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SAT Math

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Answer 50 questions in 15 minutes.
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1. If the average of a - b - and 48 is 48 - what is the value of a + b?
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

2. 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.
Multiply the numerators and multiply the denominators.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use the units to keep things straight - Snowfall inches/hours

3. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
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.
Find a common denominator - then add or subtract the numerators.

4. Counting the Total Number of Possibilities for Several Events to Occur
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

5. Adding and Subtracting Roots
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Just add or subtract the coefficients in front of the radicals.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Subtract the smallest from the largest and add 1

6. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Average the smallest and largest number
Use simple numbers like 1 and 2 and see what happens.
Average: Sum of the Terms/Number of the Terms

7. Finding the Area of a Triangle

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8. Finding the Area of a Sector

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9. Finding a Term in a Geometric Sequence
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.
Express them with a common denominator.
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 numerators and multiply the denominators.

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

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11. Solving a System of Equations
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.
-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.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

12. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
-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.
2(pie)r
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

13. Simplifying Square Roots
Subtract the smallest from the largest and add 1
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Put the equation into y=mx+b-- in which case b is the y-intercept.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

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

15. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The value that falls in the middle of the set.
Use simple numbers like 1 and 2 and see what happens.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

16. Finding the Median of a Set of Numbers
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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
The value that falls in the middle of the set.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

17. 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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Part=Percent x Whole
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.

18. Multiplying 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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Average: Sum of the Terms/Number of 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

19. Calculating the Probability that an Event will Take Place
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Average the smallest and largest number
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

20. Factoring a Polynomial ('FOIL in Reverse')
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)
Find a common denominator - then add or subtract the numerators.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

21. Finding the Rate of Speed
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use the formula distance=rate*time and its variations to help in this question.
(pie)r(squared)

22. Solving a Proportion
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 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Use the units to keep things straight - Snowfall inches/hours
Cross multiply.

23. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
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.

24. 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.
VofaRS=lwh
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

25. Expressing the Union and Intersection of Sets
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Subtract the smallest from the largest and add 1
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
Use the distributive property then combine the like terms.

26. Definition of Remainder
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
The whole number left over after division.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

27. Adding and Subtracting Fractions
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Find a common denominator - then add or subtract the numerators.

28. Adding a Positive Number to a Negative Number
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Find a common denominator - then add or subtract the numerators.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

29. Definition of an Integer
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Multiply the numerators and multiply the denominators.
(x1+x2)/2 -(y1+y2)/2

30. Finding the Slope of a Line When Given Two Points on the Line
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.
Slope=change in y/change in x
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
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.

31. Finding the Midpoint Between Two Points
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Use the distributive property then combine the like terms.
(x1+x2)/2 -(y1+y2)/2
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.

32. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Two relatively prime numbers are integers that have no common factor other than 1.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

33. Finding the GCF of Two or More Numbers
Plug in the given values for the unknowns and calculate according to PEMDAS.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

34. Solving a Radical Equation
Factor out and cancel all factors the numerator and denominator have in common.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Isolate the radical expression and use the standard rules of algebra.

35. If x(2)=7x+18 - what is the positive value of x?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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 value that appears the most often.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

36. How do you know if an integer is a multiple of 3 or 9?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

37. Characteristics of a Square
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Cancel factors common to the numerator and denominator.
The value that falls in the middle of the set.

38. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
Part=Percent x Whole
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Two relatively prime numbers are integers that have no common factor other than 1.

39. 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?
Put the equation into y=mx+b-- in which case b is the y-intercept.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

40. If 4(x(2)-10x+25) - then what is the value of x?
Isolate the radical expression and use the standard rules of algebra.
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.
Do whatever is necessary to both sides to isolate the variable.
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.

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

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42. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

43. Multiplying Binomials
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
FOIL: First - Outer - Inner - Last... Combine Like Terms
The value that appears the most often.
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. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

45. Solving an Inequality
-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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

46. Finding the Distance Between Two Points on a Coordinate Graph
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Use the units to keep things straight - Snowfall inches/hours
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

47. Properties of a 45-45-90 Triangle
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Part=Percent x Whole
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

48. Convert From a Fraction to a Decimal - Vice Versa
-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.
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 the units to keep things straight - Snowfall inches/hours
Two relatively prime numbers are integers that have no common factor other than 1.

49. Calculating Negative Exponents and Radical Exponents
-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.
-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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

50. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

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