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. Properties of the Interior and Exterior Angles of a Triangle
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
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.


2. Simplifying Square Roots
Find a common denominator - then add or subtract the numerators.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
The value that appears the most often.


3. Solving a Problem Involving Rates
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
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


4. Characteristics of a Rectangle
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.


5. Finding the Volume of a Rectangular Solid
Just add or subtract the coefficients in front of the radicals.
VofaRS=lwh
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Cancel factors common to the numerator and denominator.


6. General Procedure for Multiplying Polynomials
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Use the distributive property then combine the like terms.
Cancel factors common to the numerator and denominator.


7. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The whole number left over after division.
VofaC: (pie)r(2)h


8. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


9. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
-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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


10. 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?
Part=Percent x Whole
Subtract the smallest from the largest and add 1
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.


11. How do you know if an integer is a multiple of 3 or 9?
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Multiply the numerators and multiply the denominators.
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.


12. Dividing Fractions
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The whole number left over after division.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


13. Difference Between a Factor and a Multiple
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
-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 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.


14. 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
Adjacent angles are supplementary - Vertical angles are equal
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
-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.


15. Finding the Distance Between Two Points on a Coordinate Graph
The whole number left over after division.
Factor out and cancel all factors the numerator and denominator have in common.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


16. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Slope=change in y/change in x
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.
Isolate the radical expression and use the standard rules of algebra.


17. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


18. Number of Groups - +1 Each Time
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.
Multiply the numerators and multiply the denominators.
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


19. Knowing if an Integer is a Multiple of 2 or 4
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Factor out and cancel all factors the numerator and denominator have in common.
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.
-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.


20. Multiplying Expressions with Exponents that Have a Common Base
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The value that falls in the middle of the set.
Sum: Average x Number of Terms


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

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22. Counting Consecutive Integers
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.
Subtract the smallest from the largest and add 1
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.
Put each number in the original ratio over the sum of the numbers.


23. Finding the Length of an Arc in a Circle

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24. Direct Variation and Inverse Variation
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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
Put each number in the original ratio over the sum of the numbers.


25. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
Four equal acute angles and four equal obtuse angles.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


26. Convert From a Fraction to a Decimal - Vice Versa
(x1+x2)/2 -(y1+y2)/2
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.


27. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
-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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


28. Multiplying Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
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


29. What is the Triangle Inequality Theorem?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


30. Adding and Subtracting Polynomials
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Combine like terms.
Get the absolute value equation by itself. Solve.
Put the equation into y=mx+b-- in which case b is the y-intercept.


31. Multiplying and Dividing Roots
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
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.


32. Formula Used to Find Percent
Part=Percent x Whole
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Just add or subtract the coefficients in front of the radicals.


33. Finding a Term in a Geometric Sequence
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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


34. What value of x is not in the domain of the function f(x)=x-2/x-3?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


35. Expressing the Union and Intersection of Sets
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


36. Finding the Area of a Triangle

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37. Solving an Inequality
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
-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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


38. Comparing the values of two or more Fractions
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Express them with a common denominator.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


39. 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?
Subtract the smallest from the largest and add 1
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


40. If (Square Root: x-1)+5=12 - what is the value of x/2?
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Switch the numerator and denominator.


41. Finding the Median of a Set of Numbers
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The value that falls in the middle of the set.
Use the units to keep things straight - Snowfall inches/hours
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


42. Raising a Power to a Power
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use simple numbers like 1 and 2 and see what happens.
(pie)r(squared)


43. Properties of a 30-60-90 Triangle
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.


44. Finding the Mode of a Set of Numbers
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
Subtract the smallest from the largest and add 1
The value that appears the most often.


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

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46. An Important Property of a Line Tangent to a Circle
VofaC: (pie)r(2)h
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.


47. Finding the Area of a Sector

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48. Properties of Similar Triangles
Switch the numerator and denominator.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
-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.


49. Finding the y-intercept When Given an Equation of a Line
Factor out and cancel all factors the numerator and denominator have in common.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Put the equation into y=mx+b-- in which case b is the y-intercept.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


50. Factoring a Polynomial ('FOIL in Reverse')
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
Cancel factors common to the numerator and denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)