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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. 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
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 units to keep things straight - Snowfall inches/hours
2(pie)r

2. Finding the Area of a Circle
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.
Adjacent angles are supplementary - Vertical angles are equal
(pie)r(squared)
Use simple numbers like 1 and 2 and see what happens.

3. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

4. Multiply and Divide Positive and Negative Numbers
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
Multiply the exponents - (x^3)^4=x^3*4=x^12
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
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

5. Convert From a Fraction to a Decimal - Vice Versa
2(pie)r
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The value that appears the most often.

6. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
The value that falls in the middle of the set.
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.

7. Finding the Domain and Range of a Function
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
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

8. Evaluating an Algebraic Expression
Average: Sum of the Terms/Number of the Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

9. Solving a Proportion
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.
Cross multiply.
Isolate the radical expression and use the standard rules of algebra.
Just add or subtract the coefficients in front of the radicals.

10. Finding the Area of a Triangle

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11. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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

12. 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.
The whole number left over after division.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.

13. What value of x is not in the domain of the function f(x)=x-2/x-3?
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.
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

14. Raising a Power to a Power
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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

15. Adding and Subtracting Roots
VofaRS=lwh
Just add or subtract the coefficients in front of the radicals.
-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.
Slope=change in y/change in x

16. 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?
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.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

17. Definition of Remainder
The whole number left over after division.
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Combine like terms.

18. Multiplying Monomials
Use the distributive property then combine the like terms.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

19. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Factor out and cancel all factors the numerator and denominator have in common.
Get the absolute value equation by itself. Solve.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

20. Solving a Linear Equation
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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
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.

21. If 4(x(2)-10x+25) - then what is the value of x?
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.
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.
Use simple numbers like 1 and 2 and see what happens.

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

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23. Definition of an Irrational Number
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

24. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Four equal acute angles and four equal obtuse angles.
Just add or subtract the coefficients in front of the radicals.

25. 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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Put the equation into y=mx+b-- in which case b is the y-intercept.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

26. Expressing the Union and Intersection of Sets
A(2)+b(2)=c(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.
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

27. Finding the Mode of a Set of Numbers
Sum: Average x Number of 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.
The value that appears the most often.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

28. 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?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Switch the numerator and denominator.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Combine like terms.

29. Properties of the Interior and Exterior Angles of a Triangle
Multiply the numerators and multiply the denominators.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

30. Dividing Expressions with Exponents that Have a Common Base
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Cross multiply.

31. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Just add or subtract the coefficients in front of the radicals.
Isolate the radical expression and use the standard rules of algebra.
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.

32. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
Average the smallest and largest number
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.

33. Factoring a Polynomial ('FOIL in Reverse')
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

34. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Slope=change in y/change in x
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 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.

35. Solving a Radical Equation
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Isolate the radical expression and use the standard rules of algebra.
A(2)+b(2)=c(2)
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

36. Properties of a 45-45-90 Triangle
Multiply the numerators and multiply the denominators.
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

37. Finding the Circumference of a Circle
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
2(pie)r

38. Counting the Total Number of Possibilities for Several Events to Occur
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)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.
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.
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. 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.
Factor out and cancel all factors the numerator and denominator have in common.
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.
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

40. 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.
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.
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

41. Finding the Sum of the Average of a Series 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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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

42. Multiplying Expressions with Exponents that Have a Common Base
-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.
Just add or subtract the coefficients in front of the radicals.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

43. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
The value that falls in the middle of the set.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

44. Finding the Surface Area of a Rectangular Solid
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.

45. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
-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 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
Multiply the exponents - (x^3)^4=x^3*4=x^12

46. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
VofaC: (pie)r(2)h
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

47. What are Two Special Pythagorean Triples?

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48. If the average of a - b - and 48 is 48 - what is the value of a + b?
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

49. Converting From a Mixed Number to an Improper Fraction
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same 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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

50. Knowing if an Integer is a Multiple of 2 or 4
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
(x1+x2)/2 -(y1+y2)/2
-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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value