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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. Adding and Subtracting Fractions
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Find a common denominator - then add or subtract the numerators.
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. If x(2)=7x+18 - what is the positive value of x?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Adjacent angles are supplementary - Vertical angles are equal
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

3. Convert From a Fraction to a Decimal - Vice Versa
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Get the absolute value equation by itself. Solve.
FOIL: First - Outer - Inner - Last... Combine Like Terms

4. Simplifying an Algebraic Equation
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.
Switch the numerator and denominator.
Cancel factors common to the numerator and denominator.
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.

5. 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.
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.

6. Finding the Length of an Arc in a Circle

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7. 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?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

8. Knowing if an Integer is a Multiple of 2 or 4
Plug in the given values for the unknowns and calculate according to PEMDAS.
-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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

9. Finding the Volume of a Rectangular Solid
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
VofaRS=lwh
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

10. Converting from an Improper Fraction to a Mixed Number
-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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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.

11. Properties of a 30-60-90 Triangle
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Do whatever is necessary to both sides to isolate the variable.

12. 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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Express them with a common denominator.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

13. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Factor out and cancel all factors the numerator and denominator have in common.
Four equal acute angles and four equal obtuse angles.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

14. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
A(2)+b(2)=c(2)
Use the distributive property then combine the like terms.
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

15. Expressing the Union and Intersection of Sets
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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

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

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17. If the average of a - b - and 48 is 48 - what is the value of a + b?
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

18. Quickly Finding the Average of a Series of Evenly Spaced Numbers
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
VofaRS=lwh
Average the smallest and largest number
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.

19. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
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.
Use simple numbers like 1 and 2 and see what happens.
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

20. 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.
Express them with a common denominator.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Four equal acute angles and four equal obtuse angles.

21. Adding and Subtracting Roots
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.
Just add or subtract the coefficients in front of the radicals.
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.

22. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Factor out and cancel all factors the numerator and denominator have in common.
Switch the numerator and denominator.
Put each number in the original ratio over the sum of the numbers.
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.

23. Comparing the values of two or more Fractions
Just add or subtract the coefficients in front of the radicals.
Express them with a common denominator.
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.
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

24. Converting from part-to-part ratios to part-to-whole ratios
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Put each number in the original ratio over the sum of the numbers.
Find a common denominator - then add or subtract the numerators.
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.

25. 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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

26. 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.
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.
Adjacent angles are supplementary - Vertical angles are equal
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

27. How do you know if an integer is a multiple of 3 or 9?
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Part=Percent x Whole
Just add or subtract the coefficients in front of the radicals.

28. Increasing and Decreasing a Number by a Certain Percentage
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
-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.

29. Properties of a 45-45-90 Triangle
Cancel factors common to the numerator and denominator.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

30. Adding and Subtracting Polynomials
Combine like terms.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
A(2)+b(2)=c(2)

31. Properties of Similar Triangles
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

32. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
A(2)+b(2)=c(2)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

33. Finding the Midpoint Between Two Points
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
(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.
VofaRS=lwh

34. Finding the Reciprocal of a Fraction
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Switch the numerator and denominator.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.

35. Factoring a Polynomial ('FOIL in Reverse')
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

36. 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
Switch the numerator and denominator.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Subtract the smallest from the largest and add 1

37. 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.
Just add or subtract the coefficients in front of the radicals.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

38. Finding the Surface Area of a Rectangular Solid
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.

39. Finding the GCF of Two or More Numbers
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Put the equation into y=mx+b-- in which case b is the y-intercept.

40. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Use the distributive property then combine the like terms.
Four equal acute angles and four equal obtuse angles.

41. Multiplying Expressions with Exponents that Have a Common Base
(x1+x2)/2 -(y1+y2)/2
Slope=change in y/change in x
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

42. Solving a Linear Equation
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Adjacent angles are supplementary - Vertical angles are equal
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Do whatever is necessary to both sides to isolate the variable.

43. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Part=Percent x Whole
The whole number left over after division.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

44. Converting From a Mixed Number to an Improper Fraction
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

45. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Just add or subtract the coefficients in front of the radicals.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

46. Finding the y-intercept When Given an Equation of a Line
Multiply the exponents - (x^3)^4=x^3*4=x^12
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
Put the equation into y=mx+b-- in which case b is the y-intercept.

47. Difference Between a Factor and a Multiple
Average: Sum of the Terms/Number of the Terms
Use the formula distance=rate*time and its variations to help in this question.
Use the distributive property then combine the like terms.
-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.

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

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49. Definition of an Integer
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
VofaC: (pie)r(2)h
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

50. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
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
Cancel factors common to the numerator and denominator.
The whole number left over after division.