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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. Characteristics of a Square
Part=Percent x Whole
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

2. Solving a Proportion
Cross multiply.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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

3. Multiplying Expressions with Exponents that Have a Common Base
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

4. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Average the smallest and largest number

5. 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.
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.
Cross multiply.
Express them with a common denominator.

6. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

7. What types of angles are formed when a transversal cross parallel lines?
Adjacent angles are supplementary - Vertical angles are equal
Four equal acute angles and four equal obtuse angles.
(x1+x2)/2 -(y1+y2)/2
Multiply the exponents - (x^3)^4=x^3*4=x^12

8. General Procedure for Multiplying Polynomials
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Cross multiply.
Use the distributive property then combine the like terms.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

9. Properties of a 45-45-90 Triangle
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.
Just add or subtract the coefficients in front of the radicals.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.

10. If (Square Root: x-1)+5=12 - what is the value of x/2?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
-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.
Factor out and cancel all factors the numerator and denominator have in common.

11. What is the Triangle Inequality Theorem?
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
The value that appears the most often.
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.

12. If 3(3x)=9(x+2) - what is the value of x?
Just add or subtract the coefficients in front of the radicals.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Multiply the exponents - (x^3)^4=x^3*4=x^12
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

13. Factoring the Difference of Two Squares
Use the formula distance=rate*time and its variations to help in this question.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Adjacent angles are supplementary - Vertical angles are equal

14. Finding the LCM of Two or More Numbers

15. Adding and Subtracting Fractions
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Find a common denominator - then add or subtract the numerators.

16. Solving a System of Equations
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
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
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.

17. Finding the Missing Number in a Series When You are Given the Average
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.
(pie)r(squared)
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

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

19. Characteristics of a Parallelogram
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
(x1+x2)/2 -(y1+y2)/2
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.

20. Finding the Length of an Arc in a Circle

21. Scalene - Isosceles - and Equilateral Triangles
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.
-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.
Factor out and cancel all factors the numerator and denominator have in common.
The value that appears the most often.

22. Converting From a Mixed Number to an Improper Fraction
Combine like terms.
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

23. Finding the Area of a Circle
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
(pie)r(squared)

24. Number of Groups - +1 Each Time
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 whole number left over after division.
Subtract the smallest from the largest and add 1
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

25. Finding a Term in a Geometric Sequence
Slope=change in y/change in x
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

26. Formula to Find Average
Part=Percent x Whole
Average: Sum of the Terms/Number of the Terms
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

27. Finding the Slope When Given an Equation of a Line
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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
Average: Sum of the Terms/Number of the Terms

28. Adding and Subtracting Roots
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.
Just add or subtract the coefficients in front of the radicals.
Cancel factors common to the numerator and denominator.
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.

29. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Use the formula distance=rate*time and its variations to help in this question.
Cancel factors common to the numerator and denominator.
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

30. 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
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.
Isolate the radical expression and use the standard rules of algebra.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

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

32. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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 the formula distance=rate*time and its variations to help in this question.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

33. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
-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.
Four equal acute angles and four equal obtuse angles.

34. Increasing and Decreasing a Number by a Certain Percentage
Multiply the numerators and multiply the denominators.
-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.
Put each number in the original ratio over the sum of the numbers.
Factor out and cancel all factors the numerator and denominator have in common.

35. Finding the Domain and Range of a Function
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Average the smallest and largest number
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.
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.

36. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Average: Sum of the Terms/Number of the Terms
Use the distributive property then combine the like terms.
Put the equation into y=mx+b-- in which case b is the y-intercept.

37. Properties of the Interior and Exterior Angles of a Triangle
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.
Combine like terms.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

38. Finding the Mode of a Set of Numbers
Four equal acute angles and four equal obtuse angles.
-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.
The value that appears the most often.
Part=Percent x Whole

39. Prime Factorization of a Number
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.

40. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
VofaRS=lwh
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

41. Average Rate and How Do You Find It
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Cross multiply.
Use the units to keep things straight - Snowfall inches/hours
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

42. Simplifying a Fraction to Lowest Terms
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
Factor out and cancel all factors the numerator and denominator have in common.

43. Knowing if an Integer is a Multiple of 2 or 4
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.
-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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

44. Finding the Distance Between Two Points on a Coordinate Graph
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 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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

45. Finding the GCF of Two or More Numbers
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.

46. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
-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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Average the smallest and largest number

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
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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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

48. Formula Used to Find Percent
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.
Part=Percent x Whole
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.
Do whatever is necessary to both sides to isolate the variable.

49. 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.
Slope=change in y/change in x
Isolate the radical expression and use the standard rules of algebra.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

50. Calculating the Probability that an Event will Take Place
FOIL: First - Outer - Inner - Last... Combine Like Terms
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Part=Percent x Whole