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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. Setting Up a Ratio
The value that falls in the middle of the set.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.

2. 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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

3. 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.
(pie)r(squared)
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

4. Average Rate and How Do You Find It
The value that appears the most often.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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

5. Knowing if an Integer is a Multiple of 2 or 4
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
-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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

6. What is the Pythagorean Theorem?
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
A(2)+b(2)=c(2)
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.

7. Calculating Negative Exponents and Radical Exponents
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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

8. Adding and Subtracting Fractions
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

9. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
Use the formula distance=rate*time and its variations to help in this question.

10. Converting from an Improper Fraction to a Mixed Number
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
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Use the formula distance=rate*time and its variations to help in this question.

11. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

12. If the average of a - b - and 48 is 48 - what is the value of a + b?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Sum: Average x Number of Terms

13. Finding a Term in a Geometric Sequence
Subtract the smallest from the largest and add 1
Two relatively prime numbers are integers that have no common factor other than 1.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

14. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Multiply the numerators and multiply the denominators.

15. Finding the Surface Area of a Rectangular Solid
VofaRS=lwh
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

16. Adding and Subtracting Polynomials
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Combine like terms.

17. An Important Property of a Line Tangent to a Circle
The value that falls in the middle of the set.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.

18. 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?
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

19. Direct Variation and Inverse Variation
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Switch the numerator and denominator.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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

20. Formula to Find Average
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
VofaC: (pie)r(2)h
Average: Sum of the Terms/Number of the Terms
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

21. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

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22. Definition of Remainder
The whole number left over after division.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Two relatively prime numbers are integers that have no common factor other than 1.
Slope=change in y/change in x

23. Finding the GCF of Two or More Numbers
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
VofaC: (pie)r(2)h
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
-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.

24. Characteristics of a Parallelogram
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
The value that falls in the middle of the set.
Use the formula distance=rate*time and its variations to help in this question.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

25. Factoring the Difference of Two Squares
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

26. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
VofaC: (pie)r(2)h
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.

27. Finding the Area of a Triangle

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28. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Slope=change in y/change in x
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

29. Properties of Similar Triangles
Subtract the smallest from the largest and add 1
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
FOIL: First - Outer - Inner - Last... Combine Like Terms

30. 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?
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.
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.
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
Get the absolute value equation by itself. Solve.

31. Solving a System of Equations
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Cancel factors common to the numerator and denominator.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

32. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Plug in the given values for the unknowns and calculate according to PEMDAS.

33. Finding the Volume of a Rectangular Solid
Multiply the numerators and multiply the denominators.
VofaRS=lwh
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
Express them with a common denominator.

34. 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
Isolate the radical expression and use the standard rules of algebra.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

35. Raising a Power to a Power
Sum: Average x Number of Terms
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
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

36. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the numerators and multiply the denominators.

37. Converting From a Mixed Number to an Improper Fraction
The whole number left over after division.
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

38. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Two relatively prime numbers are integers that have no common factor other than 1.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

39. 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.
Two relatively prime numbers are integers that have no common factor other than 1.
Use simple numbers like 1 and 2 and see what happens.
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.

40. 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.
Cancel factors common to the numerator and denominator.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Isolate the radical expression and use the standard rules of algebra.

41. Simplifying an Algebraic Equation
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.
Use the distributive property then combine the like terms.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Cancel factors common to the numerator and denominator.

42. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
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.
Use the formula distance=rate*time and its variations to help in this question.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

43. If 3(3x)=9(x+2) - what is the value of x?
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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: Average x Number of Terms

44. Multiplying Fractions
Cross multiply.
Subtract the smallest from the largest and add 1
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the numerators and multiply the denominators.

45. Counting Consecutive Integers
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime 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
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Subtract the smallest from the largest and add 1

46. Multiplying Expressions with Exponents that Have a Common Base
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.
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.
Isolate the radical expression and use the standard rules of algebra.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

47. Definition of an Irrational Number
The value that falls in the middle of the set.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

48. Finding the y-intercept When Given an Equation of a Line
Find a common denominator - then add or subtract the numerators.
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

49. Solving a Problem Involving Rates
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the units to keep things straight - Snowfall inches/hours
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
(x1+x2)/2 -(y1+y2)/2

50. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.