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SAT Math

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Answer 50 questions in 15 minutes.
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1. If r#t=t(r)-r(t) - then what is 4#3?
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
The value that falls in the middle of the set.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

2. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Use the formula distance=rate*time and its variations to help in this question.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
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.

3. What types of angles are formed when two lines intersect?
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Isolate the radical expression and use the standard rules of algebra.

4. Converting From a Mixed Number to an Improper Fraction
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Average: Sum of the Terms/Number of the Terms
Factor out and cancel all factors the numerator and denominator have in common.

5. Number of Groups - +1 Each Time
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

6. Simplifying an Algebraic Equation
Cross multiply.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Cancel factors common to the numerator and denominator.
The whole number left over after division.

7. 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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Plug in the given values for the unknowns and calculate according to PEMDAS.

8. Finding the Rate of Speed
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Four equal acute angles and four equal obtuse angles.
Use the formula distance=rate*time and its variations to help in this question.
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.

9. If 3(3x)=9(x+2) - what is the value of x?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Express them with a common denominator.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

10. Finding the Volume of a Rectangular Solid
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.
VofaRS=lwh
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

11. What are Two Special Pythagorean Triples?

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12. PEMDAS
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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

13. Finding the Circumference of a Circle
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
2(pie)r
A(2)+b(2)=c(2)

14. Finding the Reciprocal of a Fraction
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Switch the numerator and denominator.

15. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
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.
The value that appears the most often.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

16. Simplifying a Fraction to Lowest Terms
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Factor out and cancel all factors the numerator and denominator have in common.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

17. Dividing Fractions
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

18. Scalene - Isosceles - and Equilateral Triangles
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Cancel factors common to the numerator and denominator.
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.
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.

19. Solving a Linear Equation
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
Do whatever is necessary to both sides to isolate the variable.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

20. What value of x is not in the domain of the function f(x)=x-2/x-3?
Just add or subtract the coefficients in front of the radicals.
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.
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
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

21. Characteristics of a Square
Find a common denominator - then add or subtract the numerators.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

22. Formula Used to Find Percent
Part=Percent x Whole
Put the equation into y=mx+b-- in which case b is the y-intercept.
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 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

23. 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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.

24. Solving a Radical Equation
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Isolate the radical expression and use the standard rules of algebra.
Average the smallest and largest number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

25. 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.
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
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.
Use the distributive property then combine the like terms.

26. Solving an Inequality
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Sum: Average x Number of Terms
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Switch the numerator and denominator.

27. Adding and Subtracting Polynomials
Combine like terms.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

28. An Important Property of a Line Tangent to a Circle
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Find a common denominator - then add or subtract the numerators.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

29. If (Square Root: x-1)+5=12 - what is the value of x/2?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
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.

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

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31. Characteristics of a Rectangle
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
Combine like terms.
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

32. Raising a Power to a Power
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Average the smallest and largest number
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.

33. Finding the Median of a Set of Numbers
Part=Percent x Whole
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The value that falls in the middle of the set.

34. Finding the Slope When Given an Equation of a Line
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use the units to keep things straight - Snowfall inches/hours
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.

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

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36. What types of angles are formed when a transversal cross parallel lines?
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Four equal acute angles and four equal obtuse angles.

37. Finding the Sum of the Interior Angles of a Polygon
2(pie)r
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Switch the numerator and denominator.

38. Finding the Sum of the Average of a Series of Numbers
-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.
-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 numerators and multiply the denominators.
Sum: Average x Number of Terms

39. Properties of the Interior and Exterior Angles of a Triangle
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 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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

40. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

41. Finding the Mode of a Set of Numbers
The value that appears the most often.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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 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.

42. 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?
-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.
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.
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

43. Finding the Volume of a Cylinder
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Part=Percent x Whole
VofaC: (pie)r(2)h
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

44. Numbers that are Relatively Prime
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

45. Prime Factorization of a Number
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

46. If x(2)=7x+18 - what is the positive value of x?
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use the units to keep things straight - Snowfall inches/hours
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

47. Finding the Length of an Arc in a Circle

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48. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
-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.
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.

49. 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
-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.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

50. Definition of an Irrational Number
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

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