SAT Math

Instructions:

• Answer 50 questions in 15 minutes.
• If you are not ready to take this test, you can study here.
• 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. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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


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

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3. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
-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.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4


4. Definition of a Rational Number
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.
Cross multiply.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.


5. If r#t=t(r)-r(t) - then what is 4#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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


6. Scalene - Isosceles - and Equilateral Triangles
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.
Do whatever is necessary to both sides to isolate the variable.
A(2)+b(2)=c(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.


7. PEMDAS
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.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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


8. Adding and Subtracting Roots
Average the smallest and largest number
Just add or subtract the coefficients in front of the radicals.
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms


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

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10. Finding the Domain and Range of a Function
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Do whatever is necessary to both sides to isolate the variable.
The whole number left over after division.
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.


11. Properties of a 45-45-90 Triangle
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.


12. Finding the Slope of a Line When Given Two Points on the Line
(pie)r(squared)
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Isolate the radical expression and use the standard rules of algebra.
Slope=change in y/change in x


13. Solving a System of Equations
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Use the units to keep things straight - Snowfall inches/hours
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


14. What value of x is not in the domain of the function f(x)=x-2/x-3?
Multiply the exponents - (x^3)^4=x^3*4=x^12
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
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Put each number in the original ratio over the sum of the numbers.


15. Properties of the Interior and Exterior Angles of a Triangle
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.
Average the smallest and largest number
Average: Sum of the Terms/Number of the Terms
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.


16. Finding the Volume of a Rectangular Solid
VofaRS=lwh
The whole number left over after division.
Adjacent angles are supplementary - Vertical angles are equal
-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.


17. What Does Solving In Terms of Mean?
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Cancel factors common to the numerator and denominator.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


18. Knowing if an Integer is a Multiple of 5 or 10
Multiply the numerators and multiply the denominators.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
-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.


19. Multiplying Expressions with Exponents that Have a Common Base
(x1+x2)/2 -(y1+y2)/2
Slope=change in y/change in x
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


20. Solving an Inequality
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
-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.
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


21. Finding the Mode of a Set of 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.
The value that appears the most often.
Average: Sum of the Terms/Number of the Terms
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


22. Finding the Length of an Arc in a Circle

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23. Finding the Area of a Sector

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24. If 4(x(2)-10x+25) - then what is the value of x?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
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.


25. 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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
Switch the numerator and denominator.


26. Properties of Similar Triangles
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4


27. Comparing the values of two or more Fractions
Express them with a common denominator.
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.
(x1+x2)/2 -(y1+y2)/2
-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.


28. Increasing and Decreasing a Number by a Certain Percentage
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


29. General Procedure for Multiplying Polynomials
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use the distributive property then combine the like terms.
Combine like terms.
Part=Percent x Whole


30. If 3(3x)=9(x+2) - what is the value of x?
Use simple numbers like 1 and 2 and see what happens.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
(pie)r(squared)


31. What is the Triangle Inequality Theorem?
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.


32. Properties of a 30-60-90 Triangle
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
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


33. Expressing the Union and Intersection of Sets
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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
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
Cancel factors common to the numerator and denominator.


34. Characteristics of a Parallelogram
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.


35. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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


36. Simplifying a Fraction to Lowest Terms
-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.
Isolate the radical expression and use the standard rules of algebra.
Factor out and cancel all factors the numerator and denominator have in common.
2(pie)r


37. What is the Pythagorean Theorem?
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
A(2)+b(2)=c(2)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


38. Finding the Area of a Circle
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
(pie)r(squared)
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


39. Adding and Subtracting Fractions
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The whole number left over after division.
Find a common denominator - then add or subtract the numerators.
Multiply the exponents - (x^3)^4=x^3*4=x^12


40. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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 simple numbers like 1 and 2 and see what happens.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


41. Finding the GCF of Two or More Numbers
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
VofaRS=lwh
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


42. Multiplying and Dividing Roots
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.
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


43. Let N represent the smallest positive integer that is a multiple of 6 and 8 - but leaves a remainder of 2 when divided by 7. What is the value of N?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


44. Factoring the Difference of Two Squares
Adjacent angles are supplementary - Vertical angles are equal
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Subtract the smallest from the largest and add 1
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.


45. Dividing Fractions
2(pie)r
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.


46. Solving a Radical Equation
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.
Isolate the radical expression and use the standard rules of algebra.
Subtract the smallest from the largest and add 1


47. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Cancel factors common to the numerator and denominator.
Get the absolute value equation by itself. Solve.
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.
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


48. Finding the Rate of Speed
Use the formula distance=rate*time and its variations to help in this question.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Cross multiply.


49. Finding the LCM of Two or More Numbers

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50. What are Two Special Pythagorean Triples?

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