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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. Definition of a Rational Number
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Use the distributive property then combine the like terms.

2. Finding the Area of a Circle
Combine like terms.
(pie)r(squared)
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

3. Finding the Volume of a Rectangular Solid
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
(x1+x2)/2 -(y1+y2)/2
VofaRS=lwh
Express them with a common denominator.

4. Adding and Subtracting Fractions
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.
Find a common denominator - then add or subtract the numerators.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
The whole number left over after division.

5. If (Square Root: x-1)+5=12 - what is the value of x/2?
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.
Four equal acute angles and four equal obtuse angles.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

6. 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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Isolate the radical expression and use the standard rules of algebra.
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.

7. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
FOIL: First - Outer - Inner - Last... Combine Like 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.
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.

8. Factoring the Difference of Two Squares
(x1+x2)/2 -(y1+y2)/2
Use the formula distance=rate*time and its variations to help in this question.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(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.

9. Finding the LCM of Two or More Numbers

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10. Multiplying and Dividing Roots
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
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Cancel factors common to the numerator and denominator.

11. If x(2)=7x+18 - what is the positive value of x?
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
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.
Use the distributive property then combine the like terms.

12. Simplifying an Algebraic Equation
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Cancel factors common to the numerator and denominator.
Two relatively prime numbers are integers that have no common factor other than 1.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

13. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
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.
-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.
Part=Percent x Whole

14. Convert From a Fraction to a Decimal - Vice Versa
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.

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

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16. Finding the Area of a Triangle

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17. 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.
Switch the numerator and denominator.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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

18. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

19. Determining Absolute Value of a 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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.

20. Direct Variation and Inverse Variation
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Factor out and cancel all factors the numerator and denominator have in common.
Multiply the numerators and multiply the denominators.

21. An Important Property of a Line Tangent to a Circle
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
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 whole number part by the denominator - then add the numerator. Keep the same denominator.

22. Finding the Circumference of a Circle
2(pie)r
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.

23. Formula Used to Find Percent
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Part=Percent x Whole
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.

24. PEMDAS
Average the smallest and largest 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
Subtract the smallest from the largest and add 1

25. How do you know if an integer is a multiple of 3 or 9?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
Switch the numerator and denominator.
Multiply the exponents - (x^3)^4=x^3*4=x^12

26. Finding the Rate of Speed
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
'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.
The value that appears the most often.

27. What is the Triangle Inequality Theorem?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.

28. Solving a Linear Equation
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Do whatever is necessary to both sides to isolate the variable.
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.
VofaRS=lwh

29. Solving an Inequality
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

30. Solving a Problem Involving Rates
Two relatively prime numbers are integers that have no common factor other than 1.
Use the units to keep things straight - Snowfall inches/hours
(x1+x2)/2 -(y1+y2)/2
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.

31. 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
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

32. Properties of a 45-45-90 Triangle
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Put the equation into y=mx+b-- in which case b is the y-intercept.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

33. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

34. What value of x is not in the domain of the function f(x)=x-2/x-3?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Find a common denominator - then add or subtract the numerators.
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

35. Prime Factorization of a Number
A(2)+b(2)=c(2)
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

36. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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

37. 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 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 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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

38. If 3(3x)=9(x+2) - what is the value of x?
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Two relatively prime numbers are integers that have no common factor other than 1.
The value that falls in the middle of the set.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

39. Factoring a Polynomial ('FOIL in Reverse')
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)
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.
The whole number left over after division.

40. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
2(pie)r
FOIL: First - Outer - Inner - Last... Combine Like Terms

41. Finding the Missing Number in a Series When You are Given the Average
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

42. If r#t=t(r)-r(t) - then what is 4#3?
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
-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.

43. If the average of a - b - and 48 is 48 - what is the value of a + b?
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

44. Dividing Fractions
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Put each number in the original ratio over the sum of the numbers.

45. Multiply and Divide Positive and Negative Numbers
Two relatively prime numbers are integers that have no common factor other than 1.
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
Just add or subtract the coefficients in front of the radicals.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

46. Finding the Area of a Sector

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47. Characteristics of a Square
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.
Average: Sum of the Terms/Number of the Terms
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

48. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Slope=change in y/change in x
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
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.

49. Comparing the values of two or more Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Adjacent angles are supplementary - Vertical angles are equal
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
Express them with a common denominator.

50. Calculating the Probability that an Event will Take Place
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
2(pie)r
Probability: Number of Favorable Outcomes/Total Possible Outcomes
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24