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 Triangle Inequality Theorem?
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 group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


2. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Use simple numbers like 1 and 2 and see what happens.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


3. Difference Between a Factor and a Multiple
-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.
Use the distributive property then combine the like terms.
Cancel factors common to the numerator and denominator.
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


4. Finding the Slope When Given an Equation of a Line
Find a common denominator - then add or subtract the numerators.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


5. Comparing the values of two or more Fractions
Express them with a common denominator.
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.
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.
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.


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

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7. Convert From a Fraction to a Decimal - Vice Versa
2(pie)r
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


8. Formula to Find Average
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Average: Sum of the Terms/Number of the Terms


9. 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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
VofaC: (pie)r(2)h
Cross multiply.


10. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


11. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
-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.
Factor out and cancel all factors the numerator and denominator have in common.


12. Counting the Total Number of Possibilities for Several Events to Occur
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Cross multiply.
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.


13. Dividing Expressions with Exponents that Have a Common Base
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
-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.


14. Dividing Fractions
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.
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.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


15. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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


16. Multiplying Expressions with Exponents that Have a Common Base
Use the distributive property then combine the like terms.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
VofaC: (pie)r(2)h
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


17. Counting Consecutive Integers
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.


18. If x(2)=7x+18 - what is the positive value of x?
Just add or subtract the coefficients in front of the radicals.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.


19. Formula Used to Find Percent
Combine like terms.
The value that falls in the middle of the set.
Part=Percent x Whole
-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.


20. Finding the Length of an Arc in a Circle

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21. Raising a Power to a Power
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply the exponents - (x^3)^4=x^3*4=x^12
VofaC: (pie)r(2)h
Subtract the smallest from the largest and add 1


22. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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.
Get the absolute value equation by itself. Solve.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


23. Definition of a Rational Number
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Put the equation into y=mx+b-- in which case b is the y-intercept.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


24. Solving an Inequality
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
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.


25. Finding the Sum of the Interior Angles of a Polygon
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


26. What value of x is not in the domain of the function f(x)=x-2/x-3?
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
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


27. Expressing the Union and Intersection of Sets
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
-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 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


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

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29. 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.
Use the distributive property then combine the like terms.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4


30. Finding the y-intercept When Given an Equation of a Line
Part=Percent x Whole
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


31. Definition of an Irrational Number
2(pie)r
Sum: Average x Number of Terms
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


32. Finding the Volume of a Cylinder
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.
VofaC: (pie)r(2)h
VofaRS=lwh
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


33. Finding the Slope of a Line When Given Two Points on the Line
2(pie)r
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Put each number in the original ratio over the sum of the numbers.
Slope=change in y/change in x


34. Converting from an Improper Fraction to a Mixed Number
-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.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.


35. If 3(3x)=9(x+2) - what is the value of x?
The whole number left over after division.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


36. 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
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.
Cross multiply.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


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

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38. Finding the Midpoint Between Two Points
Get the absolute value equation by itself. Solve.
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


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

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40. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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
Combine like terms.


41. Direct Variation and Inverse Variation
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


42. Finding a Term in a Geometric Sequence
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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 of the Angles of a Polygon: (n-2)*180 - n is the number of sides


43. Prime Factorization of a Number
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.
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
Isolate the radical expression and use the standard rules of algebra.


44. 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.
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
VofaC: (pie)r(2)h
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


45. Solving a Proportion
Cross multiply.
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.
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


46. Finding the Reciprocal of a Fraction
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Switch the numerator and denominator.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


47. Finding the Area of a Circle
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
(pie)r(squared)
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


48. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Just add or subtract the coefficients in front of the radicals.
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 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.


49. Solving a System of Equations
Cancel factors common to the numerator and denominator.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
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.


50. If 4(x(2)-10x+25) - then what is the value of x?
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.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%