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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. Direct Variation and Inverse Variation
Factor out and cancel all factors the numerator and denominator have in common.
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(2)+b(2)=c(2)
The value that falls in the middle of the set.

2. 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.
Use the formula distance=rate*time and its variations to help in this question.
-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.
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.

3. 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.
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

4. If 2+l6-xl=10 and x>0 - what is the value of 2x?
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Get the absolute value equation by itself. Solve.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.

5. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

6. Comparing the values of two or more Fractions
Cross multiply.
Express them with a common denominator.
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.
Cancel factors common to the numerator and denominator.

7. Definition of Remainder
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
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 whole number left over after division.

8. Solving a Problem Involving Rates
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use the units to keep things straight - Snowfall inches/hours
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

9. If 3(3x)=9(x+2) - what is the value of x?
-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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
Just add or subtract the coefficients in front of the radicals.

10. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
-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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

11. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-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.

12. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/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.

13. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
The value that falls in the middle of the set.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

14. Counting the Total Number of Possibilities for Several Events to Occur
Cross multiply.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
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.

15. Evaluating an Algebraic Expression
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
VofaRS=lwh
Plug in the given values for the unknowns and calculate according to PEMDAS.

16. What are Two Special Pythagorean Triples?

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17. An Important Property of a Line Tangent to a Circle
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Cancel factors common to the numerator and denominator.
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.

18. Finding the Area of a Sector

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19. If (Square Root: x-1)+5=12 - what is the value of x/2?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Isolate the radical expression and use the standard rules of algebra.
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

20. Expressing the Union and Intersection of Sets
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.
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
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

21. If 4(x(2)-10x+25) - then what is the value of x?
Express them with a common denominator.
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.
Put each number in the original ratio over the sum of the numbers.
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.

22. Finding the Midpoint Between Two Points
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
Express them with a common denominator.
(x1+x2)/2 -(y1+y2)/2
Switch the numerator and denominator.

23. Multiplying Expressions with Exponents that Have a Common Base
Two relatively prime numbers are integers that have no common factor other than 1.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Get the absolute value equation by itself. Solve.

24. Adding and Subtracting Roots
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Just add or subtract the coefficients in front of the radicals.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

25. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^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.
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.

26. Finding the Area of a Triangle

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27. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
2(pie)r

28. Adding and Subtracting Polynomials
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Combine like terms.
-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.
Subtract the smallest from the largest and add 1

29. Multiplying Binomials
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

30. Multiplying and Dividing Roots
The value that appears the most often.
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.
Find a common denominator - then add or subtract the numerators.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

31. PEMDAS
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
FOIL: First - Outer - Inner - Last... Combine Like Terms
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

32. 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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
Cancel factors common to the numerator and denominator.

33. Adding a Positive Number to a Negative Number
Just add or subtract the coefficients in front of the radicals.
Express them with a common denominator.
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

34. Multiplying Fractions
Multiply the numerators and multiply the denominators.
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: Average x Number of Terms
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

35. How do you know if an integer is a multiple of 3 or 9?
Slope=change in y/change in x
(x1+x2)/2 -(y1+y2)/2
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.
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

36. Factoring the Difference of Two Squares
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Adjacent angles are supplementary - Vertical angles are equal
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

37. 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
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
Switch the numerator and denominator.

38. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Subtract the smallest from the largest and add 1
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Cancel factors common to the numerator and denominator.

39. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

40. Finding the LCM of Two or More Numbers

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41. Finding the y-intercept When Given an Equation of a Line
Put each number in the original ratio over the sum of the numbers.
Four equal acute angles and four equal obtuse angles.
VofaC: (pie)r(2)h
Put the equation into y=mx+b-- in which case b is the y-intercept.

42. What is the Pythagorean Theorem?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
A(2)+b(2)=c(2)
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

43. Characteristics of a Square
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
A(2)+b(2)=c(2)

44. Setting Up a Ratio
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
FOIL: First - Outer - Inner - Last... Combine Like Terms
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.

45. Counting Consecutive Integers
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Subtract the smallest from the largest and add 1
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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

46. Dividing Expressions with Exponents that Have a Common Base
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 the whole number part by the denominator - then add the numerator. Keep the same denominator.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply the numerators and multiply the denominators.

47. Determining Absolute Value of a Number
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
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

48. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
(x1+x2)/2 -(y1+y2)/2
The whole number left over after division.
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.

49. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Express them with a common denominator.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

50. What is the Triangle Inequality Theorem?
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
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