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SAT Math

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. Numbers that are Relatively Prime
Just add or subtract the coefficients in front of the radicals.
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.
Two relatively prime numbers are integers that have no common factor other than 1.
Use simple numbers like 1 and 2 and see what happens.

2. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The value that falls in the middle of the set.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

3. Simplifying an Algebraic Equation
Slope=change in y/change in x
Cancel factors common to the numerator and denominator.
Do whatever is necessary to both sides to isolate the variable.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

4. 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.
Four equal acute angles and four equal obtuse angles.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
(x1+x2)/2 -(y1+y2)/2

5. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Switch the numerator and denominator.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
A(2)+b(2)=c(2)

6. Finding a Term in a Geometric Sequence
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.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Express them with a common denominator.

7. Difference Between a Factor and a Multiple
-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.
Cancel factors common to the numerator and denominator.
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

8. Finding the y-intercept When Given an Equation of a Line
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
-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.

9. If 4(x(2)-10x+25) - then what is the value of x?
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
(pie)r(squared)
Find a common denominator - then add or subtract the numerators.
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.

10. Knowing if an Integer is a Multiple of 5 or 10
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
-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.
2(pie)r
Two relatively prime numbers are integers that have no common factor other than 1.

11. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Get the absolute value equation by itself. Solve.

12. Solving a System of Equations
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Four equal acute angles and four equal obtuse angles.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

13. Finding the Mode of a Set of Numbers
Plug in the given values for the unknowns and calculate according to PEMDAS.
The value that appears the most often.
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

14. Finding the Length of an Arc in a Circle

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15. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Put the equation into y=mx+b-- in which case b is the y-intercept.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

16. Multiplying and Dividing Roots
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.
2(pie)r
Combine like terms.
Use the formula distance=rate*time and its variations to help in this question.

17. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of 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.
Switch the numerator and denominator.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

18. Expressing the Union and Intersection of Sets
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Average the smallest and largest number
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

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

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20. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
A(2)+b(2)=c(2)
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.
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.
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.

21. Finding the Circumference of a Circle
2(pie)r
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.
VofaC: (pie)r(2)h
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

22. Dividing Expressions with Exponents that Have a Common Base
Express them with a common denominator.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Cancel factors common to the numerator and denominator.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

23. What is the Triangle Inequality Theorem?
Use the formula distance=rate*time and its variations to help in this question.
Average the smallest and largest number
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.

24. Solving a Proportion
Cross multiply.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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 exponents - (x^3)^4=x^3*4=x^12

25. What are Two Special Pythagorean Triples?

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26. Finding the Area of a Circle
(pie)r(squared)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Subtract the smallest from the largest and add 1

27. Calculating Negative Exponents and Radical Exponents
Get the absolute value equation by itself. Solve.
Multiply the numerators and multiply the denominators.
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
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

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

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29. Definition of an Integer
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

30. If 3(3x)=9(x+2) - 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.
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
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

31. Finding the Slope When Given an Equation of a Line
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Multiply the exponents - (x^3)^4=x^3*4=x^12

32. Counting the Total Number of Possibilities for Several Events to Occur
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.
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.

33. Properties of a 45-45-90 Triangle
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.
Use simple numbers like 1 and 2 and see what happens.
VofaRS=lwh
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

34. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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 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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

35. What types of angles are formed when two lines intersect?
Isolate the radical expression and use the standard rules of algebra.
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.
Subtract the smallest from the largest and add 1
Adjacent angles are supplementary - Vertical angles are equal

36. Definition of Remainder
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.
The whole number left over after division.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

37. Finding the Missing Number in a Series When You are Given the Average
Put the equation into y=mx+b-- in which case b is the y-intercept.
Just add or subtract the coefficients in front of the radicals.
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.
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.

38. Convert From a Fraction to a Decimal - Vice Versa
A(2)+b(2)=c(2)
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.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

39. What is the Pythagorean Theorem?
Get the absolute value equation by itself. Solve.
A(2)+b(2)=c(2)
Cross multiply.
(x1+x2)/2 -(y1+y2)/2

40. If the average of a - b - and 48 is 48 - what is the value of a + b?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
2(pie)r
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

41. Finding the Domain and Range of a Function
Four equal acute angles and four equal obtuse angles.
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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

42. What types of angles are formed when a transversal cross parallel lines?
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.
Four equal acute angles and four equal obtuse angles.
Use the formula distance=rate*time and its variations to help in this question.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

43. Finding the GCF of Two or More Numbers
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
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
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

44. Finding the Volume of a Cylinder
Two relatively prime numbers are integers that have no common factor other than 1.
VofaC: (pie)r(2)h
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 A per B= Total A/Total B so Average Speed = Total Distance/Total Time

45. Factoring the Difference of Two Squares
Average the smallest and largest number
(x1+x2)/2 -(y1+y2)/2
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

46. 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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Plug in the given values for the unknowns and calculate according to PEMDAS.
The value that falls in the middle of the set.

47. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to 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
Use the units to keep things straight - Snowfall inches/hours

48. 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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
(pie)r(squared)

49. Finding the Median of a Set of Numbers
2(pie)r
The value that falls in the middle of the set.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Cross multiply.

50. Average Rate and How Do You Find It
The whole number left over after division.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25