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SAT Math

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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. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Use simple numbers like 1 and 2 and see what happens.

2. Finding the Distance Between Two Points on a Coordinate Graph
Switch the numerator and denominator.
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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

3. What is the Pythagorean Theorem?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
A(2)+b(2)=c(2)
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

4. Solving a Proportion
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
A(2)+b(2)=c(2)
Cross multiply.

5. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
The whole number left over after division.
Use the formula distance=rate*time and its variations to help in this question.

6. Multiplying Expressions with Exponents that Have a Common Base
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Isolate the radical expression and use the standard rules of algebra.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

7. Multiply and Divide Positive and Negative Numbers
Get the absolute value equation by itself. Solve.
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
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Use the formula distance=rate*time and its variations to help in this question.

8. Converting from an Improper Fraction to a Mixed Number
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.
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.
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.
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

9. Formula Used to Find Percent
Cross multiply.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Part=Percent x Whole
Use the units to keep things straight - Snowfall inches/hours

10. 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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.

11. PEMDAS
-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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
-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. Knowing if an Integer is a Multiple of 2 or 4
Find a common denominator - then add or subtract the numerators.
A(2)+b(2)=c(2)
(pie)r(squared)
-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.

13. 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.
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.
Express them with a common denominator.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

14. Finding the Sum of the Interior Angles of a Polygon
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

15. Solving a Linear Equation
The value that falls in the middle of the set.
Do whatever is necessary to both sides to isolate the variable.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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

16. Simplifying an Algebraic Equation
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Four equal acute angles and four equal obtuse angles.
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.
Cancel factors common to the numerator and denominator.

17. Multiplying Monomials
Switch the numerator and denominator.
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 coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

18. If 3(3x)=9(x+2) - what is the value of x?
Use the formula distance=rate*time and its variations to help in this question.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
The whole number left over after division.
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.

19. Finding a Term in a Geometric Sequence
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
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 radical expression and use the standard rules of algebra.

20. What is the positive difference between the answers to the equation 35+x(2)=12x?

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21. Factoring the Difference of Two Squares
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Put each number in the original ratio over the sum of the numbers.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

22. 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.
Factor out and cancel all factors the numerator and denominator have in common.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

23. Number of Groups - +1 Each Time
Multiply the numerators and multiply the denominators.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

24. Definition of Remainder
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
The whole number left over after division.

25. 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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
(pie)r(squared)

26. Finding the Rate of Speed
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Do whatever is necessary to both sides to isolate the variable.
Use the formula distance=rate*time and its variations to help in this question.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

27. Convert From a Fraction to a Decimal - Vice Versa
Factor out and cancel all factors the numerator and denominator have in common.
2(pie)r
A(2)+b(2)=c(2)
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.

28. Finding the Area of a Triangle

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29. Finding the Length of an Arc in a Circle

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30. Finding the Area of a Sector

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31. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
(x1+x2)/2 -(y1+y2)/2
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Use the distributive property then combine the like terms.

32. Properties of a 45-45-90 Triangle
-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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
(pie)r(squared)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

33. Definition of a Rational Number
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

34. Scalene - Isosceles - and Equilateral Triangles
Scalene- No sides or angles are equal - Isosceles- Have two equal sides. The angles opposite the equal sides are also equal - Equilateral- All three sides and angles are equal.
FOIL: First - Outer - Inner - Last... Combine Like Terms
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

35. Evaluating an Algebraic Expression
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
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

36. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
A(2)+b(2)=c(2)
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.

37. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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.
Get the absolute value equation by itself. Solve.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

38. Finding the Surface Area of a Rectangular Solid
(pie)r(squared)
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

39. Numbers that are Relatively Prime
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.
Two relatively prime numbers are integers that have no common factor other than 1.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
2(pie)r

40. Finding the GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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
Express them with a common denominator.

41. Finding the Volume of a Rectangular Solid
-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.
Average the smallest and largest number
VofaRS=lwh
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

42. Setting Up a Ratio
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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
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.

43. How do you know if an integer is a multiple of 3 or 9?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Find a common denominator - then add or subtract the numerators.
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.
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.

44. Comparing the values of two or more Fractions
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Express them with a common denominator.
Sum: Average x Number of Terms

45. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
VofaRS=lwh
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
FOIL: First - Outer - Inner - Last... Combine Like Terms

46. 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.
-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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.

47. Counting Consecutive Integers
Average: Sum of the Terms/Number of the Terms
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
-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.

48. Adding a Positive Number to a Negative Number
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Put the equation into y=mx+b-- in which case b is the y-intercept.
-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.

49. Dividing Expressions with Exponents that Have a Common Base
VofaRS=lwh
Use the distributive property then combine the like terms.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

50. An Important Property of a Line Tangent to a Circle
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.

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