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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. Finding the Circumference of a Circle
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
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
2(pie)r
The value that appears the most often.

2. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
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.
Switch the numerator and denominator.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

3. Setting Up a Ratio
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.
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
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

4. Scalene - Isosceles - and Equilateral Triangles
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)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.
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.
-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.

5. Finding the Sum of the Interior Angles of a Polygon
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Find a common denominator - then add or subtract the numerators.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

6. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.

7. Dividing Expressions with Exponents that Have a Common Base
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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

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

9. Adding a Positive Number to a Negative Number
Multiply the numerators and multiply the denominators.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

10. Knowing if an Integer is a Multiple of 2 or 4
-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.
-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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
-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.

11. Finding the y-intercept When Given an Equation of a Line
Use simple numbers like 1 and 2 and see what happens.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.

12. Adding and Subtracting Monomials
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.
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

13. Properties of the Interior and Exterior Angles of a Triangle
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
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.

14. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

15. PEMDAS
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
FOIL: First - Outer - Inner - Last... Combine Like Terms
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

16. Multiplying Fractions
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Multiply the numerators and multiply the denominators.

17. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Subtract the smallest from the largest and add 1
Put each number in the original ratio over the sum of the numbers.
The whole number left over after division.

18. What is the Triangle Inequality Theorem?
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.
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.
Subtract the smallest from the largest and add 1
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

19. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Slope=change in y/change in x
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.

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

21. Finding the Rate of Speed
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Express them with a common 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.
Use the formula distance=rate*time and its variations to help in this question.

22. Converting from part-to-part ratios to part-to-whole ratios
Use simple numbers like 1 and 2 and see what happens.
Use the distributive property then combine the like terms.
Put each number in the original ratio over the sum of the numbers.
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.

23. Finding the Area of a Circle
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
(pie)r(squared)
A(2)+b(2)=c(2)
Adjacent angles are supplementary - Vertical angles are equal

24. Finding the GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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 value that falls in the middle of the set.

25. Solving a System of Equations
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
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.
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

26. Finding the Slope When Given an Equation of a Line
Switch the numerator and denominator.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
VofaC: (pie)r(2)h
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

27. How do you know if an integer is a multiple of 3 or 9?
Average: Sum of the Terms/Number of the Terms
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
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

28. Factoring the Difference of Two Squares
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

29. Dividing Fractions
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.
Cross multiply.
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

30. Calculating Negative Exponents and Radical Exponents
Express them with a common 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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

31. Multiply and Divide Positive and Negative Numbers
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.
Average: Sum of the Terms/Number of the Terms
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

32. Characteristics of a Parallelogram
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
A(2)+b(2)=c(2)

33. Counting the Total Number of Possibilities for Several Events to Occur
-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.
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.
-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.

34. Quickly Finding the Average of a Series of Evenly Spaced Numbers
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Average the smallest and largest number
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. Comparing the values of two or more Fractions
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
Do whatever is necessary to both sides to isolate the variable.
Express them with a common denominator.

36. If 4(x(2)-10x+25) - then what is the value of x?
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Just add or subtract the coefficients in front of the radicals.
Average: Sum of the Terms/Number of the 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.

37. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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

38. Difference Between a Factor and a Multiple
Just add or subtract the coefficients in front of the radicals.
(pie)r(squared)
-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)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

39. What value of x is not in the domain of the function f(x)=x-2/x-3?
Use the formula distance=rate*time and its variations to help in this question.
Do whatever is necessary to both sides to isolate the variable.
Find a common denominator - then add or subtract the numerators.
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

40. 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?
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.
Get the absolute value equation by itself. Solve.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.

41. Multiplying Binomials
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
FOIL: First - Outer - Inner - Last... Combine Like Terms
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

42. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

43. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use simple numbers like 1 and 2 and see what happens.
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

44. Finding the Slope of a Line When Given Two Points on the Line
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Slope=change in y/change in x
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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

45. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
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.
A(2)+b(2)=c(2)
Adjacent angles are supplementary - Vertical angles are equal

46. Knowing if an Integer is a Multiple of 5 or 10
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Cancel factors common to the numerator and denominator.
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.
-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.

47. If r#t=t(r)-r(t) - then what is 4#3?
Slope=change in y/change in x
2(pie)r
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

48. Prime Factorization of a Number
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Use the formula distance=rate*time and its variations to help in this question.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

49. 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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
-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.

50. Formula to Find Average
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Average: Sum of the Terms/Number of the Terms
Multiply the numerators and multiply the denominators.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)