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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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1. Finding the Sum of the Interior Angles of a Polygon
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.
Use the distributive property then combine the like terms.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

2. 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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
2(pie)r
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

3. Finding the Domain and Range of a Function
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.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.

4. 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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
VofaRS=lwh

5. Finding the Volume of a Cylinder
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
VofaC: (pie)r(2)h
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)

6. Multiply and Divide Positive and Negative Numbers
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes

7. Counting the Total Number of Possibilities for Several Events to Occur
Get the absolute value equation by itself. Solve.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Cross multiply.

8. Finding the Area of a Triangle

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9. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
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
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

10. 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?
-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.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

11. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^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.
Use simple numbers like 1 and 2 and see what happens.

12. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
(x1+x2)/2 -(y1+y2)/2

13. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The whole number left over after division.
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.

14. Adding and Subtracting Roots
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.
Just add or subtract the coefficients in front of the radicals.
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
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.

15. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

16. Formula Used to Find Percent
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The value that appears the most often.
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
Part=Percent x Whole

17. Finding the Area of a Circle
Use simple numbers like 1 and 2 and see what happens.
(pie)r(squared)
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

18. Finding the Missing Number in a Series When You are Given the Average
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Multiply the numerators and multiply the denominators.
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.
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.

19. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
2(pie)r
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.
Multiply the numerators and multiply the denominators.
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.

20. Solving a Problem Involving Rates
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Slope=change in y/change in x
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.
Use the units to keep things straight - Snowfall inches/hours

21. Solving a Radical Equation
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Use the distributive property then combine the like terms.
Isolate the radical expression and use the standard rules of algebra.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

22. Evaluating an Algebraic Expression
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.
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
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Plug in the given values for the unknowns and calculate according to PEMDAS.

23. Finding the Distance Between Two Points on a Coordinate Graph
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
A(2)+b(2)=c(2)
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

24. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Put each number in the original ratio over the sum of the numbers.
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 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
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.

25. 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
Put each number in the original ratio over the sum of the numbers.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.

26. What Does Solving In Terms of Mean?
Combine like terms.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

27. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Average the smallest and largest number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Slope=change in y/change in x

28. Adding and Subtracting Polynomials
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Slope=change in y/change in x
Combine like terms.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

29. Definition of a Rational Number
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

30. Properties of Similar Triangles
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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 y-intercept When Given an Equation of a Line
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 the numerators and multiply the denominators.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Put the equation into y=mx+b-- in which case b is the y-intercept.

32. What is the Pythagorean Theorem?
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
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)

33. How do you know if an integer is a multiple of 3 or 9?
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

34. Multiplying and Dividing Roots
Put the equation into y=mx+b-- in which case b is the y-intercept.
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 the perfect squares under the radical - take their square roots - and put the result in front.
VofaC: (pie)r(2)h

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

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36. What are Two Special Pythagorean Triples?

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37. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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.
Two relatively prime numbers are integers that have no common factor other than 1.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

38. Setting Up a Ratio
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
VofaRS=lwh
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.

39. Numbers that are Relatively Prime
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
Two relatively prime numbers are integers that have no common factor other than 1.

40. 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.
A(2)+b(2)=c(2)
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Part=Percent x Whole

41. Scalene - Isosceles - and Equilateral Triangles
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Do whatever is necessary to both sides to isolate the variable.
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.

42. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

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43. Characteristics of a Parallelogram
Find a common denominator - then add or subtract the numerators.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
VofaC: (pie)r(2)h
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

44. Knowing if an Integer is a Multiple of 5 or 10
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.
-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.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

45. Dividing 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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Adjacent angles are supplementary - Vertical angles are equal

46. If the average of a - b - and 48 is 48 - what is the value of a + b?
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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

47. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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 equation into the slope-intercept form: y=mx+b. The slope is m.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

48. Definition of an Integer
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Express them with a common denominator.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

49. Definition of Remainder
A(2)+b(2)=c(2)
The whole number left over after division.
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

50. Characteristics of a Square
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.