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.
• Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
2(pie)r
Combine like terms.


2. Adding and Subtracting Polynomials
Use simple numbers like 1 and 2 and see what happens.
Two relatively prime numbers are integers that have no common factor other than 1.
Slope=change in y/change in x
Combine like terms.


3. Multiplying Expressions with Exponents that Have a Common Base
Isolate the radical expression and use the standard rules of algebra.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


4. Definition of Remainder
The whole number left over after division.
-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.
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 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.


5. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Get the absolute value equation by itself. Solve.
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 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.


6. Counting the Total Number of Possibilities for Several Events to Occur
Four equal acute angles and four equal obtuse angles.
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 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
Use the formula distance=rate*time and its variations to help in this question.


7. Raising a Power to a Power
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Subtract the smallest from the largest and add 1
Put each number in the original ratio over the sum of the numbers.
Multiply the exponents - (x^3)^4=x^3*4=x^12


8. Finding the Circumference of a Circle
2(pie)r
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


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

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

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11. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Use the units to keep things straight - Snowfall inches/hours
Average the smallest and largest number
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
Combine like terms.


12. What Does Solving In Terms of Mean?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Express them with a common denominator.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


13. If 4(x(2)-10x+25) - then what is the value of x?
VofaRS=lwh
Get the absolute value equation by itself. Solve.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


14. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
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.


15. Properties of a 45-45-90 Triangle
VofaRS=lwh
A(2)+b(2)=c(2)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Slope=change in y/change in x


16. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
VofaC: (pie)r(2)h
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.


17. Converting from an Improper Fraction to a Mixed Number
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


18. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
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 y=mx+b-- in which case b is the y-intercept.
Multiply the numerators and multiply the denominators.


19. Comparing the values of two or more Fractions
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
Express them with a common denominator.
The value that falls in the middle of the set.
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


20. Solving a System of Equations
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


21. Finding the Missing Number in a Series When You are Given the Average
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.


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

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23. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Adjacent angles are supplementary - Vertical angles are equal
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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
Combine like terms.


24. Finding the Length of an Arc in a Circle

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25. Finding the Volume of a Rectangular Solid
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
VofaRS=lwh
Probability: Number of Favorable Outcomes/Total Possible Outcomes
FOIL: First - Outer - Inner - Last... Combine Like Terms


26. Adding and Subtracting Fractions
Use the formula distance=rate*time and its variations to help in this question.
-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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Find a common denominator - then add or subtract the numerators.


27. Characteristics of a Square
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.
Use the formula distance=rate*time and its variations to help in this question.
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.


28. If 2+l6-xl=10 and x>0 - what is the value of 2x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Get the absolute value equation by itself. Solve.
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


29. If r#t=t(r)-r(t) - then what is 4#3?
-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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


30. Multiplying and Dividing Roots
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Do whatever is necessary to both sides to isolate the variable.


31. Properties of a 30-60-90 Triangle
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Switch the numerator and denominator.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


32. What value of x is not in the domain of the function f(x)=x-2/x-3?
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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


33. Finding a Term in a Geometric Sequence
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.
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.
Cross multiply.
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.


34. Knowing if an Integer is a Multiple of 5 or 10
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
-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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


35. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like 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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


36. 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?
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.
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


37. Dividing Fractions
The whole number left over after division.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Multiply the numerators and multiply the denominators.


38. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
-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.
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
Switch the numerator and denominator.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


39. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
FOIL: First - Outer - Inner - Last... Combine Like Terms


40. 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
Switch the numerator and denominator.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


41. Finding the LCM of Two or More Numbers

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


43. What are Two Special Pythagorean Triples?

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44. Scalene - Isosceles - and Equilateral Triangles
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.
(x1+x2)/2 -(y1+y2)/2
Do whatever is necessary to both sides to isolate the variable.
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.


45. Properties of the Interior and Exterior Angles of a Triangle
Express them with a common denominator.
Just add or subtract the coefficients in front of the radicals.
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.
Combine like terms.


46. Formula Used to Find Percent
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Part=Percent x Whole


47. An Important Property of a Line Tangent to a Circle
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Factor out and cancel all factors the numerator and denominator have in common.
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.
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


48. Finding the y-intercept When Given an Equation of a Line
Find a common denominator - then add or subtract the numerators.
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%
Adjacent angles are supplementary - Vertical angles are equal


49. Difference Between a Factor and a Multiple
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Find a common denominator - then add or subtract the numerators.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
-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.


50. Simplifying an Algebraic Equation
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.
Cancel factors common to the numerator and denominator.
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.