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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. Converting from part-to-part ratios to part-to-whole ratios
Sum: Average x Number of Terms
Put each number in the original ratio over the sum of the numbers.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

2. Finding the Rate of Speed
A(2)+b(2)=c(2)
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
-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.
Use the formula distance=rate*time and its variations to help in this question.

3. Formula to Find Average
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
Average the smallest and largest number
Average: Sum of the Terms/Number of the Terms

4. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Cancel factors common to the numerator and denominator.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The whole number left over after division.

5. Definition of Remainder
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 whole number left over after division.
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.
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.

6. Finding the Surface Area of a Rectangular Solid
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use the units to keep things straight - Snowfall inches/hours

7. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Factor out and cancel all factors the numerator and denominator have in common.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

8. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
FOIL: First - Outer - Inner - Last... Combine Like Terms
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

9. What types of angles are formed when a transversal cross parallel lines?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Four equal acute angles and four equal obtuse angles.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

10. 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?
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.
The whole number left over after division.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

11. Finding the Mode of a Set of Numbers
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The value that appears the most often.

12. Finding the Median of a Set of Numbers
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.
The value that falls in the middle of the set.
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.

13. If r#t=t(r)-r(t) - then what is 4#3?
A(2)+b(2)=c(2)
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Slope=change in y/change in x
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

14. Quickly Finding the Average of a Series of Evenly Spaced Numbers
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Four equal acute angles and four equal obtuse angles.
Average the smallest and largest number
Cross multiply.

15. Counting the Total Number of Possibilities for Several Events to Occur
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Average the smallest and largest number
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 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 slope of the line perpendicular to the line with linear equation 4x+2y=12?
Use simple numbers like 1 and 2 and see what happens.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
VofaRS=lwh
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.

17. An Important Property of a Line Tangent to a Circle
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
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.

18. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
(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.

19. Comparing the values of two or more Fractions
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.
Do whatever is necessary to both sides to isolate the variable.
Express them with a common denominator.
Average the smallest and largest number

20. What value of x is not in the domain of the function f(x)=x-2/x-3?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)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.
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
Plug in the given values for the unknowns and calculate according to PEMDAS.

21. Setting Up a Ratio
2(pie)r
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

22. Scalene - Isosceles - and Equilateral Triangles
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.
VofaC: (pie)r(2)h
Cancel factors common to the numerator and denominator.
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.

23. 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.
Get the absolute value equation by itself. Solve.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

24. Finding the LCM of Two or More Numbers

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25. If x(2)=7x+18 - what is the positive value of x?
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

26. Knowing if an Integer is a Multiple of 2 or 4
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
VofaC: (pie)r(2)h
-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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

27. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Average: Sum of the Terms/Number of the Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.

28. Adding and Subtracting Monomials
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Isolate the radical expression and use the standard rules of algebra.
Plug in the given values for the unknowns and calculate according to PEMDAS.

29. Properties of Similar Triangles
Do whatever is necessary to both sides to isolate the variable.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

30. Finding the Circumference of a Circle
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
Factor out and cancel all factors the numerator and denominator have in common.
2(pie)r
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

31. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
The whole number left over after division.
VofaC: (pie)r(2)h
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

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

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33. Properties of a 30-60-90 Triangle
Average the smallest and largest number
Express them with a common denominator.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

34. Dividing Fractions
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Isolate the radical expression and use the standard rules of algebra.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

35. If 4(x(2)-10x+25) - then what is the value of x?
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Do whatever is necessary to both sides to isolate the variable.
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.

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

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37. Multiplying and Dividing Roots
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
-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.
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.

38. Finding the Slope When Given an Equation of a Line
-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(pie)r
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

39. Characteristics of a Square
Two relatively prime numbers are integers that have no common factor other than 1.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

40. Finding a Term in a Geometric Sequence
Multiply the whole number part by the denominator - then add the numerator. Keep the same 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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

41. Finding the Distance Between Two Points on a Coordinate Graph
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

42. Definition of a Rational Number
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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
A(2)+b(2)=c(2)
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

43. What Does Solving In Terms of Mean?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

44. Finding the Domain and Range of a Function
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
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.

45. Factoring a Polynomial ('FOIL in Reverse')
VofaRS=lwh
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.

46. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
Express them with a common denominator.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Adjacent angles are supplementary - Vertical angles are equal

47. Definition of an Integer
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
The value that appears the most often.

48. If (Square Root: x-1)+5=12 - what is the value of x/2?
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

49. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
Average: Sum of the Terms/Number of the Terms
Use simple numbers like 1 and 2 and see what happens.
Adjacent angles are supplementary - Vertical angles are equal

50. 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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

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