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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 Mode of a Set of Numbers
-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.
Find a common denominator - then add or subtract the numerators.
The value that appears the most often.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

2. Solving a Problem Involving Rates
Adjacent angles are supplementary - Vertical angles are equal
Use the units to keep things straight - Snowfall inches/hours
The whole number left over after division.
FOIL: First - Outer - Inner - Last... Combine Like Terms

3. Characteristics of a Rectangle
A(2)+b(2)=c(2)
FOIL: First - Outer - Inner - Last... Combine Like Terms
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
-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.

4. Solving an Inequality
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Part=Percent x Whole
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

5. Finding the Circumference of a Circle
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
2(pie)r
Use the distributive property then combine the like terms.
Slope=change in y/change in x

6. Definition of an Irrational Number
Use the formula distance=rate*time and its variations to help in this question.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.

7. 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 distributive property then combine the like terms.
Two relatively prime numbers are integers that have no common factor other than 1.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

8. Finding the Area of a Triangle

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9. Raising a Power to a Power
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Two relatively prime numbers are integers that have no common factor other than 1.

10. What are Two Special Pythagorean Triples?

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11. Finding the Sum of the Interior Angles of a Polygon
Average the smallest and largest number
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
2(pie)r
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

12. Finding the Distance Between Two Points on a Coordinate Graph
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.

13. What is the Triangle Inequality Theorem?
Adjacent angles are supplementary - Vertical angles are equal
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.
(pie)r(squared)
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

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

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15. Increasing and Decreasing a Number by a Certain Percentage
Probability: Number of Favorable Outcomes/Total Possible Outcomes
The whole number left over after division.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
-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.

16. Finding the Sum of the Average of a Series of Numbers
Just add or subtract the coefficients in front of the radicals.
Isolate the radical expression and use the standard rules of algebra.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Sum: Average x Number of Terms

17. Finding the Missing Number in a Series When You are Given the Average
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
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
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 the formula distance=rate*time and its variations to help in this question.

18. Characteristics of a Square
Part=Percent x Whole
-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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

19. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

20. Finding the Rate of Speed
The whole number left over after division.
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 group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Use the formula distance=rate*time and its variations to help in this question.

21. Definition of Remainder
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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
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 whole number left over after division.

22. Multiplying Binomials
-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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
FOIL: First - Outer - Inner - Last... Combine Like Terms

23. Convert From a Fraction to a Decimal - Vice Versa
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
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 find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

24. Finding the Domain and Range of a Function
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
-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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.

25. Multiplying Monomials
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
Multiply the numerators and multiply the denominators.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

26. What types of angles are formed when a transversal cross parallel lines?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Four equal acute angles and four equal obtuse angles.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

27. Setting Up a Ratio
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Adjacent angles are supplementary - Vertical angles are equal

28. 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.
Adjacent angles are supplementary - Vertical angles are equal
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

29. Solving a System of Equations
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
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.

30. An Important Property of a Line Tangent to a Circle
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.
Combine like terms.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

31. Determining Absolute Value of a Number
The value that falls in the middle of the set.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

32. Multiplying and Dividing Roots
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
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.

33. Dividing Expressions with Exponents that Have a Common Base
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
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.

34. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

35. Adding and Subtracting Fractions
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.
Cancel factors common to the numerator and denominator.
Find a common denominator - then add or subtract the numerators.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

36. Finding the Area of a Sector

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37. Solving a Linear Equation
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Do whatever is necessary to both sides to isolate the variable.

38. Adding and Subtracting Polynomials
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Combine like terms.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

39. Definition of a Rational Number
The value that falls in the middle of the set.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

40. Factoring a Polynomial ('FOIL in Reverse')
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

41. If 4(x(2)-10x+25) - then what is the value of x?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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
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.
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.

42. 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.
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.
Use the distributive property then combine the like terms.
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

43. Average Rate and How Do You Find It
Switch the numerator and denominator.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.

44. Direct Variation and Inverse Variation
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
The value that appears the most often.
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

45. 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?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.

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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
The whole number left over after division.

47. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
The value that appears the most often.
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.
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

48. Counting the Total Number of Possibilities for Several Events to Occur
Get the absolute value equation by itself. 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.
Isolate the radical expression and use the standard rules of algebra.
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.

49. Number of Groups - +1 Each Time
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Put each number in the original ratio over the sum of the numbers.
Plug in the given values for the unknowns and calculate according to PEMDAS.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

50. PEMDAS
Use the formula distance=rate*time and its variations to help in this question.
Average the smallest and largest number
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.