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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. Finding the Mode of a Set of Numbers
The value that appears the most often.
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.
Multiply the numerators and multiply the denominators.
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.

2. Solving a Linear Equation
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 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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Do whatever is necessary to both sides to isolate the variable.

3. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
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.
A(2)+b(2)=c(2)
Average: Sum of the Terms/Number of the Terms

4. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
FOIL: First - Outer - Inner - Last... Combine Like Terms
Part=Percent x Whole

5. Finding the Missing Number in a Series When You are Given the Average
Cancel factors common to the numerator and denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.

6. Simplifying a Fraction to Lowest 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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Factor out and cancel all factors the numerator and denominator have in common.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

7. Dividing Expressions with Exponents that Have a Common Base
The whole number left over after division.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Isolate the radical expression and use the standard rules of algebra.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

8. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Cross multiply.
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

9. Adding and Subtracting Monomials
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.
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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

10. Finding the y-intercept When Given an Equation of a Line
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 y=mx+b-- in which case b is the y-intercept.
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

11. Finding a Term in a Geometric Sequence
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.

12. Dividing Fractions
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.

13. Simplifying Square Roots
The value that falls in the middle of the set.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

14. Properties of a 45-45-90 Triangle
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

15. 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
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Slope=change in y/change in x
Average the smallest and largest number

16. Adding and Subtracting Polynomials
Find a common denominator - then add or subtract the numerators.
Two relatively prime numbers are integers that have no common factor other than 1.
Combine like terms.
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.

17. 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.
The value that falls in the middle of the set.
Put the equation into y=mx+b-- in which case b is the y-intercept.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

18. 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.
Part=Percent x Whole
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.
Isolate the radical expression and use the standard rules of algebra.

19. 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?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

20. Properties of the Interior and Exterior Angles of a Triangle
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

21. Solving a Problem Involving Rates
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Part=Percent x Whole
Use the units to keep things straight - Snowfall inches/hours

22. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Get the absolute value equation by itself. Solve.
The value that appears the most often.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

23. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Isolate the radical expression and use the standard rules of algebra.
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.
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.
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.

24. Finding the Volume of a Cylinder
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Subtract the smallest from the largest and add 1
Multiply the exponents - (x^3)^4=x^3*4=x^12
VofaC: (pie)r(2)h

25. Finding the Area of a Circle
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.
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.
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.
(pie)r(squared)

26. Finding the Volume of a Rectangular Solid
The whole number left over after division.
VofaRS=lwh
Get the absolute value equation by itself. Solve.
Put each number in the original ratio over the sum of the numbers.

27. Finding the LCM of Two or More Numbers

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28. Definition of Remainder
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.
The whole number left over after division.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

29. Increasing and Decreasing a Number by a Certain Percentage
Put the equation into y=mx+b-- in which case b is the y-intercept.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
-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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

30. Factoring the Difference of Two Squares
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Factor out and cancel all factors the numerator and denominator have in common.
Average the smallest and largest number
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

31. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Isolate the radical expression and use the standard rules of algebra.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

32. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

33. Finding the Rate of Speed
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Use the formula distance=rate*time and its variations to help in this question.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

34. What types of angles are formed when two lines intersect?
2(pie)r
Adjacent angles are supplementary - Vertical angles are equal
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

35. Scalene - Isosceles - and Equilateral Triangles
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
Part=Percent x Whole
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.
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.

36. Solving an Inequality
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put each number in the original ratio over the sum of the numbers.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

37. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
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.
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.

38. Finding the Sum of the Interior Angles of a Polygon
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

39. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

40. Evaluating an Algebraic Expression
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
The whole number left over after division.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Plug in the given values for the unknowns and calculate according to PEMDAS.

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

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42. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
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
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.

43. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
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
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

44. Solving a Proportion
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
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.
Cross multiply.

45. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Use the units to keep things straight - Snowfall inches/hours
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

46. Knowing if an Integer is a Multiple of 5 or 10
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
-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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

47. Factoring a Polynomial ('FOIL in Reverse')
Get the absolute value equation by itself. Solve.
Factor out and cancel all factors the numerator and denominator have in common.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

48. Definition of an Irrational Number
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.
-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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

49. 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.
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

50. Comparing the values of two or more Fractions
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
The value that falls in the middle of the set.
Express them with a common denominator.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds