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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. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Use the formula distance=rate*time and its variations to help in this question.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

2. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The value that appears the most often.
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.
Cancel factors common to the numerator and denominator.

3. Finding the Mode of a Set of Numbers
Express them with a common denominator.
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.
The value that appears the most often.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

4. Determining Absolute Value of a Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

5. PEMDAS
Part=Percent x Whole
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Multiply the exponents - (x^3)^4=x^3*4=x^12

6. Finding the LCM of Two or More Numbers

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7. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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.
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.

8. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
(pie)r(squared)
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

9. Direct Variation and Inverse Variation
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Use simple numbers like 1 and 2 and see what happens.
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

10. If 4(x(2)-10x+25) - then what is the value of x?
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
FOIL: First - Outer - Inner - Last... 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.
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.

11. Average Rate and How Do You Find It
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

12. Multiplying Binomials
Subtract the smallest from the largest and add 1
Use simple numbers like 1 and 2 and see what happens.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
FOIL: First - Outer - Inner - Last... Combine Like Terms

13. Finding the Slope When Given an Equation of a Line
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Use simple numbers like 1 and 2 and see what happens.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

14. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.

15. Adding and Subtracting Polynomials
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Combine like terms.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

16. 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 two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Cross multiply.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Multiply the numerators and multiply the denominators.

17. If r#t=t(r)-r(t) - then what is 4#3?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Factor out and cancel all factors the numerator and denominator have in common.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

18. Factoring the Difference of Two Squares
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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

19. If 3(3x)=9(x+2) - what is the value of x?
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Subtract the smallest from the largest and add 1

20. Solving a System of Equations
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.
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.
VofaC: (pie)r(2)h
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.

21. Knowing if an Integer is a Multiple of 5 or 10
Just add or subtract the coefficients in front of the radicals.
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.
-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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

22. 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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Express them with a common denominator.

23. Finding the Median of a Set of Numbers
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Average the smallest and largest number
The value that falls in the middle of the set.
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

24. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
Multiply the exponents - (x^3)^4=x^3*4=x^12
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

25. Adding a Positive Number to a Negative Number
The value that falls in the middle of the set.
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
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

26. If the average of a - b - and 48 is 48 - what is the value of a + b?
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Express them with a common denominator.

27. Solving a Proportion
Cross multiply.
Adjacent angles are supplementary - Vertical angles are equal
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Use the formula distance=rate*time and its variations to help in this question.

28. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Average the smallest and largest number
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 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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

29. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
Two relatively prime numbers are integers that have no common factor other than 1.
The whole number left over after division.
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.

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

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31. Multiplying Monomials
Part=Percent x Whole
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Cancel factors common to the numerator and denominator.
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

32. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

33. Finding the Length of an Arc in a Circle

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34. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
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.
Part=Percent x Whole
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

35. Raising a Power to a Power
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 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
Multiply the exponents - (x^3)^4=x^3*4=x^12
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

36. Finding the Volume of a Rectangular Solid
VofaRS=lwh
-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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

37. Setting Up a Ratio
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Four equal acute angles and four equal obtuse angles.
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.

38. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
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.

39. 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.
Use the formula distance=rate*time and its variations to help in this question.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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

40. Number of Groups - +1 Each Time
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.

41. Multiplying Expressions with Exponents that Have a Common Base
Average: Sum of the Terms/Number of the Terms
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

42. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Two relatively prime numbers are integers that have no common factor other than 1.
The whole number left over after division.
Multiply the numerators and multiply the denominators.

43. If 2+l6-xl=10 and x>0 - what is the value of 2x?
(pie)r(squared)
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Get the absolute value equation by itself. Solve.
FOIL: First - Outer - Inner - Last... Combine Like Terms

44. 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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
Factor out and cancel all factors the numerator and denominator have in common.

45. 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?
Do whatever is necessary to both sides to isolate the variable.
Cancel factors common to the numerator and denominator.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Two relatively prime numbers are integers that have no common factor other than 1.

46. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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
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.
VofaC: (pie)r(2)h
Use simple numbers like 1 and 2 and see what happens.

47. Multiplying Fractions
Multiply the numerators and multiply the denominators.
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
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

48. Finding the Sum of the Average of a Series of Numbers
Multiply the numerators and multiply the denominators.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Sum: Average x Number of Terms
Part=Percent x Whole

49. If (Square Root: x-1)+5=12 - what is the value of x/2?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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

50. Finding the Sum of the Interior Angles of a Polygon
Use the distributive property then combine the like terms.
Express them with a common denominator.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides