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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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1. 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?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Just add or subtract the coefficients in front of the radicals.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

2. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Sum: Average x Number of Terms
Find a common denominator - then add or subtract the numerators.
Get the absolute value equation by itself. Solve.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

3. Determining Absolute Value of a Number
Use the formula distance=rate*time and its variations to help in this question.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Part=Percent x Whole
Adjacent angles are supplementary - Vertical angles are equal

4. What types of angles are formed when a transversal cross parallel lines?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Multiply the numerators and multiply the denominators.
2(pie)r
Four equal acute angles and four equal obtuse angles.

5. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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
Find a common denominator - then add or subtract the numerators.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

6. Finding the Area of a Sector
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
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
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 two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

7. Definition of an Integer
Cancel factors common to the numerator and denominator.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

8. Adding a Positive Number to a Negative Number
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Part=Percent x Whole
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

9. Simplifying an Algebraic Equation
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Cancel factors common to the numerator and denominator.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Do whatever is necessary to both sides to isolate the variable.

10. 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
Slope=change in y/change in x
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

11. Dividing Expressions with Exponents that Have a Common Base
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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
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
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

12. Simplifying a Fraction to Lowest Terms
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Factor out and cancel all factors the numerator and denominator have in common.
VofaRS=lwh

13. What value of x is not in the domain of the function f(x)=x-2/x-3?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Subtract the smallest from the largest and add 1

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

15. Finding the Rate of Speed
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use the formula distance=rate*time and its variations to help in this question.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

16. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
VofaRS=lwh

17. Setting Up a Ratio
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Combine like terms.

18. Formula to Find Average
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.
Average: Sum of the Terms/Number of the Terms
Sum: Average x Number of Terms
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. Solving a Linear Equation
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Do whatever is necessary to both sides to isolate the variable.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Combine like terms.

20. Formula Used to Find Percent
Part=Percent x Whole
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

21. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Average the smallest and largest number
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

22. Expressing the Union and Intersection of Sets
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 square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Average the smallest and largest number
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

23. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Express them with a common denominator.
Average the smallest and largest number

24. Characteristics of a Square
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

25. Calculating Negative Exponents and Radical Exponents
2(pie)r
VofaC: (pie)r(2)h
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

26. Converting from part-to-part ratios to part-to-whole ratios
Plug in the given values for the unknowns and calculate according to PEMDAS.
Isolate the radical expression and use the standard rules of algebra.
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.

27. General Procedure for Multiplying Polynomials
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Average the smallest and largest number
Use the distributive property then combine the like terms.
-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.

28. Finding the GCF of Two or More Numbers
Multiply the numerators and multiply the denominators.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Two relatively prime numbers are integers that have no common factor other than 1.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

29. Finding the Sum of the Interior Angles of a Polygon
Cancel factors common to the numerator and denominator.
Put the equation into y=mx+b-- in which case b is the y-intercept.
2(pie)r
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

30. Converting from an Improper Fraction to a Mixed Number
The value that falls in the middle of the set.
Slope=change in y/change in x
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

31. Finding the Median of a Set of Numbers
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The value that falls in the middle of the set.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Sum: Average x Number of Terms

32. Finding the Distance Between Two Points on a Coordinate Graph
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
-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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Two relatively prime numbers are integers that have no common factor other than 1.

33. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Put each number in the original ratio over the sum of the numbers.

34. Definition of Remainder
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Switch the numerator and denominator.
The whole number left over after division.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

35. Finding the Missing Number in a Series When You are Given the Average
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
-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.
Put the equation into y=mx+b-- in which case b is the y-intercept.

36. Prime Factorization of a 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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Express them with a common denominator.

37. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
A(2)+b(2)=c(2)
Put each number in the original ratio over the sum of the numbers.
Just add or subtract the coefficients in front of the radicals.

38. 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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

39. What is a Function and how do you Evaluate one?
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.

40. If the average of a - b - and 48 is 48 - what is the value of a + b?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

41. Properties of a 45-45-90 Triangle
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

42. Multiply and Divide Positive and Negative Numbers
Find a common denominator - then add or subtract the numerators.
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.

43. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
VofaRS=lwh
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.
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.

44. Finding the Sum of the Average of a Series of Numbers
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.
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
Sum: Average x Number of Terms
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

45. Adding and Subtracting Polynomials
-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.
Isolate the radical expression and use the standard rules of algebra.
Two relatively prime numbers are integers that have no common factor other than 1.
Combine like terms.

46. Counting the Total Number of Possibilities for Several Events to Occur
Find a common denominator - then add or subtract the numerators.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Do whatever is necessary to both sides to isolate the variable.
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. Convert From a Fraction to a Decimal - Vice Versa
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Put each number in the original ratio over the sum of the numbers.

48. Evaluating an Algebraic Expression
Use the units to keep things straight - Snowfall inches/hours
Combine like terms.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Plug in the given values for the unknowns and calculate according to PEMDAS.

49. Finding the Mode of a Set of Numbers
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
The value that appears the most often.
Use the units to keep things straight - Snowfall inches/hours

50. Raising a Power to a Power
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Four equal acute angles and four equal obtuse angles.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

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