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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. Counting the Total Number of Possibilities for Several Events to Occur
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
A(2)+b(2)=c(2)
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

2. Solving a Proportion
Multiply the exponents - (x^3)^4=x^3*4=x^12
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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Cross multiply.

3. Calculating the Probability that an Event will Take Place
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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
Use the units to keep things straight - Snowfall inches/hours

4. Finding the Circumference of a Circle
2(pie)r
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
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

5. What is the Triangle Inequality Theorem?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Part=Percent x Whole
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 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.

6. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
The value that falls in the middle of the set.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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

7. Finding the Rate of Speed
Use the formula distance=rate*time and its variations to help in this question.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
-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.
Subtract the smallest from the largest and add 1

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

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9. Multiplying Expressions with Exponents that Have a Common Base
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Slope=change in y/change in x
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

10. 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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Use the distributive property then combine the like terms.
The whole number left over after division.

11. Direct Variation and Inverse Variation
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
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

12. Converting from part-to-part ratios to part-to-whole ratios
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

13. Knowing if an Integer is a Multiple of 2 or 4
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
-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.
Put each number in the original ratio over the sum of the numbers.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

14. Finding the Area of a Sector

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15. Number of Groups - +1 Each Time
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

16. Prime Factorization of a 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
Multiply the numerators and multiply the denominators.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

17. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
2(pie)r

18. Finding the Length of an Arc in a Circle

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19. Expressing the Union and Intersection of Sets
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Find a common denominator - then add or subtract the numerators.

20. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

21. Finding the GCF of Two or More Numbers
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

22. What are Two Special Pythagorean Triples?

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23. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Subtract the smallest from the largest and add 1
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

24. If (Square Root: x-1)+5=12 - what is the value of x/2?
Average the smallest and largest number
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Use the units to keep things straight - Snowfall inches/hours
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.

25. Factoring a Polynomial ('FOIL in Reverse')
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
A(2)+b(2)=c(2)

26. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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
Adjacent angles are supplementary - Vertical angles are equal
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

27. Finding the Missing Number in a Series When You are Given the Average
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 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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

28. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
(x1+x2)/2 -(y1+y2)/2
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
-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.

29. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
Express them with a common denominator.
Find a common denominator - then add or subtract the numerators.

30. Definition of an Integer
Cancel factors common to the numerator and denominator.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

31. Converting From a Mixed Number to an Improper Fraction
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Average: Sum of the Terms/Number of the Terms
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

32. Adding and Subtracting Monomials
VofaC: (pie)r(2)h
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Adjacent angles are supplementary - Vertical angles are equal
Use simple numbers like 1 and 2 and see what happens.

33. 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
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
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

34. General Procedure for Multiplying Polynomials
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Use the distributive property then combine the like terms.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

35. Finding the Sum of the Interior Angles of a Polygon
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

36. Factoring the Difference of Two Squares
Sum: Average x Number of Terms
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

37. Definition of an Irrational Number
Express them with a common denominator.
Isolate the radical expression and use the standard rules of algebra.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
-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.

38. 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 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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Adjacent angles are supplementary - Vertical angles are equal
Subtract the smallest from the largest and add 1

39. Finding the Median of a Set of Numbers
Use the formula distance=rate*time and its variations to help in this question.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
The value that falls in the middle of the set.

40. Difference Between a Factor and a Multiple
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 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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Probability: Number of Favorable Outcomes/Total Possible Outcomes

41. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Put each number in the original ratio over the sum of the numbers.
Use simple numbers like 1 and 2 and see what happens.

42. 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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

43. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

44. 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?
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
-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.
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 two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

45. Characteristics of a Rectangle
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The value that falls in the middle of the set.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

46. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Do whatever is necessary to both sides to isolate the variable.

47. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
-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.
Isolate the radical expression and use the standard rules of algebra.
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

48. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

49. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.

50. Dividing Expressions with Exponents that Have a Common Base
Find a common denominator - then add or subtract the numerators.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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