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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. Comparing the values of two or more Fractions
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Express them with a common denominator.
-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.

2. Characteristics of a Rectangle
-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.
Just add or subtract the coefficients in front of the radicals.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

3. Finding the Area of a Circle
(pie)r(squared)
The value that appears the most often.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Express them with a common denominator.

4. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Use simple numbers like 1 and 2 and see what happens.
Multiply the exponents - (x^3)^4=x^3*4=x^12
(x1+x2)/2 -(y1+y2)/2

5. Formula to Find Average
Four equal acute angles and four equal obtuse angles.
Average: Sum of the Terms/Number of the Terms
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Cross multiply.

6. Factoring the Difference of Two Squares
Cross multiply.
Express them with a common denominator.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

7. Finding the Rate of Speed
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Use the formula distance=rate*time and its variations to help in this question.
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.

8. Multiply and Divide Positive and Negative Numbers
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
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
VofaRS=lwh

9. Scalene - Isosceles - and Equilateral Triangles
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Use the formula distance=rate*time and its variations to help in this question.

10. Raising a Power to a Power
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.

11. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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 simple numbers like 1 and 2 and see what happens.
-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.

12. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

13. Simplifying a Fraction to Lowest Terms
The whole number left over after division.
-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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Factor out and cancel all factors the numerator and denominator have in common.

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

15. Calculating Negative Exponents and Radical Exponents
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
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.

16. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Do whatever is necessary to both sides to isolate the variable.
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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

17. Prime Factorization of a 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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.

18. What types of angles are formed when a transversal cross parallel lines?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Four equal acute angles and four equal obtuse angles.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

19. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.

20. 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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

21. Properties of the Interior and Exterior Angles of a Triangle
Use simple numbers like 1 and 2 and see what happens.
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.
Just add or subtract the coefficients in front of the radicals.
Find a common denominator - then add or subtract the numerators.

22. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
FOIL: First - Outer - Inner - Last... Combine Like Terms

23. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest 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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

24. What are Two Special Pythagorean Triples?

25. Finding the Missing Number in a Series When You are Given the Average
2(pie)r
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

26. 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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Just add or subtract the coefficients in front of the radicals.

27. 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.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

28. Finding the Volume of a Rectangular Solid
VofaC: (pie)r(2)h
VofaRS=lwh
Cancel factors common to the numerator and denominator.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

29. Determining Absolute Value of a Number
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Factor out and cancel all factors the numerator and denominator have in common.

30. Counting Consecutive Integers
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Subtract the smallest from the largest and add 1
Plug in the given values for the unknowns and calculate according to PEMDAS.
Average: Sum of the Terms/Number of the Terms

31. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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.
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 variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Get the absolute value equation by itself. Solve.

32. Finding the GCF of Two or More Numbers
Cancel factors common to the numerator and denominator.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

33. An Important Property of a Line Tangent to a Circle
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.
Express them with a common denominator.
Adjacent angles are supplementary - Vertical angles are equal
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.

34. Adding and Subtracting Roots
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Use the formula distance=rate*time and its variations to help in this question.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Just add or subtract the coefficients in front of the radicals.

35. Finding the y-intercept When Given an Equation of a Line
Use the formula distance=rate*time and its variations to help in this question.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

36. Multiplying Binomials
Use the formula distance=rate*time and its variations to help in this question.
FOIL: First - Outer - Inner - Last... 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.
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.

37. Finding the Area of a Sector

38. Finding the Slope When Given an Equation of a Line
FOIL: First - Outer - Inner - Last... Combine Like Terms
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.

39. Dividing Expressions with Exponents that Have a Common Base
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

40. Finding the Circumference of a Circle
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.
2(pie)r
Use simple numbers like 1 and 2 and see what happens.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

41. Calculating the Probability that an Event will Take Place
Do whatever is necessary to both sides to isolate the variable.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Probability: Number of Favorable Outcomes/Total Possible Outcomes

42. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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
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.
(pie)r(squared)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

43. If r#t=t(r)-r(t) - then what is 4#3?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Get the absolute value equation by itself. Solve.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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. Finding the Area of a Triangle

45. What Does Solving In Terms of Mean?
Get the absolute value equation by itself. Solve.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

46. 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.
Four equal acute angles and four equal obtuse angles.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Express them with a common denominator.

47. Definition of Remainder
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.
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.
The whole number left over after division.

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

49. Finding the Slope of a Line When Given Two Points on the Line
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use the formula distance=rate*time and its variations to help in this question.
Slope=change in y/change in x

50. Finding the Surface Area of a Rectangular Solid
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.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The value that falls in the middle of the set.