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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. General Procedure for Multiplying Polynomials
The whole number left over after division.
Use the distributive property then combine the like terms.
The value that falls in the middle of the set.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

2. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
Put each number in the original ratio over the sum of the numbers.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

3. If 3(3x)=9(x+2) - what is the value of x?
Part=Percent x Whole
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

4. Finding the Area of a Circle
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
(pie)r(squared)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

5. Finding the Domain and Range of a Function
Four equal acute angles and four equal obtuse angles.
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.
2(pie)r
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.

6. Prime Factorization of a Number
A(2)+b(2)=c(2)
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Put each number in the original ratio over the sum of the numbers.
Two relatively prime numbers are integers that have no common factor other than 1.

7. Converting From a Mixed Number to an Improper Fraction
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
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.

8. Expressing the Union and Intersection of Sets
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 units to keep things straight - Snowfall inches/hours
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
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

9. Determining Absolute Value of a Number
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
VofaRS=lwh

10. Adding and Subtracting Roots
Slope=change in y/change in x
Just add or subtract the coefficients in front of the radicals.
Combine like terms.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

11. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

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

13. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

14. 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?
Just add or subtract the coefficients in front of the radicals.
FOIL: First - Outer - Inner - Last... Combine Like Terms
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.

15. Number of Groups - +1 Each Time
VofaRS=lwh
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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)

16. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
Cancel factors common to the numerator and denominator.

17. What is the Pythagorean Theorem?
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
A(2)+b(2)=c(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.

18. Evaluating an Algebraic Expression
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Plug in the given values for the unknowns and calculate according to PEMDAS.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.

19. What are Two Special Pythagorean Triples?

20. Finding the Slope When Given an Equation of a Line
Express them with a common denominator.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

21. Characteristics of a Parallelogram
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

22. Finding the y-intercept When Given an Equation of a Line
Use simple numbers like 1 and 2 and see what happens.
The value that falls in the middle of the set.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

23. Finding the Mode of a Set of Numbers
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
The value that appears the most often.
Isolate the radical expression and use the standard rules of algebra.

24. Characteristics of a Rectangle
Slope=change in y/change in x
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.
Four equal acute angles and four equal obtuse angles.

25. Counting Consecutive Integers
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Subtract the smallest from the largest and add 1

26. Finding the Slope of a Line When Given Two Points on the Line
Factor out and cancel all factors the numerator and denominator have in common.
Use the formula distance=rate*time and its variations to help in this question.
Slope=change in y/change in x
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

27. Properties of Similar Triangles
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

28. Characteristics of a Square
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

29. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Average the smallest and largest number

30. Multiplying Fractions
Multiply the numerators and multiply the denominators.
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.
Sum: Average x Number of Terms
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

31. Finding the Distance Between Two Points on a Coordinate Graph
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

32. Formula to Find Average
The value that appears the most often.
Multiply the numerators and multiply the denominators.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Average: Sum of the Terms/Number of the Terms

33. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
FOIL: First - Outer - Inner - Last... Combine Like Terms

34. Average Rate and How Do You Find It
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
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
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.

35. Finding the LCM of Two or More Numbers

36. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

37. Definition of Remainder
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.
The whole number left over after division.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

38. Properties of a 30-60-90 Triangle
(pie)r(squared)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

39. How do you know if an integer is a multiple of 3 or 9?
Two relatively prime numbers are integers that have no common factor other than 1.
Part=Percent x Whole
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.

40. Multiplying and Dividing Roots
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

41. If 4(x(2)-10x+25) - then what is the value of x?
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Switch the numerator and denominator.
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.
(pie)r(squared)

42. An Important Property of a Line Tangent to a Circle
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.
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.
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
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.

43. Finding the GCF of Two or More Numbers
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Use the units to keep things straight - Snowfall inches/hours
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

44. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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
Get the absolute value equation by itself. Solve.

45. Solving a Problem Involving Rates
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Combine like terms.
Use the units to keep things straight - Snowfall inches/hours
Adjacent angles are supplementary - Vertical angles are equal

46. Finding the Midpoint Between Two Points
FOIL: First - Outer - Inner - Last... Combine Like Terms
Factor out and cancel all factors the numerator and denominator have in common.
(x1+x2)/2 -(y1+y2)/2
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

47. What types of angles are formed when two lines intersect?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Factor out and cancel all factors the numerator and denominator have in common.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Adjacent angles are supplementary - Vertical angles are equal

48. Finding the Missing Number in a Series When You are Given the Average
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
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.
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.
The value that appears the most often.

49. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Isolate the radical expression and use the standard rules of algebra.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
VofaC: (pie)r(2)h
Do whatever is necessary to both sides to isolate the variable.

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