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 Sum of the Interior Angles of a Polygon
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply the numerators and multiply the denominators.


2. How do you know if an integer is a multiple of 3 or 9?
Just add or subtract the coefficients in front of the radicals.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Use the units to keep things straight - Snowfall inches/hours
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.


3. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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
Express them with a common denominator.


4. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Get the absolute value equation by itself. Solve.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


5. 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?
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.
Four equal acute angles and four equal obtuse angles.
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle


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

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7. Convert From a Fraction to a Decimal - Vice Versa
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Sum: Average x Number of Terms
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.


8. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Sum: Average x Number of Terms


9. Finding the Area of a Triangle

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10. Solving an Inequality
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Just add or subtract the coefficients in front of the radicals.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Use simple numbers like 1 and 2 and see what happens.


11. Finding the Mode of a Set of Numbers
The value that appears the most often.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Use simple numbers like 1 and 2 and see what happens.


12. Number of Groups - +1 Each Time
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
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


13. Converting from an Improper Fraction to a Mixed Number
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
VofaRS=lwh
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.
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.


14. Solving a Radical Equation
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.
Isolate the radical expression and use the standard rules of algebra.
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
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


15. Definition of an Integer
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
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
-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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


16. Dividing Expressions with Exponents that Have a Common Base
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Factor out and cancel all factors the numerator and denominator have in common.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


17. Prime Factorization of a Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
-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.
The value that appears the most often.


18. Simplifying Square Roots
Isolate the radical expression and use the standard rules of algebra.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


19. Multiplying Fractions
Multiply the numerators and multiply the denominators.
FOIL: First - Outer - Inner - Last... Combine Like 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.
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.


20. Comparing the values of two or more Fractions
Express them with a common denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


21. Finding the Length of an Arc in a Circle

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22. Adding and Subtracting Fractions
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
Find a common denominator - then add or subtract the numerators.


23. Adding and Subtracting Monomials
Part=Percent x Whole
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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


24. Expressing the Union and Intersection of Sets
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.


25. Definition of an Irrational Number
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


26. Dividing Fractions
Four equal acute angles and four equal obtuse angles.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


27. Solving a Linear Equation
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Do whatever is necessary to both sides to isolate the variable.


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

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29. Adding and Subtracting Polynomials
Combine like terms.
Find a common denominator - then add or subtract the numerators.
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.
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.


30. What is a Function and how do you Evaluate one?

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31. Multiplying Binomials
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Express them with a common denominator.


32. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.


33. PEMDAS
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


34. Finding the Volume of a Cylinder
A(2)+b(2)=c(2)
VofaC: (pie)r(2)h
-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.
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


35. Increasing and Decreasing a Number by a Certain Percentage
Put the equation into y=mx+b-- in which case b is the y-intercept.
Substitute r=4 and t=3 and evaluate the exponents before subtracting 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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle


36. 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.
2(pie)r
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)


37. 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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


38. Finding the Area of a Circle
-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.
(pie)r(squared)
Do whatever is necessary to both sides to isolate the variable.


39. Knowing if an Integer is a Multiple of 5 or 10
-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.
Do whatever is necessary to both sides to isolate the variable.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.


40. Properties of Similar Triangles
Find a common denominator - then add or subtract the numerators.
Get the absolute value equation by itself. Solve.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.


41. If r#t=t(r)-r(t) - then what is 4#3?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


42. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


43. Characteristics of a Parallelogram
Put each number in the original ratio over the sum of the numbers.
Subtract the smallest from the largest and add 1
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
The whole number left over after division.


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

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45. Solving a Proportion
Use simple numbers like 1 and 2 and see what happens.
Cross multiply.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The whole number left over after division.


46. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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
-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.


47. Characteristics of a Square
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
Get the absolute value equation by itself. Solve.


48. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
Get the absolute value equation by itself. Solve.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


49. Adding a Positive Number to a Negative Number
The whole number left over after division.
Cancel factors common to the numerator and denominator.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.


50. Finding the Sum of the Average of a Series of Numbers
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Sum: Average x Number of Terms
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.