality
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Isolate the radical expression and use the standard rules of algebra.

30. Multiplying and Dividing Roots
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 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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

31. Multiply and Divide Positive and Negative Numbers
Two relatively prime numbers are integers that have no common factor other than 1.
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.
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

32. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Use the units to keep things straight - Snowfall inches/hours
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

33. Finding the LCM of Two or More Numbers

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34. Dividing Fractions
Use simple numbers like 1 and 2 and see what happens.
(pie)r(squared)
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

35. Adding and Subtracting Monomials
Put each number in the original ratio over the sum of the numbers.
Find a common denominator - then add or subtract the numerators.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.

36. PEMDAS
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

37. Finding the Surface Area of a Rectangular Solid
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

38. Definition of a Rational Number
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
-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.

39. Converting from part-to-part ratios to part-to-whole ratios
Multiply the numerators and multiply the denominators.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Put each number in the original ratio over the sum of the numbers.
Use the formula distance=rate*time and its variations to help in this question.

40. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

41. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Plug in the given values for the unknowns and calculate according to PEMDAS.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of 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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

42. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Subtract the smallest from the largest and add 1
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Sum: Average x Number of Terms

43. Determining Absolute Value of a Number
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

44. Finding the Median of a Set of Numbers
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
The value that falls in the middle of the set.

45. 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?
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
Combine like terms.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

46. What types of angles are formed when two lines intersect?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Adjacent angles are supplementary - Vertical angles are equal

47. What Does Solving In Terms of Mean?
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
-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.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

48. Converting From a Mixed Number to an Improper Fraction
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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
(x1+x2)/2 -(y1+y2)/2
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

49. If (Square Root: x-1)+5=12 - what is the value of x/2?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

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

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