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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. Definition of Remainder
The whole number left over after division.
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.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

2. Evaluating an Algebraic Expression
Average: Sum of the Terms/Number of the Terms
Two relatively prime numbers are integers that have no common factor other than 1.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Plug in the given values for the unknowns and calculate according to PEMDAS.

3. Factoring a Polynomial ('FOIL in Reverse')
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 group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

4. Finding the Surface Area of a Rectangular Solid
-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.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

5. 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.
Part=Percent x Whole
Use the formula distance=rate*time and its variations to help in this question.
Get the absolute value equation by itself. Solve.

6. Finding the Mode of a Set of Numbers
Use simple numbers like 1 and 2 and see what happens.
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.
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 value that appears the most often.

7. Comparing the values of two or more Fractions
Express them with a common denominator.
FOIL: First - Outer - Inner - Last... Combine Like Terms
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

8. Formula to Find Average
x(2)-5x+6 - What factors of +6 also have a sum of -5? (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
Average: Sum of the Terms/Number of the Terms
Get the absolute value equation by itself. Solve.

9. Finding the Volume of a Cylinder
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

10. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
The value that appears the most often.
Cancel factors common to the numerator and denominator.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

11. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
A(2)+b(2)=c(2)

12. 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.
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.
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.
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

13. Finding the y-intercept When Given an Equation of a Line
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.
Combine like terms.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.

14. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
-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.

15. Knowing if an Integer is a Multiple of 2 or 4
-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.
-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.
Four equal acute angles and four equal obtuse angles.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

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

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17. Finding the Area of a Sector

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18. Definition of an Integer
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.
Put each number in the original ratio over the sum of the numbers.
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

19. Finding the Sum of the Average of a Series of Numbers
Average the smallest and largest number
Use the formula distance=rate*time and its variations to help in this question.
Sum: Average x Number of 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.

20. 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
Adjacent angles are supplementary - Vertical angles are equal
Cross multiply.
Switch the numerator and denominator.

21. Finding the GCF of Two or More Numbers
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
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Put the equation into y=mx+b-- in which case b is the y-intercept.

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

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23. Finding the Area of a Triangle

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24. Adding and Subtracting Fractions
-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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Find a common denominator - then add or subtract the numerators.
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

25. 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
VofaC: (pie)r(2)h
Four equal acute angles and four equal obtuse angles.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

26. Multiplying Fractions
Average the smallest and largest number
Multiply the numerators and multiply the denominators.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Just add or subtract the coefficients in front of the radicals.

27. Adding and Subtracting Roots
Use the distributive property then combine the like terms.
Just add or subtract the coefficients in front of the radicals.
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

28. Difference Between a Factor and a Multiple
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 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.
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
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.

29. Multiplying Expressions with Exponents that Have a Common Base
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Four equal acute angles and four equal obtuse angles.

30. Finding the Area of a Circle
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
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.
(pie)r(squared)

31. Finding the Reciprocal of a Fraction
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Switch 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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

32. Calculating Negative Exponents and Radical Exponents
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.
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.
Do whatever is necessary to both sides to isolate the variable.

33. What types of angles are formed when two lines intersect?
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.
Sum: Average x Number of Terms
Cross multiply.
Adjacent angles are supplementary - Vertical angles are equal

34. If r#t=t(r)-r(t) - then what is 4#3?
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Multiply the exponents - (x^3)^4=x^3*4=x^12
-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.

35. Scalene - Isosceles - and Equilateral Triangles
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
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.

36. Prime Factorization of a Number
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
-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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

37. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

38. 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
Switch the numerator and denominator.
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.
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.

39. What types of angles are formed when a transversal cross parallel lines?
Multiply the exponents - (x^3)^4=x^3*4=x^12
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Four equal acute angles and four equal obtuse angles.
Subtract the smallest from the largest and add 1

40. 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.
The value that appears the most often.
Average: Sum of the Terms/Number of the Terms
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

41. Expressing the Union and Intersection of Sets
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
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
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

42. What is the Pythagorean Theorem?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
A(2)+b(2)=c(2)

43. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
-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.

44. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Use simple numbers like 1 and 2 and see what happens.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

45. Solving a Linear Equation
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
The value that falls in the middle of the set.
Do whatever is necessary to both sides to isolate the variable.

46. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
The whole number left over after division.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

47. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Subtract the smallest from the largest and add 1
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

48. Counting the Total Number of Possibilities for Several Events to Occur
A(2)+b(2)=c(2)
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

49. Average Rate and How Do You Find It
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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
Average: Sum of the Terms/Number of the Terms

50. What is the Triangle Inequality Theorem?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Use the units to keep things straight - Snowfall inches/hours
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.