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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 y-intercept When Given an Equation of a Line
Find a common denominator - then add or subtract the numerators.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put the equation into y=mx+b-- in which case b is the y-intercept.

2. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Combine like terms.
Get the absolute value equation by itself. Solve.

3. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Put the equation into y=mx+b-- in which case b is the y-intercept.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Get the absolute value equation by itself. Solve.

4. Multiplying Binomials
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
-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.
FOIL: First - Outer - Inner - Last... Combine Like Terms

5. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
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

6. 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
VofaRS=lwh
Average the smallest and largest number
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

7. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Average the smallest and largest number
Put each number in the original ratio over the sum of the numbers.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

8. An Important Property of a Line Tangent to a Circle
The value that falls in the middle of the set.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

9. If the average of a - b - and 48 is 48 - what is the value of a + b?
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
2(pie)r
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

10. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
(x1+x2)/2 -(y1+y2)/2
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.
A(2)+b(2)=c(2)
-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.

11. Difference Between a Factor and a Multiple
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Adjacent angles are supplementary - Vertical angles are equal
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 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.

12. Finding the Rate of Speed
Multiply the numerators and multiply the denominators.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Use the formula distance=rate*time and its variations to help in this question.

13. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Isolate the radical expression and use the standard rules of algebra.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
-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.
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

14. Finding the Circumference of a Circle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
The value that appears the most often.
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
2(pie)r

15. Finding the Length of an Arc in a Circle

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16. Knowing if an Integer is a Multiple of 5 or 10
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
-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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.

17. If r#t=t(r)-r(t) - then what is 4#3?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.

18. Adding a Positive Number to a Negative Number
The whole number left over after division.
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

19. Number of Groups - +1 Each Time
Express them with a common denominator.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
The value that appears the most often.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

20. Finding the Sum of the Interior Angles of a Polygon
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

21. Multiplying and Dividing Roots
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

22. Properties of a 30-60-90 Triangle
A(2)+b(2)=c(2)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

23. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Subtract the smallest from the largest and add 1
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
2(pie)r

24. If 3(3x)=9(x+2) - what is the value of x?
-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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

25. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
Average: Sum of the Terms/Number of the Terms
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.
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.

26. 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?
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Four equal acute angles and four equal obtuse angles.
Express them with a common denominator.

27. Characteristics of a Square
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Get the absolute value equation by itself. Solve.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

28. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Switch the numerator and denominator.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

29. Finding the Midpoint Between Two Points
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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Use the formula distance=rate*time and its variations to help in this question.
(x1+x2)/2 -(y1+y2)/2

30. Adding and Subtracting Fractions
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
Express them with a common denominator.
Subtract the smallest from the largest and add 1
Find a common denominator - then add or subtract the numerators.

31. Converting from part-to-part ratios to part-to-whole ratios
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Put each number in the original ratio over the sum of the numbers.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

32. Simplifying a Fraction to Lowest Terms
Average: Sum of the Terms/Number of the Terms
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Factor out and cancel all factors the numerator and denominator have in common.

33. Calculating Negative Exponents and Radical Exponents
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Adjacent angles are supplementary - Vertical angles are equal
Combine like terms.

34. Finding the Area of a Circle
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
(pie)r(squared)

35. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
(x1+x2)/2 -(y1+y2)/2
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

36. Solving an Inequality
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
Just add or subtract the coefficients in front of the radicals.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

37. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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
Average the smallest and largest number

38. Adding and Subtracting Polynomials
Four equal acute angles and four equal obtuse angles.
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.
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.
Combine like terms.

39. Finding the Sum of the Average of a Series of Numbers
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.

40. Finding the Slope of a Line When Given Two Points on the Line
2(pie)r
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
The value that appears the most often.
Slope=change in y/change in x

41. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

42. What are Two Special Pythagorean Triples?

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43. 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.
Four equal acute angles and four equal obtuse angles.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.

44. Comparing the values of two or more Fractions
Express them with a common denominator.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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

45. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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.
Switch the numerator and denominator.
Get the absolute value equation by itself. Solve.
Two relatively prime numbers are integers that have no common factor other than 1.

46. Definition of Remainder
The whole number left over after division.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Average: Sum of the Terms/Number of the Terms
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

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

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48. Converting From a Mixed Number to an Improper Fraction
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

49. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
-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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

50. What is the Triangle Inequality Theorem?
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.
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 the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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