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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. What is the Triangle Inequality Theorem?
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

2. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the distributive property then combine the like terms.
The value that falls in the middle of the set.

3. Adding a Positive Number to a Negative Number
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
VofaC: (pie)r(2)h
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

4. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Put each number in the original ratio over the sum of the numbers.
Four equal acute angles and four equal obtuse angles.

5. Characteristics of a Rectangle
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.
(pie)r(squared)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The whole number left over after division.

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?
-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.
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.
Use the distributive property then combine the like terms.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

7. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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
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.
Get the absolute value equation by itself. Solve.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

8. Knowing if an Integer is a Multiple of 2 or 4
Isolate the radical expression and use the standard rules of algebra.
-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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

9. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

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10. Finding the Rate of Speed
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Use the formula distance=rate*time and its variations to help in this question.
Just add or subtract the coefficients in front of the radicals.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

11. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
2(pie)r
(x1+x2)/2 -(y1+y2)/2
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

12. Solving a Problem Involving Rates
Do whatever is necessary to both sides to isolate the variable.
Use the units to keep things straight - Snowfall inches/hours
Sum: Average x Number of Terms
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

13. Multiply and Divide Positive and Negative Numbers
Get the absolute value equation by itself. Solve.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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 the numerators and multiply the denominators.

14. Adding and Subtracting Polynomials
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Combine like terms.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

15. Converting from part-to-part ratios to part-to-whole ratios
Average: Sum of the Terms/Number of the Terms
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
(x1+x2)/2 -(y1+y2)/2
Put each number in the original ratio over the sum of the numbers.

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

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17. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Cross multiply.

18. Finding the Sum of the Average of a Series of Numbers
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Sum: Average x Number of Terms

19. Prime Factorization of a Number
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

20. What are Two Special Pythagorean Triples?

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21. 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.
Cancel factors common to the numerator and denominator.
Cross multiply.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

22. Calculating Negative Exponents and Radical Exponents
The value that appears the most often.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
-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.

23. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

24. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
-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.
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
The value that appears the most often.

25. What is the Pythagorean Theorem?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
A(2)+b(2)=c(2)
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

26. What Does Solving In Terms of Mean?
Just add or subtract the coefficients in front of the radicals.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Probability: Number of Favorable Outcomes/Total Possible Outcomes

27. 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
-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.
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.
Cross multiply.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

28. Properties of a 45-45-90 Triangle
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.
Use the distributive property then combine the like terms.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

29. Finding the Mode of a Set of Numbers
The value that appears the most often.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

30. Convert From a Fraction to a Decimal - Vice Versa
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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
Use the distributive property then combine the like terms.
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.

31. Numbers that are Relatively Prime
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Two relatively prime numbers are integers that have no common factor other than 1.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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

32. Determining Absolute Value of a Number
(pie)r(squared)
Combine like 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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

33. Converting From a Mixed Number to an Improper Fraction
-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.
-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.
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.

34. Finding the Slope When Given an Equation of a Line
A(2)+b(2)=c(2)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

35. Multiplying and Dividing Roots
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

36. Finding the Volume of a Cylinder
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.
Just add or subtract the coefficients in front of the radicals.
VofaC: (pie)r(2)h
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

37. Number of Groups - +1 Each Time
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.
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 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.
Part=Percent x Whole

38. What types of angles are formed when two lines intersect?
Get the absolute value equation by itself. Solve.
2(pie)r
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Adjacent angles are supplementary - Vertical angles are equal

39. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

40. 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.
Slope=change in y/change in x
Part=Percent x Whole
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

41. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
-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.

42. Finding the Circumference of a Circle
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
2(pie)r
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

43. Counting the Total Number of Possibilities for Several Events to Occur
Two relatively prime numbers are integers that have no common factor other than 1.
Adjacent angles are supplementary - Vertical angles are equal
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.
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.

44. Solving a Proportion
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
Part=Percent x Whole
Cross multiply.
Just add or subtract the coefficients in front of the radicals.

45. Formula to Find Average
Adjacent angles are supplementary - Vertical angles are equal
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.
Average: Sum of the Terms/Number of the 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.

46. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
FOIL: First - Outer - Inner - Last... Combine Like Terms
2(pie)r
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.

47. Increasing and Decreasing a Number by a Certain Percentage
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
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
(pie)r(squared)
-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.

48. Definition of an Irrational Number
(x1+x2)/2 -(y1+y2)/2
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Average: Sum of the Terms/Number of the Terms
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

49. Properties of a 30-60-90 Triangle
Just add or subtract the coefficients in front of the radicals.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Cancel factors common to the numerator and denominator.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

50. 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?
Get the absolute value equation by itself. Solve.
Find a common denominator - then add or subtract the numerators.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)