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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 Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
-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.
Two relatively prime numbers are integers that have no common factor other than 1.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

2. Converting from an Improper Fraction to a Mixed Number
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
Use the distributive property then combine the like terms.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

3. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Isolate the radical expression and use the standard rules of algebra.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

4. Multiplying Binomials
Cancel factors common to the numerator and denominator.
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
FOIL: First - Outer - Inner - Last... Combine Like Terms

5. Dividing Expressions with Exponents that Have a Common Base
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
-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.

6. Calculating Negative Exponents and Radical Exponents
FOIL: First - Outer - Inner - Last... Combine Like Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Cross multiply.
Just add or subtract the coefficients in front of the radicals.

7. Properties of a 45-45-90 Triangle
Average the smallest and largest number
Combine like 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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

8. If 4(x(2)-10x+25) - then what is the value of x?
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

9. Comparing the values of two or more Fractions
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Express them with a common denominator.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

10. Definition of an Integer
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

11. Scalene - Isosceles - and Equilateral Triangles
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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
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.
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.

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

13. Solving a Problem Involving Rates
Put each number in the original ratio over the sum of the numbers.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Use the units to keep things straight - Snowfall inches/hours
Cross multiply.

14. Characteristics of a Rectangle
Use the units to keep things straight - Snowfall inches/hours
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

15. Counting Consecutive Integers
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.
Subtract the smallest from the largest and add 1
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

16. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
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 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.
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.

17. Finding the Domain and Range of a Function
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
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

18. Solving an Inequality
Factor out and cancel all factors the numerator and denominator have in common.
Cancel factors common to 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.

19. 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?
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

20. 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?
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

21. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Sum: Average x Number of Terms
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Plug in the given values for the unknowns and calculate according to PEMDAS.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

22. Adding a Positive Number to a Negative Number
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply the numerators and multiply the denominators.
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

23. What is the slope of the line perpendicular to the line with linear equation 4x+2y=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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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.

24. Finding the Reciprocal of a Fraction
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.
Switch 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.

25. Setting Up a Ratio
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Subtract the smallest from the largest and add 1
Sum: Average x Number of Terms
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

26. General Procedure for Multiplying Polynomials
A(2)+b(2)=c(2)
Sum: Average x Number of Terms
Use the distributive property then combine the like terms.
Find a common denominator - then add or subtract the numerators.

27. Dividing Fractions
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

28. Average Rate and How Do You Find It
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

29. What are Two Special Pythagorean Triples?

30. Finding the Midpoint Between Two Points
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Average: Sum of the Terms/Number of the Terms
(x1+x2)/2 -(y1+y2)/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.

31. Counting the Total Number of Possibilities for Several Events to Occur
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
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.

32. PEMDAS
Multiply the exponents - (x^3)^4=x^3*4=x^12
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Do whatever is necessary to both sides to isolate the variable.

33. Converting from part-to-part ratios to part-to-whole ratios
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Put each number in the original ratio over the sum of the numbers.
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
Switch the numerator and denominator.

34. Solving a Radical Equation
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Isolate the radical expression and use the standard rules of algebra.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

35. 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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

36. Evaluating an Algebraic Expression
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply the numerators and multiply the denominators.
Plug in the given values for the unknowns and calculate according to PEMDAS.

37. What is the Triangle Inequality Theorem?
-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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
Just add or subtract the coefficients in front of the radicals.

38. Knowing if an Integer is a Multiple of 2 or 4
-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.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

39. Finding the Volume of a Cylinder
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
VofaC: (pie)r(2)h

40. Prime Factorization of a Number
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.
Cancel factors common to the numerator and denominator.
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

41. Finding the Sum of the Interior Angles of a Polygon
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Isolate the radical expression and use the standard rules of algebra.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

42. What types of angles are formed when two lines intersect?
(pie)r(squared)
Adjacent angles are supplementary - Vertical angles are equal
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

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

44. Characteristics of a Parallelogram
The value that falls in the middle of the set.
Sum: Average x Number of Terms
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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

45. 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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Plug in the given values for the unknowns and calculate according to PEMDAS.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

46. Multiplying Fractions
Just add or subtract the coefficients in front of the radicals.
The value that appears the most often.
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 numerators and multiply the denominators.

47. Properties of Similar Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
2(pie)r
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

48. Number of Groups - +1 Each Time
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Slope=change in y/change in x
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.

49. Adding and Subtracting Polynomials
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
Combine like terms.

50. Finding the Surface Area of a Rectangular Solid
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.