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SAT Math

Subjects : sat, math

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Answer 50 questions in 15 minutes.
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1. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Get the absolute value equation by itself. Solve.
Two relatively prime numbers are integers that have no common factor other than 1.

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

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3. Characteristics of a Rectangle
Use the units to keep things straight - Snowfall inches/hours
VofaC: (pie)r(2)h
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

4. If (Square Root: x-1)+5=12 - what is the value of x/2?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

5. Finding the Mode of a Set of Numbers
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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 appears the most often.
The value that falls in the middle of the set.

6. 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?
Average the smallest and largest number
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.

7. Adding and Subtracting Fractions
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
(x1+x2)/2 -(y1+y2)/2
Find a common denominator - then add or subtract the numerators.
Do whatever is necessary to both sides to isolate the variable.

8. Simplifying an Algebraic Equation
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Cancel factors common to the numerator and denominator.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Multiply the numerators and multiply the denominators.

9. What are Two Special Pythagorean Triples?

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10. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

11. Properties of a 30-60-90 Triangle
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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

12. Finding the Reciprocal of a Fraction
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Switch the numerator and denominator.
Factor out and cancel all factors the numerator and denominator have in common.
Use the units to keep things straight - Snowfall inches/hours

13. Converting from an Improper Fraction to a Mixed Number
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.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

14. Solving a Radical Equation
-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.
Do whatever is necessary to both sides to isolate the variable.
2(pie)r
Isolate the radical expression and use the standard rules of algebra.

15. Finding the Distance Between Two Points on a Coordinate Graph
Express them with a common denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
-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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

16. Definition of a Rational Number
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Cross multiply.

17. Formula to Find Average
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Combine like terms.
Average: Sum of the Terms/Number of the Terms
Cancel factors common to the numerator and denominator.

18. If x(2)=7x+18 - what is the positive value of x?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Use the distributive property then combine the like terms.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

19. Comparing the values of two or more Fractions
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Express them with a common denominator.
-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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

20. Finding the Surface Area of a Rectangular Solid
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The value that falls in the middle of the set.
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.

21. 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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Factor out and cancel all factors the numerator and denominator have in common.
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

22. Number of Groups - +1 Each Time
The value that appears the most often.
Part=Percent x Whole
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.

23. Counting the Total Number of Possibilities for Several Events to Occur
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.
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 value that appears the most often.
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.

24. If 2+l6-xl=10 and x>0 - what is the value of 2x?
The whole number left over after division.
-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.
-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.
Get the absolute value equation by itself. Solve.

25. Calculating Negative Exponents and Radical Exponents
-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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Average: Sum of the Terms/Number of the Terms
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

26. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Find a common denominator - then add or subtract the numerators.
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.

27. Solving a System of Equations
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.
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.
Cancel factors common to the numerator and denominator.
VofaRS=lwh

28. Quickly Finding the Average of a Series of Evenly Spaced Numbers
VofaC: (pie)r(2)h
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.
Adjacent angles are supplementary - Vertical angles are equal
Average the smallest and largest number

29. Finding the Area of a Circle
Use the distributive property then combine the like terms.
(pie)r(squared)
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

30. Knowing if an Integer is a Multiple of 2 or 4
-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.
VofaRS=lwh
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.
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.

31. Finding the Domain and Range of a Function
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Express them with a common denominator.
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

32. Finding the Area of a Sector

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33. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Put the equation into y=mx+b-- in which case b is the y-intercept.
Just add or subtract the coefficients in front of the radicals.

34. Prime Factorization of a Number
Just add or subtract the coefficients in front of the radicals.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
VofaC: (pie)r(2)h
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.

35. Adding a Positive Number to a Negative Number
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

36. Multiplying Binomials
FOIL: First - Outer - Inner - Last... 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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Multiply the exponents - (x^3)^4=x^3*4=x^12

37. Counting Consecutive Integers
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Subtract the smallest from the largest and add 1

38. Multiplying and Dividing Roots
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.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

39. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
The value that falls in the middle of the set.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Sum: Average x Number of Terms

40. Characteristics of a Parallelogram
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.
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.
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.

41. If 4(x(2)-10x+25) - then what is the value of x?
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
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.

42. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

43. Definition of an Irrational Number
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
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

44. Solving a Proportion
Cross multiply.
Use the formula distance=rate*time and its variations to help in this question.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

45. Solving an Inequality
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.
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.

46. What types of angles are formed when two lines intersect?
Cross multiply.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Find a common denominator - then add or subtract the numerators.
Adjacent angles are supplementary - Vertical angles are equal

47. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

48. 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
Subtract the smallest from the largest and add 1
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

49. 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
Put the equation into y=mx+b-- in which case b is the y-intercept.
Use the units to keep things straight - Snowfall inches/hours
(x1+x2)/2 -(y1+y2)/2

50. Multiply and Divide Positive and Negative Numbers
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Put each number in the original ratio over the sum of the numbers.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

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