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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. Finding the Midpoint Between Two Points
(x1+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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Slope=change in y/change in x

2. 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.
-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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

3. Multiplying and Dividing Roots
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.
Use the distributive property then combine the like terms.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

4. Difference Between a Factor and a Multiple
VofaRS=lwh
The whole number left over after division.
Two relatively prime numbers are integers that have no common factor other than 1.
-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.

5. If (Square Root: x-1)+5=12 - what is the value of x/2?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
2(pie)r
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

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

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7. Scalene - Isosceles - and Equilateral Triangles
The value that falls in the middle of the set.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
2(pie)r

8. Numbers that are Relatively Prime
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Two relatively prime numbers are integers that have no common factor other than 1.
Part=Percent x Whole

9. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Combine like terms.

10. Increasing and Decreasing a Number by a Certain Percentage
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
VofaRS=lwh
-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.

11. 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
Isolate the radical expression and use the standard rules of algebra.
-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 formula distance=rate*time and its variations to help in this question.

12. 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
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
The value that appears the most often.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

13. Finding the Reciprocal of a Fraction
Cancel factors common to the numerator and denominator.
Switch 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.
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.

14. Convert From a Fraction to a Decimal - Vice Versa
A(2)+b(2)=c(2)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
VofaC: (pie)r(2)h
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.

15. Expressing the Union and Intersection of Sets
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
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

16. Definition of an Irrational Number
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Probability: Number of Favorable Outcomes/Total Possible Outcomes

17. Finding a Term in a Geometric Sequence
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 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.
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.
Two relatively prime numbers are integers that have no common factor other than 1.

18. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
Use the units to keep things straight - Snowfall inches/hours
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
(x1+x2)/2 -(y1+y2)/2

19. What is the positive difference between the answers to the equation 35+x(2)=12x?

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

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21. Characteristics of a Square
Use the formula distance=rate*time and its variations to help in this question.
Average the smallest and largest number
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
VofaRS=lwh

22. 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.
Do whatever is necessary to both sides to isolate the variable.
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.

23. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Express them with a common denominator.

24. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
VofaC: (pie)r(2)h
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.

25. Finding the Volume of a Cylinder
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
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.
VofaC: (pie)r(2)h

26. 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?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.

27. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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

28. Properties of the Interior and Exterior Angles of a Triangle
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Put each number in the original ratio over the sum of the numbers.
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.

29. Definition of a Rational Number
The value that appears the most often.
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.
VofaRS=lwh
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

30. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Find a common denominator - then add or subtract the numerators.
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
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.

31. Adding and Subtracting Fractions
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Find a common denominator - then add or subtract the numerators.
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.

32. Factoring a Polynomial ('FOIL in Reverse')
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

33. 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
Just add or subtract the coefficients in front of the radicals.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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

34. If 2+l6-xl=10 and x>0 - what is the value of 2x?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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
Get the absolute value equation by itself. Solve.

35. What are Two Special Pythagorean Triples?

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36. Multiplying Binomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Sum: Average x Number of Terms
FOIL: First - Outer - Inner - Last... Combine Like Terms

37. Comparing the values of two or more Fractions
Express them with a common denominator.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
-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.
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.

38. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
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.
Use the units to keep things straight - Snowfall inches/hours
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.

39. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
-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

40. Counting the Total Number of Possibilities for Several Events to Occur
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.
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.
Cross multiply.
Subtract the smallest from the largest and add 1

41. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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 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
(x1+x2)/2 -(y1+y2)/2
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.

42. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
-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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

43. Definition of an Integer
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Slope=change in y/change in x
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Just add or subtract the coefficients in front of the radicals.

44. An Important Property of a Line Tangent to a Circle
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
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.
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.

45. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Four equal acute angles and four equal obtuse angles.
VofaC: (pie)r(2)h

46. Finding the Missing Number in a Series When You are Given the Average
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

47. 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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

48. If 4(x(2)-10x+25) - then what is the value of x?
Sum: Average x Number of Terms
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

49. Adding and Subtracting Monomials
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Slope=change in y/change in x
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

50. If r#t=t(r)-r(t) - then what is 4#3?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Average the smallest and largest number