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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 an Integer
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
-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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

2. Average Rate and How Do You Find It
Plug in the given values for the unknowns and calculate according to PEMDAS.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Subtract the smallest from the largest and add 1
-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.

3. Finding the Median of a Set of Numbers
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
The value that falls in the middle of the set.
Find a common denominator - then add or subtract the numerators.
Put each number in the original ratio over the sum of the numbers.

4. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Four equal acute angles and four equal obtuse angles.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.

5. Raising a Power to a Power
A(2)+b(2)=c(2)
Do whatever is necessary to both sides to isolate the variable.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.

6. Prime Factorization of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The whole number left over after division.
Switch the numerator and denominator.

7. 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?
Two relatively prime numbers are integers that have no common factor other than 1.
Combine like 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.
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.

8. What is the Pythagorean Theorem?
Average: Sum of the Terms/Number of the Terms
Get the absolute value equation by itself. Solve.
A(2)+b(2)=c(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.

9. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

10. If the average of a - b - and 48 is 48 - what is the value of a + b?
(x1+x2)/2 -(y1+y2)/2
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

11. Finding a Term in a Geometric Sequence
The value that appears the most often.
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.
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
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.

12. Number of Groups - +1 Each Time
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.
The whole number left over after division.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

13. Solving a Radical Equation
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Isolate the radical expression and use the standard rules of algebra.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

14. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.

15. Finding the Domain and Range of a Function
Cancel factors common to the numerator and denominator.
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.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

16. Counting Consecutive Integers
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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)

17. Formula Used to Find Percent
Part=Percent x Whole
(x1+x2)/2 -(y1+y2)/2
VofaC: (pie)r(2)h
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.

18. Adding and Subtracting Fractions
Put each number in the original ratio over the sum of the numbers.
Find a common denominator - then add or subtract the numerators.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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

19. Finding the Rate of Speed
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Use the formula distance=rate*time and its variations to help in this question.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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. 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?
Combine like terms.
Isolate the radical expression and use the standard rules of algebra.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

21. Calculating Negative Exponents and Radical Exponents
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.
Do whatever is necessary to both sides to isolate the variable.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

22. Finding the Area of a Sector

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23. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Cross multiply.

24. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Subtract the smallest from the largest and add 1
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use simple numbers like 1 and 2 and see what happens.

25. Finding the Circumference of a Circle
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
2(pie)r
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 distributive property then combine the like terms.

26. Solving a Problem Involving Rates
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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 formula distance=rate*time and its variations to help in this question.
Use the units to keep things straight - Snowfall inches/hours

27. Formula to Find Average
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.
-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.
Average: Sum of the Terms/Number of the Terms
Use the units to keep things straight - Snowfall inches/hours

28. Finding the Slope of a Line When Given Two Points on the Line
Express them with a common denominator.
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
Slope=change in y/change in x
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.

29. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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
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.
Do whatever is necessary to both sides to isolate the variable.

30. Direct Variation and Inverse Variation
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
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

31. What is the Triangle Inequality Theorem?
Four equal acute angles and four equal obtuse angles.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

32. If r#t=t(r)-r(t) - then what is 4#3?
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.
Cross multiply.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use the formula distance=rate*time and its variations to help in this question.

33. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.

34. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
(x1+x2)/2 -(y1+y2)/2
Express them with a common denominator.

35. Quickly Finding the Average of a Series of Evenly Spaced Numbers
-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.
Average the smallest and largest number
The value that appears the most often.
Put the equation into y=mx+b-- in which case b is the y-intercept.

36. 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
Do whatever is necessary to both sides to isolate the variable.
-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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

37. 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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Subtract the smallest from the largest and add 1
Four equal acute angles and four equal obtuse angles.

38. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
A(2)+b(2)=c(2)
Cross multiply.

39. Converting from an Improper Fraction to a Mixed 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 value that falls in the middle of the set.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.

40. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
Express them with a common denominator.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Two relatively prime numbers are integers that have no common factor other than 1.

41. Properties of a 30-60-90 Triangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.

42. What Does Solving In Terms of Mean?
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

43. 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?
VofaC: (pie)r(2)h
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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

44. 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.
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
2(pie)r

45. Solving a Linear Equation
Combine like terms.
VofaRS=lwh
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Do whatever is necessary to both sides to isolate the variable.

46. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Do whatever is necessary to both sides to isolate the variable.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.

47. Finding the Volume of a Rectangular Solid
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
VofaRS=lwh
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.

48. Numbers that are Relatively Prime
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.
Use the distributive property then combine the like terms.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Two relatively prime numbers are integers that have no common factor other than 1.

49. Solving a Proportion
Cancel factors common to the numerator and denominator.
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
Cross multiply.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

50. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Sum: Average x Number of Terms