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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 Similar Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Average: Sum of the Terms/Number of the Terms
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

2. Finding the Circumference of a Circle
Put the equation into y=mx+b-- in which case b is the y-intercept.
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 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.
2(pie)r

3. 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.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Isolate the radical expression and use the standard rules of algebra.

4. 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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

5. Multiplying Binomials
-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.
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.

6. Solving a Linear Equation
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
Do whatever is necessary to both sides to isolate the variable.

7. Definition of an Integer
2(pie)r
Find a common denominator - then add or subtract the numerators.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

8. Determining Absolute Value of a Number
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

9. Finding the Slope of a Line When Given Two Points on the Line
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Slope=change in y/change in x
Do whatever is necessary to both sides to isolate the variable.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

10. Adding and Subtracting Roots
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Just add or subtract the coefficients in front of the radicals.
The value that falls in the middle of the set.
Cancel factors common to the numerator and denominator.

11. Adding and Subtracting Fractions
The value that appears the most often.
Find a common denominator - then add or subtract the numerators.
Four equal acute angles and four equal obtuse angles.
Slope=change in y/change in x

12. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
Sum: Average x Number of Terms
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The whole number left over after division.

13. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
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
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

14. Finding the Length of an Arc in a Circle

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15. Solving a Proportion
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.
Cross multiply.
Sum: Average x Number of Terms
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

16. 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
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%
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.
Part=Percent x Whole

17. Finding the Domain and Range of a Function
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Average the smallest and largest number
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 - 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.

18. 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
Plug in the given values for the unknowns and calculate according to PEMDAS.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.

19. Finding the LCM of Two or More Numbers

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20. Dividing Expressions with Exponents that Have a Common Base
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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 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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

21. Solving an Inequality
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

22. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
The value that falls in the middle of the set.

23. Simplifying Square Roots
Put each number in the original ratio over the sum of the numbers.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

24. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

25. What are Two Special Pythagorean Triples?

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26. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

27. 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?
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Put each number in the original ratio over the sum of the numbers.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

28. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
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.
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
-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.

29. 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?
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Multiply the numerators and multiply the denominators.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

30. Finding the Volume of a Rectangular Solid
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
-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.
VofaRS=lwh
VofaC: (pie)r(2)h

31. What is the Pythagorean Theorem?
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
A(2)+b(2)=c(2)
Subtract the smallest from the largest and add 1
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

32. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

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

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34. Finding the Missing Number in a Series When You are Given the Average
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.
The whole number left over after division.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.

35. How do you know if an integer is a multiple of 3 or 9?
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
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.
Express them with a common denominator.

36. Converting from an Improper Fraction to a Mixed Number
-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.
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.
Do whatever is necessary to both sides to isolate the variable.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

37. 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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
The value that falls in the middle of the set.

38. General Procedure for Multiplying Polynomials
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.
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.
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 the distributive property then combine the like terms.

39. Numbers that are Relatively Prime
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.
Cross multiply.
Two relatively prime numbers are integers that have no common factor other than 1.
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

40. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

41. Properties of a 30-60-90 Triangle
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

42. Finding the Rate of Speed
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
(x1+x2)/2 -(y1+y2)/2
Use the formula distance=rate*time and its variations to help in this question.
The value that appears the most often.

43. Finding the Distance Between Two Points on a Coordinate Graph
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.

44. 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.
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

45. Calculating the Probability that an Event will Take Place
Do whatever is necessary to both sides to isolate the variable.
Two relatively prime numbers are integers that have no common factor other than 1.
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

46. Number of Groups - +1 Each Time
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.
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.

47. Counting the Total Number of Possibilities for Several Events to Occur
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
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.

48. Increasing and Decreasing a Number by a Certain Percentage
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
-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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

49. If x(2)=7x+18 - what is the positive value of x?
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

50. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Factor out and cancel all factors the numerator and denominator have in common.
Use simple numbers like 1 and 2 and see what happens.