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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. Properties of the Interior and Exterior Angles of a Triangle
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.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

2. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Adjacent angles are supplementary - Vertical angles are equal
Cross multiply.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

3. 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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
(x1+x2)/2 -(y1+y2)/2

4. Difference Between a Factor and a Multiple
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
-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.
Do whatever is necessary to both sides to isolate the variable.
The value that appears the most often.

5. Definition of an Integer
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
The whole number left over after division.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

6. Average Rate and How Do You Find It
Find a common denominator - then add or subtract the numerators.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Probability: Number of Favorable Outcomes/Total Possible Outcomes

7. 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%.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
-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.

8. Multiplying Fractions
Do whatever is necessary to both sides to isolate the variable.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Multiply the numerators and multiply the denominators.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

9. Factoring a Polynomial ('FOIL in Reverse')
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use the units to keep things straight - Snowfall inches/hours

10. Adding and Subtracting Polynomials
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Cross multiply.
Combine like terms.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

11. Solving a Linear Equation
(pie)r(squared)
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.
VofaRS=lwh

12. Converting from an Improper Fraction to a Mixed Number
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.

13. Increasing and Decreasing a Number by a Certain Percentage
Two relatively prime numbers are integers that have no common factor other than 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.
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.

14. Characteristics of a Parallelogram
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
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

15. If x(2)=7x+18 - what is the positive value of x?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Use the distributive property then combine the like terms.
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

16. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Do whatever is necessary to both sides to isolate the variable.
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12

17. Solving a Problem Involving Rates
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Use the units to keep things straight - Snowfall inches/hours
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

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

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19. Adding a Positive Number to a Negative Number
2(pie)r
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

20. Adding and Subtracting Roots
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Cross multiply.
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.

21. Prime Factorization of a Number
Average the smallest and largest number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
-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.

22. 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.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Average the smallest and largest number

23. An Important Property of a Line Tangent to a Circle
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
The whole number left over after division.
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.

24. Adding and Subtracting Monomials
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Put the equation into y=mx+b-- in which case b is the y-intercept.
-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.

25. Counting Consecutive Integers
-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.
The value that appears the most often.
Subtract the smallest from the largest and add 1
Use the distributive property then combine the like terms.

26. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Slope=change in y/change in x
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Switch the numerator and denominator.

27. 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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
(x1+x2)/2 -(y1+y2)/2

28. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
Use the formula distance=rate*time and its variations to help in this question.
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.
Multiply the numerators and multiply the denominators.

29. 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
Factor out and cancel all factors the numerator and denominator have in common.
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.
Get the absolute value equation by itself. Solve.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

30. What is the Triangle Inequality Theorem?
Plug in the given values for the unknowns and calculate according to PEMDAS.
Average: Sum of the Terms/Number of the Terms
Get the absolute value equation by itself. Solve.
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.

31. 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.
-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.
-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 find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

32. 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?
Isolate the radical expression and use the standard rules of algebra.
-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.
Part=Percent x Whole
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.

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

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34. What value of x is not in the domain of the function f(x)=x-2/x-3?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

35. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
Two relatively prime numbers are integers that have no common factor other than 1.
Get the absolute value equation by itself. Solve.
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

36. Expressing the Union and Intersection of Sets
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Express them with a common denominator.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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

37. Setting Up a Ratio
2(pie)r
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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 number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

38. Factoring the Difference of Two Squares
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
(x1+x2)/2 -(y1+y2)/2

39. If 4(x(2)-10x+25) - then what is the value of 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.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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. Finding the y-intercept When Given an Equation of a Line
A(2)+b(2)=c(2)
-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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Average: Sum of the Terms/Number of the Terms

41. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Switch the numerator and denominator.
VofaRS=lwh

42. If (Square Root: x-1)+5=12 - what is the value of x/2?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
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 and cancel all factors the numerator and denominator have in common.

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

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44. 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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Switch the numerator and denominator.
Cancel factors common to the numerator and denominator.

45. Finding the Sum of the Interior Angles of a Polygon
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

46. Converting from part-to-part ratios to part-to-whole ratios
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
Put each number in the original ratio over the sum of the numbers.

47. Multiplying Expressions with Exponents that Have a Common Base
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 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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

48. If 3(3x)=9(x+2) - what is the value of x?
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
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

49. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
-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.
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.

50. Properties of a 30-60-90 Triangle
Average: Sum of the Terms/Number of the Terms
Express them with a common denominator.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle