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 Area of a Sector

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2. Finding the Missing Number in a Series When You are Given the Average
The value that appears the most often.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


3. Solving a Linear Equation
Put each number in the original ratio over the sum of the numbers.
Do whatever is necessary to both sides to isolate the variable.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.


4. Characteristics of a Rectangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Multiply the numerators and multiply the denominators.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


5. Converting from part-to-part ratios to part-to-whole ratios
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Put each number in the original ratio over the sum of the numbers.
Sum: Average x Number of Terms


6. Formula to Find Average
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Average: Sum of the Terms/Number of the Terms


7. Convert From a Fraction to a Decimal - Vice Versa
Sum: Average x Number of Terms
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.
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


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


9. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


10. Finding the LCM of Two or More Numbers

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11. Factoring the Difference of Two Squares
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.
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.
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.


12. What is the Triangle Inequality Theorem?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


13. 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.
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.
VofaRS=lwh
-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.


14. Increasing and Decreasing a Number by a Certain Percentage
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
-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 Area of a Triangle

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16. Setting Up a Ratio
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


17. Solving a Problem Involving Rates
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Use the units to keep things straight - Snowfall inches/hours
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


18. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Adjacent angles are supplementary - Vertical angles are equal
Put each number in the original ratio over the sum of the numbers.
Get the absolute value equation by itself. Solve.


19. Definition of an Integer
Plug in the given values for the unknowns and calculate according to PEMDAS.
Combine like terms.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


20. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Average: Sum of the Terms/Number of the Terms
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
Express them with a common denominator.
(x1+x2)/2 -(y1+y2)/2


21. Finding a Term in a Geometric Sequence
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
Adjacent angles are supplementary - Vertical angles are equal
Put the equation into y=mx+b-- in which case b is the y-intercept.


22. Adding and Subtracting Polynomials
Use the distributive property then combine the like terms.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Combine like terms.
The value that appears the most often.


23. Properties of a 45-45-90 Triangle
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Put each number in the original ratio over the sum of the numbers.


24. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
2(pie)r
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
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


25. Multiplying and Dividing Roots
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
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.
Put each number in the original ratio over the sum of the numbers.


26. What are Two Special Pythagorean Triples?

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

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28. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Switch the numerator and denominator.
Factor out and cancel all factors the numerator and denominator have in common.


29. If 4(x(2)-10x+25) - then what is the value of x?
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.
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.
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.


30. Counting the Total Number of Possibilities for Several Events to Occur
Multiply the numerators and multiply the denominators.
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.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


31. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Factor out and cancel all factors the numerator and denominator have in common.
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.


32. Finding the Volume of a Cylinder
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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
VofaC: (pie)r(2)h
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


33. 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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Do whatever is necessary to both sides to isolate the variable.


34. PEMDAS
VofaRS=lwh
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


35. General Procedure for Multiplying Polynomials
Plug in the given values for the unknowns and calculate according to PEMDAS.
Isolate the radical expression and use the standard rules of algebra.
Use the distributive property then combine the like terms.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


36. 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.
Cross multiply.
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


37. 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.
A(2)+b(2)=c(2)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.


38. Direct Variation and Inverse Variation
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
Just add or subtract the coefficients in front of the radicals.
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


39. Finding the Mode of a Set of Numbers
2(pie)r
The value that appears the most often.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
-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.


40. If x(2)=7x+18 - what is the positive value of x?
Use simple numbers like 1 and 2 and see what happens.
Cross multiply.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


41. Adding a Positive Number to a Negative Number
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Factor out and cancel all factors the numerator and denominator have in common.
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


42. Solving an Inequality
Combine like terms.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


43. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
(x1+x2)/2 -(y1+y2)/2
The whole number left over after division.
Part=Percent x Whole


44. Characteristics of a Parallelogram
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Get the absolute value equation by itself. Solve.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Find a common denominator - then add or subtract the numerators.


45. Finding the Distance Between Two Points on a Coordinate Graph
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


46. Properties of a 30-60-90 Triangle
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)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


47. Number of Groups - +1 Each Time
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


48. Definition of Remainder
FOIL: First - Outer - Inner - Last... Combine Like Terms
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The whole number left over after division.


49. What value of x is not in the domain of the function f(x)=x-2/x-3?
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.
Do whatever is necessary to both sides to isolate the variable.
Put each number in the original ratio over the sum of the numbers.
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


50. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
(pie)r(squared)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Plug in the given values for the unknowns and calculate according to PEMDAS.