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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 Volume of a Cylinder
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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 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
VofaC: (pie)r(2)h

2. Converting from an Improper Fraction to a Mixed Number
Use the units to keep things straight - Snowfall inches/hours
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
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.

3. Multiplying Expressions with Exponents that Have a Common Base
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
VofaC: (pie)r(2)h
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

4. Finding the GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Express them with a common denominator.

5. Adding and Subtracting Monomials
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

6. What types of angles are formed when two lines intersect?
Isolate the radical expression and use the standard rules of algebra.
Adjacent angles are supplementary - Vertical angles are equal
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.

7. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Average the smallest and largest number
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.
Two relatively prime numbers are integers that have no common factor other than 1.

8. Evaluating an Algebraic Expression
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
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

9. Adding and Subtracting Polynomials
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Combine like terms.
Subtract the smallest from the largest and add 1
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

10. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

11. Convert From a Fraction to a Decimal - Vice Versa
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

12. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Slope=change in y/change in x

13. Solving a System of Equations
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

14. Simplifying a Fraction to Lowest Terms
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Factor out and cancel all factors the numerator and denominator have in common.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Cross multiply.

15. 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%.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

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

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17. Finding the Midpoint Between Two Points
Multiply the numerators and multiply the denominators.
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
(x1+x2)/2 -(y1+y2)/2

18. Finding the Mode of a Set of Numbers
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.
Get the absolute value equation by itself. Solve.
The value that appears the most often.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

19. What is the Triangle Inequality Theorem?
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.
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 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.
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.

20. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Subtract the smallest from the largest and add 1
Put the equation into y=mx+b-- in which case b is the y-intercept.
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

21. Finding the Slope When Given an Equation of a Line
(pie)r(squared)
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

22. 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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Use the distributive property then combine the like terms.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

23. Definition of an Irrational Number
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
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

24. Raising a Power to a Power
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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 exponents - (x^3)^4=x^3*4=x^12
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

25. Multiplying Monomials
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
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.
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.

26. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Put each number in the original ratio over the sum of the numbers.
The whole number left over after division.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

27. Comparing the values of two or more Fractions
Express them with a common denominator.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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
Combine like terms.

28. 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.
The value that appears the most often.
(x1+x2)/2 -(y1+y2)/2
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.

29. What Does Solving In Terms of Mean?
VofaRS=lwh
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Slope=change in y/change in x

30. If (Square Root: x-1)+5=12 - what is the value of x/2?
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.
Use simple numbers like 1 and 2 and see what happens.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Express them with a common denominator.

31. Expressing the Union and Intersection of Sets
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Adjacent angles are supplementary - Vertical angles are equal
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
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.

32. 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.
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.
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.
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

33. Adding a Positive Number to a Negative Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.

34. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Part=Percent x Whole

35. Difference Between a Factor and a Multiple
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
-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.
-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.

36. Finding the Rate of Speed
Use the formula distance=rate*time and its variations to help in this question.
The value that appears the most often.
Four equal acute angles and four equal obtuse angles.
Plug in the given values for the unknowns and calculate according to PEMDAS.

37. 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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

38. If x(2)=7x+18 - what is the positive value of x?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
2(pie)r
Express them with a common denominator.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

39. Finding the Reciprocal of a Fraction
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Switch the numerator and denominator.
Cross multiply.

40. 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.
Subtract the smallest from the largest and add 1
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 two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

41. Numbers that are Relatively Prime
Multiply the numerators and multiply the denominators.
The value that appears the most often.
Express them with a common denominator.
Two relatively prime numbers are integers that have no common factor other than 1.

42. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Factor out and cancel all factors the numerator and denominator have in common.
Adjacent angles are supplementary - Vertical angles are equal
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
FOIL: First - Outer - Inner - Last... Combine Like Terms

43. 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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

44. Finding the Volume of a Rectangular Solid
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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
VofaRS=lwh
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

45. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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

46. If 3(3x)=9(x+2) - what is the value of x?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime 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.

47. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
VofaC: (pie)r(2)h

48. Properties of the Interior and Exterior Angles of a Triangle
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.
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Use simple numbers like 1 and 2 and see what happens.

49. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
(pie)r(squared)
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

50. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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 value that falls in the middle of the set.
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.