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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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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. General Procedure for Multiplying Polynomials
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply the exponents - (x^3)^4=x^3*4=x^12
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 distributive property then combine the like terms.

2. Knowing if an Integer is a Multiple of 2 or 4
Average: Sum of the Terms/Number of the Terms
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Combine like terms.
-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.

3. Finding the y-intercept When Given an Equation of a Line
Use the distributive property then combine the like terms.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
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.

4. Formula to Find Average
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.
Average: Sum of the Terms/Number of the Terms
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

5. Finding the LCM of Two or More Numbers

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6. What value of x is not in the domain of the function f(x)=x-2/x-3?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Part=Percent x Whole
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
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.

7. Finding the Area of a Circle
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Factor out and cancel all factors the numerator and denominator 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.
(pie)r(squared)

8. Definition of Remainder
The whole number left over after division.
Subtract the smallest from the largest and add 1
Probability: Number of Favorable Outcomes/Total Possible Outcomes
(pie)r(squared)

9. Scalene - Isosceles - and Equilateral Triangles
Just add or subtract the coefficients in front of the radicals.
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.
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 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.

10. Finding a Term in a Geometric Sequence
Multiply the numerators and multiply the denominators.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.

11. Finding the Slope When Given an Equation of a Line
Average: Sum of the Terms/Number of the Terms
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

12. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
-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.
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.

13. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
Average: Sum of the Terms/Number of the Terms
Put each number in the original ratio over the sum of the numbers.
Cancel factors common to the numerator and denominator.

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

15. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Plug in the given values for the unknowns and calculate according to PEMDAS.
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
Average the smallest and largest number
(x1+x2)/2 -(y1+y2)/2

16. Definition of an Integer
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.

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

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18. Counting the Total Number of Possibilities for Several Events to Occur
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
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.
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.

19. Comparing the values of two or more Fractions
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Express them with a common denominator.

20. Finding the Rate of Speed
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.
Find a common denominator - then add or subtract the numerators.
Slope=change in y/change in x
Use the formula distance=rate*time and its variations to help in this question.

21. Simplifying an Algebraic Equation
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Cancel factors common to the numerator and denominator.

22. Raising a Power to a Power
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Subtract the smallest from the largest and add 1
Multiply the exponents - (x^3)^4=x^3*4=x^12

23. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
-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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
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

24. 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.
Switch the numerator and denominator.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Adjacent angles are supplementary - Vertical angles are equal

25. An Important Property of a Line Tangent to 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.
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
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.
Cancel factors common to the numerator and denominator.

26. Multiplying Fractions
Multiply the numerators and multiply the denominators.
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
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

27. How do you know if an integer is a multiple of 3 or 9?
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.

28. Difference Between a Factor and a Multiple
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.
Isolate the radical expression and use the standard rules of algebra.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

29. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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
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
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.

30. If x(2)=7x+18 - what is the positive value of x?
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.

31. 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.
-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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

32. Finding the Volume of a Cylinder
Use simple numbers like 1 and 2 and see what happens.
Find a common denominator - then add or subtract the numerators.
Multiply the numerators and multiply the denominators.
VofaC: (pie)r(2)h

33. Finding the Surface Area of a Rectangular Solid
(pie)r(squared)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Switch the numerator and denominator.

34. Knowing if an Integer is a Multiple of 5 or 10
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
-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.
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.
Use the distributive property then combine the like terms.

35. Finding the Sum of the Interior Angles of a Polygon
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

36. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
Get the absolute value equation by itself. Solve.
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

37. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Slope=change in y/change in x
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Put the equation into y=mx+b-- in which case b is the y-intercept.

38. Factoring a Polynomial ('FOIL in Reverse')
Use the distributive property then combine the like terms.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
The value that falls in the middle of the set.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

39. 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
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.
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

40. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Cancel factors common to the numerator and denominator.
Get the absolute value equation by itself. Solve.
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.

41. 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?
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.
Four equal acute angles and four equal obtuse angles.
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

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 value that appears the most often.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Combine like terms.

43. Finding the Circumference of a Circle
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
(x1+x2)/2 -(y1+y2)/2
2(pie)r

44. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
A(2)+b(2)=c(2)
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Sum: Average x Number of Terms

45. Sale Price of a Jacket Marked Down 30% Each Week for 3 Weeks - What % of the Original Price is the Cost of the Jacket After the 3 Week Sale Period
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%
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
The value that falls in the middle of the set.

46. 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
Use the formula distance=rate*time and its variations to help in this question.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

47. Calculating the Probability that an Event will Take Place
(pie)r(squared)
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Factor out and cancel all factors the numerator and denominator have in common.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

48. Finding the GCF of Two or More Numbers
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

49. Finding the Sum of the Average of a Series of Numbers
Multiply the exponents - (x^3)^4=x^3*4=x^12
Part=Percent x Whole
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Sum: Average x Number of Terms

50. Finding the Reciprocal of a Fraction
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
Switch the numerator and denominator.