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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 Circumference of a Circle
Switch the numerator and denominator.
2(pie)r
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.
The whole number left over after division.

2. Adding and Subtracting Polynomials
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Combine like terms.
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

3. Converting from an Improper Fraction to a Mixed Number
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Multiply the numerators and multiply the denominators.
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.

4. Multiplying Monomials
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Multiply the numerators and multiply the denominators.
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

5. Counting the Total Number of Possibilities for Several Events to Occur
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.
Use the distributive property then combine the like terms.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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

6. 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.
Put each number in the original ratio over the sum of the numbers.
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 variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

7. Simplifying Square Roots
Do whatever is necessary to both sides to isolate the variable.
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

8. Direct Variation and Inverse Variation
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.
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

9. Finding the Distance Between Two Points on a Coordinate Graph
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.

10. Properties of the Interior and Exterior Angles of a Triangle
-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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Isolate the radical expression and use the standard rules of algebra.

11. Multiplying Binomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Cancel factors common to the numerator and denominator.

12. Definition of an Irrational Number
2(pie)r
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

13. Definition of Remainder
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The whole number left over after division.
(x1+x2)/2 -(y1+y2)/2

14. PEMDAS
Get the absolute value equation by itself. Solve.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

15. Comparing the values of two or more Fractions
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.
Express them with a common denominator.
Combine like terms.
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.

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

17. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
2(pie)r
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

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

19. 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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Do whatever is necessary to both sides to isolate the variable.

20. Multiplying 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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Find a common denominator - then add or subtract the numerators.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

21. Quickly Finding the Average of a Series of Evenly Spaced Numbers
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Average the smallest and largest number
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.

22. Finding the Mode of a Set of Numbers
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
The value that appears the most often.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

23. Finding the Sum of the Interior Angles of a Polygon
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.

24. Determining Absolute Value of a Number
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Two relatively prime numbers are integers that have no common factor other than 1.
Cancel factors common to the numerator and denominator.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

25. Multiplying Fractions
The value that appears the most often.
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
Multiply the numerators and multiply the denominators.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

26. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
Use the distributive property then combine the like terms.
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 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.

27. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
Use the units to keep things straight - Snowfall inches/hours
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.
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.

28. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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
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

29. Definition of an Integer
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
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The whole number left over after division.

30. Multiplying and Dividing Roots
Use simple numbers like 1 and 2 and see what happens.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
The whole number left over after division.
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.

31. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Multiply the whole number part by the denominator - then add the numerator. Keep the same 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.

32. Finding the Domain and Range of a Function
Average the smallest and largest number
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Part=Percent x Whole

33. Number of Groups - +1 Each Time
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

34. Finding the Missing Number in a Series When You are Given the Average
Find a common denominator - then add or subtract the numerators.
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.
-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.
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.

35. Formula to Find Average
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.
Average: Sum of the Terms/Number of the Terms
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

36. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Do whatever is necessary to both sides to isolate the variable.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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.

37. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
(pie)r(squared)
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
Use the distributive property then combine the like 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.

38. Knowing if an Integer is a Multiple of 5 or 10
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.
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 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
Use the units to keep things straight - Snowfall inches/hours

39. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Sum: Average x Number of Terms
(x1+x2)/2 -(y1+y2)/2
The value that falls in the middle of the set.

40. Convert From a Fraction to a Decimal - Vice Versa
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Sum: Average x Number of Terms
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 units to keep things straight - Snowfall inches/hours

41. Formula Used to Find Percent
Part=Percent x Whole
VofaRS=lwh
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Average: Sum of the Terms/Number of the Terms

42. Factoring a Polynomial ('FOIL in Reverse')
Slope=change in y/change in x
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Sum: Average x Number of Terms
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

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

44. If 3(3x)=9(x+2) - what is the value of x?
VofaC: (pie)r(2)h
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

45. 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 value that falls in the middle of the set.
Use simple numbers like 1 and 2 and see what happens.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

46. What are Two Special Pythagorean Triples?

47. General Procedure for Multiplying Polynomials
VofaRS=lwh
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use the distributive property then combine the like terms.
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.

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

49. Solving a System of Equations
Use simple numbers like 1 and 2 and see what happens.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

50. What is the Pythagorean Theorem?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
-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.
A(2)+b(2)=c(2)