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

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2. Properties of a 30-60-90 Triangle
Combine like terms.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


3. Comparing the values of two or more Fractions
Get the absolute value equation by itself. Solve.
Express them with a common denominator.
Two relatively prime numbers are integers that have no common factor other than 1.
(pie)r(squared)


4. Finding the Length of an Arc in a Circle

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5. Finding the Distance Between Two Points on a Coordinate Graph
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


6. 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?
Do whatever is necessary to both sides to isolate the variable.
Subtract the smallest from the largest and add 1
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


7. Simplifying Square Roots
-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.
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.
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


8. What types of angles are formed when a transversal cross parallel lines?
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.
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.
Four equal acute angles and four equal obtuse angles.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


9. Finding the Reciprocal of a Fraction
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Switch the numerator and denominator.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


10. Expressing the Union and Intersection of Sets
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.
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
Get the absolute value equation by itself. Solve.


11. Finding the Volume of a Cylinder
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
VofaC: (pie)r(2)h


12. Counting the Total Number of Possibilities for Several Events to Occur
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.


13. Definition of an Integer
Put the equation into y=mx+b-- in which case b is the y-intercept.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
VofaC: (pie)r(2)h
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


14. What are Two Special Pythagorean Triples?

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15. Formula to Find Average
Do whatever is necessary to both sides to isolate the variable.
Average: Sum of the Terms/Number of the Terms
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


16. Factoring the Difference of Two Squares
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
2(pie)r
Multiply the exponents - (x^3)^4=x^3*4=x^12


17. Multiplying and Dividing Roots
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
Average the smallest and largest number


18. Properties of Similar Triangles
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.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


19. Simplifying a Fraction to Lowest Terms
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Factor out and cancel all factors the numerator and denominator have in common.


20. Formula Used to Find Percent
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Sum: Average x Number of Terms
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.
Part=Percent x Whole


21. PEMDAS
VofaC: (pie)r(2)h
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Do whatever is necessary to both sides to isolate the variable.


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

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23. Evaluating an Algebraic Expression
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


24. Determining Absolute Value of a Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Average the smallest and largest number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Multiply the numerators and multiply the denominators.


25. What value of x is not in the domain of the function f(x)=x-2/x-3?
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 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.
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
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.


26. Scalene - Isosceles - and Equilateral Triangles
Do whatever is necessary to both sides to isolate the variable.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
2(pie)r


27. Solving a Radical Equation
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Switch the numerator and denominator.
Isolate the radical expression and use the standard rules of algebra.
A(2)+b(2)=c(2)


28. Finding the Sum of the Interior Angles of a Polygon
Combine like terms.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.


29. Finding the Area of a Sector

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30. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Get the absolute value equation by itself. Solve.


31. Adding and Subtracting Roots
Put each number in the original ratio over the sum of the numbers.
Just add or subtract the coefficients in front of the radicals.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


32. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
The value that appears the most often.
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.


33. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Switch the numerator and denominator.


34. Increasing and Decreasing a Number by a Certain Percentage
Use the formula distance=rate*time and its variations to help in this question.
-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.
-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.
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.


35. Adding and Subtracting Monomials
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
VofaC: (pie)r(2)h
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


36. Finding the y-intercept When Given an Equation of a Line
Probability: Number of Favorable Outcomes/Total Possible Outcomes
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Put the equation into y=mx+b-- in which case b is the y-intercept.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


37. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
Find a common denominator - then add or subtract the numerators.
Multiply the numerators and multiply the denominators.


38. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use simple numbers like 1 and 2 and see what happens.
The whole number left over after division.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle


39. Solving a Linear Equation
Average: Sum of the Terms/Number of 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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Do whatever is necessary to both sides to isolate the variable.


40. How do you know if an integer is a multiple of 3 or 9?
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Average: Sum of the Terms/Number of the Terms


41. If 4(x(2)-10x+25) - then what is the value of x?
A(2)+b(2)=c(2)
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


42. Finding the GCF of Two or More Numbers
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Average: Sum of the Terms/Number of the 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


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

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44. Dividing Fractions
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Find a common denominator - then add or subtract the numerators.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


45. Solving a Proportion
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Cross 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
-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.


46. Simplifying an Algebraic Equation
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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
-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.
Cancel factors common to the numerator and denominator.


47. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
The value that appears the most often.
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 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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


48. Finding the Slope When Given an Equation of a Line
Sum: Average x Number of Terms
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
The value that falls in the middle of the set.
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.


49. If x(2)=7x+18 - what is the positive value of x?
Factor out and cancel all factors the numerator and denominator have in common.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Probability: Number of Favorable Outcomes/Total Possible Outcomes


50. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Subtract the smallest from the largest and add 1
Use the units to keep things straight - Snowfall inches/hours