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 a 45-45-90 Triangle
Do whatever is necessary to both sides to isolate the variable.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


2. Adding a Positive Number to a Negative Number
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
-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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Get the absolute value equation by itself. Solve.


3. Characteristics of a Rectangle
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.
Subtract the smallest from the largest and add 1
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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


4. Finding the Length of an Arc in a Circle

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5. Converting from part-to-part ratios to part-to-whole ratios
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
2(pie)r
Put each number in the original ratio over the sum of the numbers.
The value that appears the most often.


6. If r#t=t(r)-r(t) - then what is 4#3?
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


7. Definition of Remainder
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 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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
The whole number left over after division.


8. Evaluating an Algebraic Expression
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
(pie)r(squared)
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.


9. Formula Used to Find Percent
Cross multiply.
Part=Percent x Whole
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


10. Multiplying Expressions with Exponents that Have a Common Base
Four equal acute angles and four equal obtuse angles.
Cancel factors common to the numerator and denominator.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
(pie)r(squared)


11. 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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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 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.


12. Characteristics of a Parallelogram
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


13. Multiplying Binomials
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
FOIL: First - Outer - Inner - Last... Combine Like 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.
Average the smallest and largest number


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.
(x1+x2)/2 -(y1+y2)/2
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


15. Expressing the Union and Intersection of Sets
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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


16. Direct Variation and Inverse Variation
Multiply the exponents - (x^3)^4=x^3*4=x^12
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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


17. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
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.


18. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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 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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
-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.


19. Finding the Midpoint Between Two Points
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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
(x1+x2)/2 -(y1+y2)/2


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

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21. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Switch the numerator and denominator.
(pie)r(squared)
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


23. An Important Property of a Line Tangent to a Circle
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
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.


24. Solving a Problem Involving Rates
The whole number left over after division.
Use the units to keep things straight - Snowfall inches/hours
A(2)+b(2)=c(2)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


25. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Part=Percent x Whole
Use simple numbers like 1 and 2 and see what happens.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.


26. Prime Factorization of a Number
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.
Do whatever is necessary to both sides to isolate the variable.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


27. Calculating Negative Exponents and Radical Exponents
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Factor out and cancel all factors the numerator and denominator have in common.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


28. Adding and Subtracting Roots
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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.


29. Increasing and Decreasing a Number by a Certain Percentage
Switch the numerator and denominator.
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.
-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.
-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.


30. Converting From a Mixed Number to an Improper Fraction
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
2(pie)r
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Isolate the radical expression and use the standard rules of algebra.


31. Adding and Subtracting Polynomials
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Combine like terms.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


32. If (Square Root: x-1)+5=12 - what is the value of x/2?
Express them with a common denominator.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


33. Comparing the values of two or more Fractions
Express them with a common denominator.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


34. Difference Between a Factor and a Multiple
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.
VofaRS=lwh
-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.
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.


35. Dividing Expressions with Exponents that Have a Common Base
Factor out and cancel all factors the numerator and denominator have in common.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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


36. Raising a Power to a Power
Put the equation into y=mx+b-- in which case b is the y-intercept.
Multiply the exponents - (x^3)^4=x^3*4=x^12
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


37. 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?
A(2)+b(2)=c(2)
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


38. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


39. Characteristics of a Square
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 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.
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


40. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


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

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


43. Finding the Sum of the Interior Angles of a Polygon
The value that falls in the middle of the set.
VofaC: (pie)r(2)h
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.


44. Properties of a 30-60-90 Triangle
Isolate the radical expression and use the standard rules of algebra.
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


45. Convert From a Fraction to a Decimal - Vice Versa
Part=Percent x Whole
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
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.
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.


46. If x(2)=7x+18 - what is the positive value of x?
Use the distributive property then combine the 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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


47. Scalene - Isosceles - and Equilateral Triangles
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
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.


48. Definition of an Irrational Number
Combine like terms.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Express them with a common denominator.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


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

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50. Finding the LCM of Two or More Numbers

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