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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 a 45-45-90 Triangle
Do whatever is necessary to both sides to isolate the variable.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

2. 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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Just add or subtract the coefficients in front of the radicals.
Plug in the given values for the unknowns and calculate according to PEMDAS.

3. What is a Function and how do you Evaluate one?

4. 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
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
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

5. Raising a Power to a Power
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

6. Finding the Slope When Given an Equation of a Line
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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

7. Finding the Surface Area of a Rectangular Solid
Get the absolute value equation by itself. Solve.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

8. Finding the Missing Number in a Series When You are Given the Average
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Switch the numerator and denominator.
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.

9. Finding the Median of a Set of Numbers
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.
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 value that falls in the middle of the set.

10. Characteristics of a Parallelogram
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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. What types of angles are formed when two lines intersect?
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
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.

12. Multiplying Monomials
Combine 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
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.

13. Finding the Volume of a Cylinder
(pie)r(squared)
Use the formula distance=rate*time and its variations to help in this question.
VofaC: (pie)r(2)h
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

14. PEMDAS
Cross multiply.
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
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

15. Definition of Remainder
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The whole number left over after division.

16. Finding the Mode of a Set of Numbers
Get the absolute value equation by itself. Solve.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
The value that appears the most often.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

17. Simplifying a Fraction to Lowest Terms
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.
Factor out and cancel all factors the numerator and denominator have in common.
Average: Sum of the Terms/Number of the Terms
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

18. Adding and Subtracting Monomials
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
-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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.

19. Converting From a Mixed Number to an Improper Fraction
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.
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

20. Finding the Distance Between Two Points on a Coordinate Graph
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

21. 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
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Isolate the radical expression and use the standard rules of algebra.
Get the absolute value equation by itself. Solve.

22. Characteristics of a Square
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Combine like terms.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

23. If the average of a - b - and 48 is 48 - what is the value of a + b?
FOIL: First - Outer - Inner - Last... Combine Like Terms
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

24. Finding the Volume of a Rectangular Solid
Get the absolute value equation by itself. Solve.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Cross multiply.
VofaRS=lwh

25. If 3(3x)=9(x+2) - what is the value of x?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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

26. Properties of the Interior and Exterior Angles of a Triangle
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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
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.

27. Definition of a Rational Number
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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 coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

28. Difference Between a Factor and a Multiple
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
-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.
Use the formula distance=rate*time and its variations to help in this question.
VofaC: (pie)r(2)h

29. If x(2)=7x+18 - what is the positive value of 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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
VofaC: (pie)r(2)h
Part=Percent x Whole

30. Definition of an Integer
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Sum: Average x Number of Terms
Average: Sum of the Terms/Number of the Terms
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

31. 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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Put each number in the original ratio over the sum of the numbers.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

32. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
VofaRS=lwh
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
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

33. Increasing and Decreasing a Number by a Certain Percentage
-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.
Combine like terms.
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
Plug in the given values for the unknowns and calculate according to PEMDAS.

34. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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 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.
Part=Percent x Whole

35. Calculating Negative Exponents and Radical Exponents
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
FOIL: First - Outer - Inner - Last... Combine Like Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

36. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
-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.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.

37. Solving an Inequality
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

38. Multiplying Expressions with Exponents that Have a Common Base
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
VofaRS=lwh
VofaC: (pie)r(2)h
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

39. What value of x is not in the domain of the function f(x)=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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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
Use the distributive property then combine the like terms.

40. Finding the Length of an Arc in a Circle

41. Counting the Total Number of Possibilities for Several Events to Occur
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.
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.
Use simple numbers like 1 and 2 and see what happens.
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.

42. 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.
Sum: Average x Number of Terms
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

43. Finding the Area of a Circle
Cancel factors common to the numerator and denominator.
Two relatively prime numbers are integers that have no common factor other than 1.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
(pie)r(squared)

44. Converting from part-to-part ratios to part-to-whole ratios
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
Put each number in the original ratio over the sum of the numbers.
VofaC: (pie)r(2)h
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

45. Converting from an Improper Fraction to a Mixed Number
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.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

46. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
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
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.

47. How do you know if an integer is a multiple of 3 or 9?
Switch 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
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

48. Finding the Sum of the Average of a Series of Numbers
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.
Average: Sum of the Terms/Number of the Terms
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Sum: Average x Number of Terms

49. Simplifying an Algebraic Equation
Do whatever is necessary to both sides to isolate the variable.
Cancel factors common to the numerator and denominator.
Multiply the numerators and multiply the denominators.
Slope=change in y/change in x

50. Finding the Domain and Range of a Function
The value that falls in the middle of the set.
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.
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.
The whole number left over after division.