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. Formula to Find Average
The whole number left over after division.
Average: Sum of the Terms/Number of the Terms
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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


2. Determining Absolute Value of a Number
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.


3. Average Rate and How Do You Find It
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Multiply the exponents - (x^3)^4=x^3*4=x^12
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


4. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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 simple numbers like 1 and 2 and see what happens.
The value that falls in the middle of the set.
-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.


5. Expressing the Union and Intersection of Sets
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Multiply the numerators and multiply the denominators.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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


6. Calculating the Probability that an Event will Take Place
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Just add or subtract the coefficients in front of the radicals.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.


7. Finding the Area of a Sector

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8. Solving a Linear Equation
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.
If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side.
Do whatever is necessary to both sides to isolate the variable.
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.


9. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


10. Finding the Volume of a Rectangular Solid
VofaRS=lwh
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.


11. Finding the Domain and Range of a Function
FOIL: First - Outer - Inner - Last... Combine Like Terms
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 value that appears the most often.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


12. Finding the Slope When Given an Equation of a Line
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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


13. Finding the Surface Area of a Rectangular Solid
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side.


14. How do you know if an integer is a multiple of 3 or 9?
Use the formula distance=rate*time and its variations to help in this question.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.


15. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


16. If 4(x(2)-10x+25) - then what is the value of x?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Part=Percent x Whole
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.


17. Definition of a Rational Number
Multiply the numerators and multiply the denominators.
Use the distributive property then combine the like terms.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


18. Counting Consecutive Integers
Multiply the numerators and multiply the denominators.
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.
Subtract the smallest from the largest and add 1
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


19. Properties of Similar Triangles
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


20. Multiplying Binomials
Probability: Number of Favorable Outcomes/Total Possible Outcomes
FOIL: First - Outer - Inner - Last... Combine Like Terms
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.


21. If the average of a - b - and 48 is 48 - what is the value of a + b?
Do whatever is necessary to both sides to isolate the variable.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.


22. If 2+l6-xl=10 and x>0 - what is the value of 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.
Cross 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.
Get the absolute value equation by itself. Solve.


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

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24. Finding the y-intercept When Given an Equation of a Line
The whole number left over after division.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Put the equation into y=mx+b-- in which case b is the y-intercept.


25. 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
Use the units to keep things straight - Snowfall inches/hours
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Slope=change in y/change in x


26. Comparing the values of two or more Fractions
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 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.
Express them with a common denominator.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


27. Dividing Fractions
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.


28. Finding the Volume of a Cylinder
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
-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.
Use simple numbers like 1 and 2 and see what happens.
VofaC: (pie)r(2)h


29. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
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.
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


30. Number of Groups - +1 Each Time
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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Slope=change in y/change in x


31. Prime Factorization of a 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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
VofaC: (pie)r(2)h
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. What is a Function and how do you Evaluate one?

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33. PEMDAS
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
2(pie)r
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.


34. If r#t=t(r)-r(t) - then what is 4#3?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
-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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Subtract the smallest from the largest and add 1


35. Finding the Length of an Arc in a Circle

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36. Numbers that are Relatively Prime
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Isolate the radical expression and use the standard rules of algebra.
Two relatively prime numbers are integers that have no common factor other than 1.


37. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
Multiply the numerators and multiply the denominators.


38. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


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

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40. Knowing if an Integer is a Multiple of 2 or 4
Adjacent angles are supplementary - Vertical angles are equal
Cross 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.
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.


41. Converting from an Improper Fraction to a Mixed Number
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
Isolate the radical expression and use the standard rules of algebra.


42. 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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Multiply the exponents - (x^3)^4=x^3*4=x^12


43. 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?
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


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

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45. Finding the Mode of a Set of Numbers
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.
Use the formula distance=rate*time and its variations to help in this question.
Part=Percent x Whole
The value that appears the most often.


46. Direct Variation and Inverse Variation
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


47. Finding the Median of a Set of Numbers
-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.
The value that falls in the middle of the set.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


48. 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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
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


49. If x(2)=7x+18 - what is the positive value of x?
Just add or subtract the coefficients in front of the radicals.
Subtract the smallest from the largest and add 1
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


50. Knowing if an Integer is a Multiple of 5 or 10
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.
-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 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
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.