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SAT Math

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. Solving a System of Equations
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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

2. Knowing if an Integer is a Multiple of 2 or 4
Multiply the numerators and multiply the denominators.
-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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
VofaC: (pie)r(2)h

3. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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
FOIL: First - Outer - Inner - Last... Combine Like Terms
-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.

4. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
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
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

5. Simplifying Square Roots
Combine like terms.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

6. Scalene - Isosceles - and Equilateral Triangles
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
Adjacent angles are supplementary - Vertical angles are equal
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.

7. Finding the GCF of Two or More Numbers
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
Average the smallest and largest number
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

8. Solving an Inequality
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 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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

9. Finding the Volume of a Rectangular Solid
Probability: Number of Favorable Outcomes/Total Possible Outcomes
VofaRS=lwh
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Sum: Average x Number of Terms

10. Finding the Missing Number in a Series When You are Given the Average
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
Put each number in the original ratio over the sum of the numbers.

11. Finding the Slope of a Line When Given Two Points on the Line
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The value that appears the most often.
Slope=change in y/change in x
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

12. Finding the Median of a Set of Numbers
Multiply the numerators and multiply the denominators.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The value that falls in the middle of the set.
Use the formula distance=rate*time and its variations to help in this question.

13. Difference Between a Factor and a Multiple
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
-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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
-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.

14. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Get the absolute value equation by itself. Solve.
-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.
-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.

15. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

16. If r#t=t(r)-r(t) - then what is 4#3?
Combine like terms.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
VofaC: (pie)r(2)h

17. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
VofaRS=lwh
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

18. Numbers that are Relatively Prime
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
Two relatively prime numbers are integers that have no common factor other than 1.
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.
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.

19. Finding the Sum of the Interior Angles of a Polygon
VofaRS=lwh
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Average: Sum of the Terms/Number of the Terms
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.

20. 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?
-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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

21. 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.
Use the units to keep things straight - Snowfall inches/hours
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

22. Multiplying and Dividing Roots
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
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.

23. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
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.
-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.
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.

24. Formula to Find Average
The whole number left over after division.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Average: Sum of the Terms/Number of the Terms
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

25. Characteristics of a Square
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Get the absolute value equation by itself. Solve.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

26. Calculating Negative Exponents and Radical Exponents
The whole number left over after division.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

27. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
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.
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
Switch the numerator and denominator.

28. Factoring the Difference of Two Squares
Switch the numerator and denominator.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Subtract the smallest from the largest and add 1

29. 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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.

30. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Use the formula distance=rate*time and its variations to help in this question.
Use simple numbers like 1 and 2 and see what happens.

31. Knowing if an Integer is a Multiple of 5 or 10
FOIL: First - Outer - Inner - Last... Combine Like Terms
-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.
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.
Average the smallest and largest number

32. Finding the Volume of a Cylinder
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 relatively prime numbers are integers that have no common factor other than 1.
VofaC: (pie)r(2)h
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

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

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34. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
Subtract the smallest from the largest and add 1
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply the numerators and multiply the denominators.

35. Definition of a Rational Number
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.
Factor out and cancel all factors the numerator and denominator have in common.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
-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.

36. 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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

37. Converting from part-to-part ratios to part-to-whole ratios
VofaC: (pie)r(2)h
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Put each number in the original ratio over the sum of the numbers.
Multiply the numerators and multiply the denominators.

38. Definition of Remainder
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
The value that appears the most often.
-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.
The whole number left over after division.

39. Dividing Expressions with Exponents that Have a Common Base
(x1+x2)/2 -(y1+y2)/2
Average the smallest and largest number
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

40. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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
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.

41. Finding the Circumference of a Circle
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
2(pie)r

42. Properties of the Interior and Exterior Angles of a Triangle
(pie)r(squared)
VofaRS=lwh
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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. Multiplying Fractions
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
(pie)r(squared)
Multiply the numerators and multiply the denominators.

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

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45. Properties of a 30-60-90 Triangle
FOIL: First - Outer - Inner - Last... Combine Like Terms
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
The whole number left over after division.

46. Multiply and Divide Positive and Negative Numbers
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.
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 whole number left over after division.

47. Finding the Mode of a Set of Numbers
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Use the distributive property then combine the like terms.
FOIL: First - Outer - Inner - Last... Combine Like Terms
The value that appears the most often.

48. Counting the Total Number of Possibilities for Several Events to Occur
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

49. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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 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

50. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
A(2)+b(2)=c(2)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.