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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. Calculating the Probability that an Event will Take Place
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

2. Solving a Proportion
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.
Cross multiply.
Slope=change in y/change in x
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

3. General Procedure for Multiplying 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.
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.
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.
Use the distributive property then combine the like terms.

4. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
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.
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.
Use simple numbers like 1 and 2 and see what happens.

5. 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?
Slope=change in y/change in x
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

6. Finding the Rate of Speed
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.
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%
Use the formula distance=rate*time and its variations to help in this question.

7. What types of angles are formed when a transversal cross parallel lines?
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Cross multiply.
Four equal acute angles and four equal obtuse angles.
Factor out and cancel all factors the numerator and denominator have in common.

8. What Does Solving In Terms of Mean?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Sum: Average x Number of 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.

9. PEMDAS
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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.

10. Increasing and Decreasing a Number by a Certain Percentage
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The whole number left over after division.
Get the absolute value equation by itself. Solve.
-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. Finding the Volume of a Rectangular Solid
VofaRS=lwh
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

12. 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
Combine like terms.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

13. Finding the Missing Number in a Series When You are Given the Average
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Factor out and cancel all factors the numerator and denominator have in common.

14. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Just add or subtract the coefficients in front of the radicals.
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.
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
Sum: Average x Number of Terms

15. 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.
Cross multiply.
A(2)+b(2)=c(2)
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

16. Definition of an Integer
FOIL: First - Outer - Inner - Last... Combine Like Terms
Use simple numbers like 1 and 2 and see what happens.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Factor out and cancel all factors the numerator and denominator have in common.

17. Number of Groups - +1 Each Time
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Just add or subtract the coefficients in front of the radicals.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

18. Finding the Slope of a Line When Given Two Points on the Line
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.
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

19. Finding the Area of a Circle
(pie)r(squared)
A(2)+b(2)=c(2)
Get the absolute value equation by itself. Solve.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

20. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

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21. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Put the equation into y=mx+b-- in which case b is the y-intercept.

22. Multiplying Fractions
Multiply the numerators and multiply the denominators.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

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
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.
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.
Cancel factors common to the numerator and denominator.

24. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.

25. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the numerators and multiply the denominators.

26. Numbers that are Relatively Prime
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.

27. Formula to Find Average
-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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Average: Sum of the Terms/Number of the Terms
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

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

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29. Finding a Term in a Geometric Sequence
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.
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.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

30. 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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

31. 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.
-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.
A(2)+b(2)=c(2)
Average the smallest and largest number

32. Finding the Length of an Arc in a Circle

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33. Finding the Distance Between Two Points on a Coordinate Graph
(x1+x2)/2 -(y1+y2)/2
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

34. Finding the Median of a Set of Numbers
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Plug in the given values for the unknowns and calculate according to PEMDAS.
The value that falls in the middle of the set.

35. Multiplying Monomials
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The value that falls in the middle of the set.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

36. If x(2)=7x+18 - what is the positive value of x?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Sum: Average x Number of Terms
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
(pie)r(squared)

37. Definition of a Rational Number
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.

38. Multiplying and Dividing Roots
Express them with a common 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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

39. Adding and Subtracting Monomials
-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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.

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

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41. Definition of an Irrational Number
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.
Sum: Average x Number of Terms
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

42. Counting Consecutive Integers
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Subtract the smallest from the largest and add 1
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

43. Adding and Subtracting Fractions
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.
VofaC: (pie)r(2)h
Find a common denominator - then add or subtract the numerators.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

44. Finding the Mode of a Set of Numbers
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
The value that appears the most often.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

45. Converting from an Improper Fraction to a Mixed Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Average the smallest and largest number

46. 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
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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
Slope=change in y/change in x

47. Solving a Problem Involving Rates
Use the distributive property then combine the like terms.
-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.
Use the units to keep things straight - Snowfall inches/hours
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. Calculating Negative Exponents and Radical Exponents
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Subtract the smallest from the largest and add 1
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.

49. Characteristics of a Square
Use the units to keep things straight - Snowfall inches/hours
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
VofaRS=lwh
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

50. How do you know if an integer is a multiple of 3 or 9?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
2(pie)r