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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
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.
Use the distributive property then combine the like terms.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.

2. Characteristics of a Parallelogram
VofaRS=lwh
2(pie)r
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Switch the numerator and denominator.

3. Finding the Slope of a Line When Given Two Points on the Line
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Use the distributive property then combine the like terms.
Slope=change in y/change in x
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

4. Finding the Area of a Sector

5. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

6. Setting Up a Ratio
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Adjacent angles are supplementary - Vertical angles are equal
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

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.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use the units to keep things straight - Snowfall inches/hours

8. 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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.

9. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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.
Use simple numbers like 1 and 2 and see what happens.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

10. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
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
Do whatever is necessary to both sides to isolate the variable.
Use the formula distance=rate*time and its variations to help in this question.

11. 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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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

12. If (Square Root: x-1)+5=12 - what is the value of x/2?
Cross multiply.
Get the absolute value equation by itself. Solve.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
(pie)r(squared)

13. What Does Solving In Terms of Mean?
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Two relatively prime numbers are integers that have no common factor other than 1.

14. Finding the Slope When Given an Equation of a Line
Multiply the exponents - (x^3)^4=x^3*4=x^12
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
-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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

15. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Subtract the smallest from the largest and add 1
Multiply the exponents - (x^3)^4=x^3*4=x^12
Average the smallest and largest number
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.

16. If r#t=t(r)-r(t) - then what is 4#3?
Part=Percent x Whole
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

17. Finding the Reciprocal of a Fraction
Just add or subtract the coefficients in front of the radicals.
Switch the numerator and denominator.
VofaRS=lwh
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

18. Definition of Remainder
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use the formula distance=rate*time and its variations to help in this question.
The whole number left over after division.

19. Raising a Power to a Power
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the exponents - (x^3)^4=x^3*4=x^12

20. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
A(2)+b(2)=c(2)
Get the absolute value equation by itself. Solve.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.

21. Characteristics of a Rectangle
Sum: Average x Number of Terms
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

22. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Multiply the numerators and multiply the denominators.

23. 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.
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

24. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.

25. What is the Pythagorean Theorem?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
A(2)+b(2)=c(2)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Switch the numerator and denominator.

26. Adding a Positive Number to a Negative Number
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
-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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

27. Converting from an Improper Fraction to a Mixed Number
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.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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

28. An Important Property of a Line Tangent to a Circle
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Put each number in the original ratio over the sum of the numbers.
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.

29. Difference Between a Factor and a Multiple
-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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Average the smallest and largest number
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

30. Finding the Volume of a Rectangular Solid
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Get the absolute value equation by itself. Solve.
VofaRS=lwh
Adjacent angles are supplementary - Vertical angles are equal

31. What is the Triangle Inequality Theorem?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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 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.
Put the equation into y=mx+b-- in which case b is the y-intercept.

32. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
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 the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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

33. Solving a Linear Equation
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
VofaC: (pie)r(2)h
Do whatever is necessary to both sides to isolate the variable.

34. PEMDAS
Find a common denominator - then add or subtract the numerators.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

36. Solving a Proportion
Cross multiply.
Use the units to keep things straight - Snowfall inches/hours
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.
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. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

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

39. Increasing and Decreasing a Number by a Certain Percentage
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Cancel factors common to the numerator and denominator.
-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.
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.

40. Simplifying a Fraction to Lowest Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.
Factor out and cancel all factors the numerator and denominator have in common.
Do whatever is necessary to both sides to isolate the variable.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

41. Finding the Length of an Arc in a Circle

42. Numbers that are Relatively Prime
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.
Two relatively prime numbers are integers that have no common factor other than 1.
2(pie)r
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.

43. Knowing if an Integer is a Multiple of 2 or 4
-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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Four equal acute angles and four equal obtuse angles.
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

44. Expressing the Union and Intersection of Sets
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.
(pie)r(squared)
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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

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

46. Evaluating an Algebraic Expression
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Get the absolute value equation by itself. Solve.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Plug in the given values for the unknowns and calculate according to PEMDAS.

47. If the average of a - b - and 48 is 48 - what is the value of a + b?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Four equal acute angles and four equal obtuse angles.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

48. Finding the Domain and Range of a Function
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Sum: Average x Number of Terms
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

49. If 3(3x)=9(x+2) - what is the value of x?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Isolate the radical expression and use the standard rules of algebra.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

50. Finding the y-intercept When Given an Equation of a Line
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Subtract the smallest from the largest and add 1
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.