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SAT Math

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Answer 50 questions in 15 minutes.
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1. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

2. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

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3. Characteristics of a Square
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.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

4. Raising a Power to a Power
Plug in the given values for the unknowns and calculate according to PEMDAS.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply the exponents - (x^3)^4=x^3*4=x^12
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

5. Finding the y-intercept When Given an Equation of a Line
Use the units to keep things straight - Snowfall inches/hours
The value that falls in the middle of the set.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.

6. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Find a common denominator - then add or subtract the numerators.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

7. Finding the Domain and Range of a Function
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.

8. What is the greatest of three consecutive odd integers where the sum of the third and twice the first is equal to nine more than twice the second?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
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.

9. How do you know if an integer is a multiple of 3 or 9?
Multiply the numerators and multiply the denominators.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.

10. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/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.
Sum: Average x Number of Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

11. 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
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.
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

12. Increasing and Decreasing a Number by a Certain Percentage
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Just add or subtract the coefficients in front of the radicals.
-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.

13. Characteristics of a Rectangle
Express them with a common denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

14. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Use simple numbers like 1 and 2 and see what happens.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

15. Prime Factorization of a Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Slope=change in y/change in x
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
Multiply the exponents - (x^3)^4=x^3*4=x^12

16. Properties of the Interior and Exterior Angles of a Triangle
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
2(pie)r
-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.

17. An Important Property of a Line Tangent to a Circle
(x1+x2)/2 -(y1+y2)/2
Use simple numbers like 1 and 2 and see what happens.
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.
Find a common denominator - then add or subtract the numerators.

18. If the average of a - b - and 48 is 48 - what is the value of a + b?
Part=Percent x Whole
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

19. Determining Absolute Value of a Number
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

20. Comparing the values of two or more Fractions
Express them with a common denominator.
Use simple numbers like 1 and 2 and see what happens.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Use the units to keep things straight - Snowfall inches/hours

21. What is the Pythagorean Theorem?
-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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
VofaRS=lwh
A(2)+b(2)=c(2)

22. What are Two Special Pythagorean Triples?

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23. 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?
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 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

24. Solving a Proportion
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Cross multiply.
-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.
Put each number in the original ratio over the sum of the numbers.

25. Formula Used to Find Percent
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Part=Percent x Whole
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Just add or subtract the coefficients in front of the radicals.

26. Definition of a Rational Number
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

27. Converting From a Mixed Number to an Improper Fraction
Express them with a common denominator.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

28. Finding the Area of a Sector

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29. Solving a Problem Involving Rates
Subtract the smallest from the largest and add 1
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Use the units to keep things straight - Snowfall inches/hours

30. Scalene - Isosceles - and Equilateral Triangles
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
The value that falls in the middle of the set.
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.

31. If r#t=t(r)-r(t) - then what is 4#3?
Get the absolute value equation by itself. Solve.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

32. Finding the Rate of Speed
Use the formula distance=rate*time and its variations to help in this question.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The value that appears the most often.

33. 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.
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.
Adjacent angles are supplementary - Vertical angles are equal
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

34. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Express them with a common denominator.

35. Finding the Mode of a Set of Numbers
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The value that appears the most often.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
The value that falls in the middle of the set.

36. Number of Groups - +1 Each Time
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

37. Solving an Inequality
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

38. Adding and Subtracting Monomials
Isolate the radical expression and use the standard rules of algebra.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Get the absolute value equation by itself. Solve.
Cancel factors common to the numerator and denominator.

39. What types of angles are formed when two lines intersect?
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.
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.
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)

40. Knowing if an Integer is a Multiple of 5 or 10
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
-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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Adjacent angles are supplementary - Vertical angles are equal

41. If x(2)=7x+18 - what is the positive value of x?
Factor out and cancel all factors the numerator and denominator have in common.
Subtract the smallest from the largest and add 1
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.

42. Solving a Linear Equation
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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

43. Finding the Slope When Given an Equation of a Line
Multiply the exponents - (x^3)^4=x^3*4=x^12
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

44. Convert From a Fraction to a Decimal - Vice Versa
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Multiply the numerators and multiply the denominators.

45. Evaluating an Algebraic Expression
FOIL: First - Outer - Inner - Last... Combine Like Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

46. Finding the Circumference of a Circle
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
2(pie)r
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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

47. 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
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
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Slope=change in y/change in x

48. Finding the Area of a Circle
(pie)r(squared)
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Cancel factors common to the numerator and denominator.
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

49. 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.
Isolate the radical expression and use the standard rules of algebra.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

50. What types of angles are formed when a transversal cross parallel lines?
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Four equal acute angles and four equal obtuse angles.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

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