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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. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
Use the formula distance=rate*time and its variations to help in this question.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

2. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Use the distributive property then combine the like terms.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

3. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
A(2)+b(2)=c(2)
Plug in the given values for the unknowns and calculate according to PEMDAS.

4. Multiplying Monomials
Sum: Average x Number of Terms
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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

5. Prime Factorization of a Number
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.
2(pie)r
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

6. An Important Property of a Line Tangent to a Circle
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
-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.

7. Characteristics of a Rectangle
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Multiply the exponents - (x^3)^4=x^3*4=x^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.

8. If 4(x(2)-10x+25) - then what is the value of x?
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Just add or subtract the coefficients in front of the radicals.

9. General Procedure for Multiplying Polynomials
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use the distributive property then combine the like terms.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Subtract the smallest from the largest and add 1

10. Finding the Slope When Given an Equation of a Line
Factor out and cancel all factors the numerator and denominator have in common.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

11. Simplifying an Algebraic Equation
Four equal acute angles and four equal obtuse angles.
Do whatever is necessary to both sides to isolate the variable.
Cancel factors common to the numerator and denominator.
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.

12. Formula to Find Average
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.
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
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.
Average: Sum of the Terms/Number of the Terms

13. 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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
(x1+x2)/2 -(y1+y2)/2

14. 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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Factor out and cancel all factors the numerator and denominator have in common.

15. Finding the Circumference of a Circle
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
2(pie)r

16. Converting from an Improper Fraction to a Mixed Number
Switch the numerator and denominator.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.

17. Finding the Distance Between Two Points on a Coordinate Graph
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.
2(pie)r
Factor out and cancel all factors the numerator and denominator have in common.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

18. Finding a Term in a Geometric Sequence
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Just add or subtract the coefficients in front of the radicals.

19. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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.
The whole number left over after division.
Use simple numbers like 1 and 2 and see what happens.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

20. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
Get the absolute value equation by itself. Solve.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.

21. Finding the Median of a Set of Numbers
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Average the smallest and largest number
The value that falls in the middle of the set.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

22. Factoring a Polynomial ('FOIL in Reverse')
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 - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.

23. If 3(3x)=9(x+2) - what is the value of x?
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.
(x1+x2)/2 -(y1+y2)/2
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

24. Increasing and Decreasing a Number by a Certain Percentage
-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 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%
Cancel factors common to the numerator and denominator.

25. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Average the smallest and largest number
Subtract the smallest from the largest and add 1
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

26. Simplifying Square Roots
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Two relatively prime numbers are integers that have no common factor other than 1.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

27. Finding the Sum of the Average of a Series of Numbers
-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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Sum: Average x Number of Terms

28. Raising a Power to a Power
Part=Percent x Whole
Multiply the exponents - (x^3)^4=x^3*4=x^12
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
The value that appears the most often.

29. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Express them with a common denominator.
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.
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.

30. If x(2)=7x+18 - what is the positive value of x?
-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.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

31. Knowing if an Integer is a Multiple of 2 or 4
The value that falls in the middle of the set.
-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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Use simple numbers like 1 and 2 and see what happens.

32. Quickly Finding the Average of a Series of Evenly Spaced Numbers
-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.
Switch the numerator and denominator.
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.
Average the smallest and largest number

33. Definition of an Irrational Number
Switch the numerator and denominator.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.

34. 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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Switch the numerator and denominator.

35. Dividing Expressions with Exponents that Have a Common Base
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
VofaRS=lwh

36. 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?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Use the units to keep things straight - Snowfall inches/hours
VofaRS=lwh
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

37. What are Two Special Pythagorean Triples?

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38. Definition of an Integer
VofaC: (pie)r(2)h
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

39. Average Rate and How Do You Find It
Average: Sum of the Terms/Number of the Terms
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

40. Formula Used to Find Percent
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Part=Percent x Whole
Use the distributive property then combine the like terms.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

41. Adding and Subtracting Monomials
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.

42. Calculating Negative Exponents and Radical Exponents
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
The whole number left over after division.

43. Finding the Volume of a Cylinder
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
VofaC: (pie)r(2)h
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

44. 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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Do whatever is necessary to both sides to isolate the variable.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

45. Solving a Radical Equation
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
Isolate the radical expression and use the standard rules of algebra.

46. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Cancel factors common to the numerator and 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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

47. 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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
The value that appears the most often.

48. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Part=Percent x Whole
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
The value that falls in the middle of the set.

49. Finding the Rate of Speed
Use the formula distance=rate*time and its variations to help in this question.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

50. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
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.
Isolate the radical expression and use the standard rules of algebra.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds