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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. Dividing Fractions
A(2)+b(2)=c(2)
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Sum: Average x Number of Terms

2. Finding the Length of an Arc in a Circle

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3. Finding the Volume of a Rectangular Solid
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.
Slope=change in y/change in x
VofaRS=lwh

4. Adding and Subtracting Roots
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Just add or subtract the coefficients in front of the radicals.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of 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.

5. Finding the y-intercept When Given an Equation of a Line
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Multiply the numerators and multiply the denominators.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Use the formula distance=rate*time and its variations to help in this question.

6. Setting Up a Ratio
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
-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.

7. Simplifying Square Roots
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Multiply the numerators and multiply the denominators.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

8. Multiplying and Dividing Roots
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.

9. Number of Groups - +1 Each Time
Do whatever is necessary to both sides to isolate the variable.
Plug in the given values for the unknowns and calculate according to PEMDAS.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

10. Scalene - Isosceles - and Equilateral Triangles
2(pie)r
Put the equation into y=mx+b-- in which case b is the y-intercept.
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

11. Raising a Power to a Power
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^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
Multiply the exponents - (x^3)^4=x^3*4=x^12

12. Finding the Reciprocal of a Fraction
Four equal acute angles and four equal obtuse angles.
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.
Average the smallest and largest number
Switch the numerator and denominator.

13. Simplifying a Fraction to Lowest Terms
Use the units to keep things straight - Snowfall inches/hours
Use the distributive property then combine the like terms.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Factor out and cancel all factors the numerator and denominator have in common.

14. Dividing 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 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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

15. Converting From a Mixed Number to an Improper Fraction
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
(x1+x2)/2 -(y1+y2)/2
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

16. Finding the Mode of a Set of Numbers
The value that appears the most often.
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

17. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The value that falls in the middle of the set.
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

18. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

19. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

20. Calculating Negative Exponents and Radical Exponents
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.
Part=Percent x Whole
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
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

21. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Use simple numbers like 1 and 2 and see what happens.
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

22. Formula Used to Find Percent
Part=Percent x Whole
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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
VofaC: (pie)r(2)h

23. Factoring the Difference of Two Squares
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.
The value that appears the most often.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Just add or subtract the coefficients in front of the radicals.

24. 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?
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

25. General Procedure for Multiplying Polynomials
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Use the distributive property then combine the like terms.
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.

26. Adding and Subtracting Polynomials
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.
Combine like terms.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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

27. Finding the Sum of the Average of a Series of Numbers
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Sum: Average x Number of Terms
Average the smallest and largest number

28. Finding the Missing Number in a Series When You are Given the Average
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.
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 solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

29. Finding the Area of a Circle
(pie)r(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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

30. Finding the Circumference of a Circle
2(pie)r
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
(x1+x2)/2 -(y1+y2)/2
Multiply the numerators and multiply the denominators.

31. Finding the Area of a Sector

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32. Finding the Volume of a Cylinder
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Combine like terms.
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

33. Difference Between a Factor and a Multiple
Slope=change in y/change in 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 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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

34. Simplifying an Algebraic Equation
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Cancel factors common to the numerator and denominator.
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.

35. What is the Triangle Inequality Theorem?
A(2)+b(2)=c(2)
VofaRS=lwh
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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. Multiplying Fractions
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Multiply the numerators and multiply the denominators.
2(pie)r
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

37. Characteristics of a Square
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Switch the numerator and denominator.

38. Factoring a Polynomial ('FOIL in Reverse')
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.

39. Properties of the Interior and Exterior Angles of a Triangle
Multiply the exponents - (x^3)^4=x^3*4=x^12
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
-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.

40. Finding the GCF of Two or More Numbers
Switch the numerator and denominator.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
-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.

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

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42. Knowing if an Integer is a Multiple of 5 or 10
-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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
The value that falls in the middle of the set.

43. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
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.

44. Convert From a Fraction to a Decimal - Vice Versa
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Do whatever is necessary to both sides to isolate the variable.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

45. If (Square Root: x-1)+5=12 - what is the value of x/2?
Cancel factors common to the numerator and denominator.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

46. 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?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

47. 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
VofaC: (pie)r(2)h
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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
A(2)+b(2)=c(2)

48. Direct Variation and Inverse Variation
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

49. What is the Pythagorean Theorem?
A(2)+b(2)=c(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.
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
Average: Sum of the Terms/Number of the Terms

50. 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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.