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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. Knowing if an Integer is a Multiple of 5 or 10
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
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.
-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. Properties of a 30-60-90 Triangle
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
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.

3. 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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

4. If the average of a - b - and 48 is 48 - what is the value of a + b?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Isolate the radical expression and use the standard rules of algebra.

5. How do you know if an integer is a multiple of 3 or 9?
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

6. 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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
-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.

7. Finding the Rate of Speed
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.
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.
Use the formula distance=rate*time and its variations to help in this question.
Use the units to keep things straight - Snowfall inches/hours

8. Finding the Volume of a Rectangular Solid
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use simple numbers like 1 and 2 and see what happens.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
VofaRS=lwh

9. Dividing Fractions
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

10. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use the distributive property then combine the like terms.
Part=Percent x Whole
Two relatively prime numbers are integers that have no common factor other than 1.

11. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
2(pie)r

12. Finding the y-intercept When Given an Equation of a Line
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
Put the equation into y=mx+b-- in which case b is the y-intercept.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.

13. Converting from part-to-part ratios to part-to-whole ratios
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Put each number in the original ratio over the sum of the numbers.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

14. PEMDAS
2(pie)r
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

15. Adding and Subtracting Fractions
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Find a common denominator - then add or subtract the numerators.
(pie)r(squared)
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

16. Properties of Similar Triangles
VofaRS=lwh
Just add or subtract the coefficients in front of the radicals.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

17. 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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

18. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
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 simple numbers like 1 and 2 and see what happens.

19. Finding the Area of a Triangle

20. What value of x is not in the domain of the function f(x)=x-2/x-3?
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.
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.
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

21. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
Two relatively prime numbers are integers that have no common factor other than 1.
-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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

22. Finding the Slope When Given an Equation of a Line
Just add or subtract the coefficients in front of the radicals.
Use the distributive property then combine the like terms.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Two relatively prime numbers are integers that have no common factor other than 1.

23. Finding the Mode of a Set of Numbers
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The value that appears the most often.

24. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

25. Dividing Expressions with Exponents that Have a Common Base
Slope=change in y/change in x
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

26. Finding the Domain and Range of a Function
VofaRS=lwh
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)
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.

27. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Find a common denominator - then add or subtract the numerators.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
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

28. What are Two Special Pythagorean Triples?

29. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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

30. Setting Up a Ratio
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
(pie)r(squared)
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
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

31. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.

32. Finding the Slope of a Line When Given Two Points on the Line
Use the units to keep things straight - Snowfall inches/hours
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Slope=change in y/change in x
The whole number left over after division.

33. Multiplying Expressions with Exponents that Have a Common Base
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

34. Finding a Term in a Geometric Sequence
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Average: Sum of the Terms/Number of the Terms
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

35. Comparing the values of two or more Fractions
Express them with a common denominator.
-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.
Average: Sum of the Terms/Number of the Terms
Average the smallest and largest number

36. Calculating Negative Exponents and Radical Exponents
Use simple numbers like 1 and 2 and see what happens.
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.
Do whatever is necessary to both sides to isolate the variable.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

37. Properties of a 45-45-90 Triangle
(x1+x2)/2 -(y1+y2)/2
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use the formula distance=rate*time and its variations to help in this question.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

38. Adding and Subtracting Roots
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
Just add or subtract the coefficients in front of the radicals.

39. Adding and Subtracting Monomials
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Factor out and cancel all factors the numerator and denominator have in common.
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.

40. Finding the Distance Between Two Points on a Coordinate Graph
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
(x1+x2)/2 -(y1+y2)/2

41. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

42. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
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.
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. 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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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
Combine like terms.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

44. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
-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.
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. 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?
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

46. Adding and Subtracting Polynomials
Combine like terms.
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

47. If (Square Root: x-1)+5=12 - what is the value of x/2?
Part=Percent x Whole
Subtract the smallest from the largest and add 1
The value that falls in the middle of the set.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

48. Factoring the Difference of Two Squares
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

49. Calculating the Probability that an Event will Take Place
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

50. What is the Triangle Inequality Theorem?
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 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.
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.
(x1+x2)/2 -(y1+y2)/2