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 length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Cross multiply.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
(pie)r(squared)
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.


2. PEMDAS
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
A(2)+b(2)=c(2)
Put the equation into y=mx+b-- in which case b is the y-intercept.


3. Adding and Subtracting Fractions
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Sum: Average x Number of Terms
Find a common denominator - then add or subtract the numerators.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


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

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5. Multiplying Expressions with Exponents that Have a Common Base
Put each number in the original ratio over the sum of the numbers.
Plug in the given values for the unknowns and calculate according to PEMDAS.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


6. Finding the Volume of a Cylinder
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
VofaC: (pie)r(2)h
FOIL: First - Outer - Inner - Last... Combine Like Terms


7. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
The value that appears the most often.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.


8. 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.
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.
Average the smallest and largest number
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


9. Adding and Subtracting Roots
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
Just add or subtract the coefficients in front of the radicals.


10. Expressing the Union and Intersection of Sets
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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
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.
Slope=change in y/change in x


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

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12. Characteristics of a Square
Express them with a common denominator.
A(2)+b(2)=c(2)
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


13. Finding the Sum of the Average of a Series of Numbers
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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Four equal acute angles and four equal obtuse angles.
Sum: Average x Number of Terms


14. Finding the Volume of a Rectangular Solid
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Use simple numbers like 1 and 2 and see what happens.
Average the smallest and largest number
VofaRS=lwh


15. Dividing Expressions with Exponents that Have a Common Base
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Express them with a common denominator.


16. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
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
Factor out and cancel all factors the numerator and denominator have in common.
Get the absolute value equation by itself. Solve.


17. Finding the GCF of Two or More Numbers
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Subtract the smallest from the largest and add 1
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


18. Number of Groups - +1 Each Time
Sum: Average x Number of Terms
-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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


19. Finding the Domain and Range of a Function
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 the numerators and multiply the denominators.
Cross multiply.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


20. Finding the Missing Number in a Series When You are Given the Average
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.


21. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Combine like terms.


22. Definition of a Rational Number
(x1+x2)/2 -(y1+y2)/2
Isolate the radical expression and use the standard rules of algebra.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


23. Counting the Total Number of Possibilities for Several Events to Occur
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.
Adjacent angles are supplementary - Vertical angles are equal
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.


24. Dividing Fractions
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


25. Formula to Find Average
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Average: Sum of the Terms/Number of the Terms


26. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Use simple numbers like 1 and 2 and see what happens.
A(2)+b(2)=c(2)


27. Formula Used to Find Percent
Factor out and cancel all factors the numerator and denominator have in common.
Part=Percent x Whole
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.
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. Finding the Distance Between Two Points on a Coordinate Graph
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Use simple numbers like 1 and 2 and see what happens.


29. Finding a Term in a Geometric Sequence
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
VofaC: (pie)r(2)h
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.


30. Converting from an Improper Fraction to a Mixed Number
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.
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.
VofaRS=lwh
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.


31. Finding the Circumference of a Circle
-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.
2(pie)r
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.
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.


32. What types of angles are formed when two lines intersect?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Adjacent angles are supplementary - Vertical angles are equal
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


33. Calculating the Probability that an Event will Take Place
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Factor out and cancel all factors the numerator and denominator have in common.


34. Factoring the Difference of Two Squares
VofaC: (pie)r(2)h
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
(x1+x2)/2 -(y1+y2)/2


35. Multiplying and Dividing Roots
Use the units to keep things straight - Snowfall inches/hours
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


36. Solving a Proportion
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Cross multiply.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


37. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Isolate the radical expression and use the standard rules of algebra.
VofaC: (pie)r(2)h


38. What value of x is not in the domain of the function f(x)=x-2/x-3?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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
Put each number in the original ratio over the sum of the numbers.


39. If x(2)=7x+18 - what is the positive value of x?
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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


40. If (Square Root: x-1)+5=12 - what is the value of x/2?
Just add or subtract the coefficients in front of the radicals.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.


41. Raising a Power to a Power
Factor out and cancel all factors the numerator and denominator have in common.
(pie)r(squared)
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 the exponents - (x^3)^4=x^3*4=x^12


42. Properties of Similar Triangles
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


43. How do you know if an integer is a multiple of 3 or 9?
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
Put each number in the original ratio over the sum of the numbers.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


44. Simplifying a Fraction to Lowest Terms
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.
(x1+x2)/2 -(y1+y2)/2
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


45. Solving a Radical Equation
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


46. Finding the LCM of Two or More Numbers

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

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48. Difference Between a Factor and a Multiple
Just add or subtract the coefficients in front of the radicals.
-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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


49. Finding the Area of a Triangle

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50. If the average of a - b - and 48 is 48 - what is the value of a + b?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96