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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. Multiply and Divide Positive and Negative Numbers
Multiply the numerators and multiply the denominators.
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 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
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

2. Properties of Similar Triangles
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

3. Solving a Linear Equation
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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
Do whatever is necessary to both sides to isolate the variable.

4. Simplifying an Algebraic Equation
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.
Cancel factors common to the numerator and denominator.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

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

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6. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total 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.
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

7. What Does Solving In Terms of Mean?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
-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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

8. Evaluating an Algebraic Expression
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.
Subtract the smallest from the largest and add 1
Plug in the given values for the unknowns and calculate according to PEMDAS.
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

9. If r#t=t(r)-r(t) - then what is 4#3?
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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
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

10. Factoring the Difference of Two Squares
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

11. What are Two Special Pythagorean Triples?

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12. Finding the Area of a Triangle

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13. Solving a Proportion
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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Cross multiply.

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

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15. Dividing Expressions with Exponents that Have a Common Base
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.
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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

16. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Adjacent angles are supplementary - Vertical angles are equal
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
The value that falls in the middle of the set.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

17. Finding the Circumference of a Circle
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
2(pie)r
VofaC: (pie)r(2)h

18. Multiplying and Dividing Roots
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
A(2)+b(2)=c(2)
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.

19. Finding the Domain and Range of a Function
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.

20. Knowing if an Integer is a Multiple of 5 or 10
-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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Combine like terms.
Put the equation into y=mx+b-- in which case b is the y-intercept.

21. Finding the Missing Number in a Series When You are Given the Average
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.
Express them with a common denominator.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.

22. Solving a System of Equations
Four equal acute angles and four equal obtuse angles.
Use the formula distance=rate*time and its variations to help in this question.
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.

23. Dividing Fractions
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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

24. Finding the Reciprocal of a Fraction
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Switch the numerator and denominator.
Use the distributive property then combine the like terms.
FOIL: First - Outer - Inner - Last... Combine Like Terms

25. Finding the Distance Between Two Points on a Coordinate Graph
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

26. Finding the y-intercept When Given an Equation of a Line
Multiply the numerators and multiply the denominators.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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. Solving a Problem Involving Rates
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Use the units to keep things straight - Snowfall inches/hours
A(2)+b(2)=c(2)
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

28. Adding and Subtracting Polynomials
Slope=change in y/change in x
Combine like terms.
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.
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.

29. Finding the Surface Area of a Rectangular Solid
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

30. Let N represent the smallest positive integer that is a multiple of 6 and 8 - but leaves a remainder of 2 when divided by 7. What is the value of N?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

31. 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.
Just add or subtract the coefficients in front of the radicals.
Average: Sum of the Terms/Number of the Terms
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

32. 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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

33. Adding and Subtracting Fractions
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
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.
Find a common denominator - then add or subtract the numerators.

34. Finding the Mode of a Set of Numbers
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
(pie)r(squared)
The value that appears the most often.
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.

35. Properties of a 30-60-90 Triangle
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
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
The value that falls in the middle of the set.
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.

36. Counting Consecutive Integers
The value that appears the most often.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Subtract the smallest from the largest and add 1
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.

37. Definition of a Rational 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.
Multiply the numerators and multiply the denominators.
Average the smallest and largest number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

38. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
(x1+x2)/2 -(y1+y2)/2
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

39. Finding the Volume of a Rectangular Solid
Use the distributive property then combine the like terms.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
VofaRS=lwh

40. What value of x is not in the domain of the function f(x)=x-2/x-3?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Use the distributive property then combine the like terms.
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

41. Expressing the Union and Intersection of Sets
Just add or subtract the coefficients in front of the radicals.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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

42. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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.
(x1+x2)/2 -(y1+y2)/2
Get the absolute value equation by itself. Solve.

43. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Get the absolute value equation by itself. Solve.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

44. Characteristics of a Square
(x1+x2)/2 -(y1+y2)/2
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.
Use the formula distance=rate*time and its variations to help in this question.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

45. What is the Triangle Inequality Theorem?
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.
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Put the equation into y=mx+b-- in which case b is the y-intercept.

46. Converting from part-to-part ratios to part-to-whole ratios
FOIL: First - Outer - Inner - Last... Combine Like Terms
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Put each number in the original ratio over the sum of the numbers.

47. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Part=Percent x Whole
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
2(pie)r
Average the smallest and largest number

48. What types of angles are formed when a transversal cross parallel lines?
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
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.
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.
Four equal acute angles and four equal obtuse angles.

49. Definition of an Integer
Multiply the exponents - (x^3)^4=x^3*4=x^12
Slope=change in y/change in x
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

50. General Procedure for Multiplying Polynomials
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
Find a common denominator - then add or subtract the numerators.
Use the distributive property then combine the like terms.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.