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. Scalene - Isosceles - and Equilateral Triangles
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.
Slope=change in y/change in x
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
2(pie)r


2. Increasing and Decreasing a Number by a Certain Percentage
-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.
Put each number in the original ratio over the sum of the numbers.
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.
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.


3. Numbers that are Relatively Prime
Cross multiply.
Two relatively prime numbers are integers that have no common factor other than 1.
Factor out and cancel all factors the numerator and denominator have in common.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


4. 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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


5. Number of Groups - +1 Each Time
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


6. Solving a System of Equations
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
-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.
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.


7. What is the Triangle Inequality Theorem?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the formula distance=rate*time and its variations to help in this question.
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.


8. If 3(3x)=9(x+2) - what is the value of x?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
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.
Put each number in the original ratio over the sum of the numbers.


9. Definition of an Integer
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


10. Finding the Area of a Circle
(pie)r(squared)
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Two relatively prime numbers are integers that have no common factor other than 1.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


11. Finding the Area of a Triangle

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12. Solving a Radical Equation
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
Slope=change in y/change in x


13. Converting From a Mixed Number to an Improper Fraction
Adjacent angles are supplementary - Vertical angles are equal
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Combine like terms.


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

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15. If r#t=t(r)-r(t) - then what is 4#3?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Average the smallest and largest number
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


16. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


17. Finding the Area of a Sector

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18. 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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Cross multiply.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


19. Dividing Expressions with Exponents that Have a Common Base
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.


20. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use the units to keep things straight - Snowfall inches/hours


21. Converting from part-to-part ratios to part-to-whole ratios
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Put each number in the original ratio over the sum of the numbers.
(x1+x2)/2 -(y1+y2)/2
The value that appears the most often.


22. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Find a common denominator - then add or subtract the numerators.


23. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


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

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25. Multiplying Fractions
Switch the numerator and denominator.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply the numerators and multiply the denominators.


26. Multiplying Expressions with Exponents that Have a Common Base
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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


27. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Average the smallest and largest number
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


28. Characteristics of a Rectangle
Use simple numbers like 1 and 2 and see what happens.
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Find a common denominator - then add or subtract the numerators.


29. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
-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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


30. Finding the Mode of a Set of Numbers
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.
Use the formula distance=rate*time and its variations to help in this question.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
The value that appears the most often.


31. Factoring a Polynomial ('FOIL in Reverse')
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
-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.
Cancel factors common to the numerator and denominator.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


32. Finding the Circumference of a Circle
-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.
2(pie)r
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Part=Percent x Whole


33. PEMDAS
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


34. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
Multiply the numerators and multiply the denominators.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Four equal acute angles and four equal obtuse angles.


35. Raising a Power to a Power
Do whatever is necessary to both sides to isolate the variable.
Multiply the exponents - (x^3)^4=x^3*4=x^12
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.


36. If (Square Root: x-1)+5=12 - what is the value of x/2?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
Cancel factors common to the numerator and denominator.


37. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
Four equal acute angles and four equal obtuse angles.
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.
Put each number in the original ratio over the sum of the numbers.


38. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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.
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
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


39. If 4(x(2)-10x+25) - then what is the value of x?
Just add or subtract the coefficients in front of the radicals.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


40. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
'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. Properties of a 30-60-90 Triangle
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Four equal acute angles and four equal obtuse angles.


42. Finding a Term in a Geometric Sequence
Change the division sign to a multiplication sign - invert the second fraction - and 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.
Find a common denominator - then add or subtract the numerators.
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.


43. Calculating the Probability that an Event will Take Place
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Switch the numerator and denominator.


44. Finding the Reciprocal of a Fraction
Express them with a common denominator.
Put each number in the original ratio over the sum of the numbers.
Switch the numerator and denominator.
Two relatively prime numbers are integers that have no common factor other than 1.


45. Calculating Negative Exponents and Radical Exponents
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Four equal acute angles and four equal obtuse angles.


46. What is the greatest of three consecutive odd integers where the sum of the third and twice the first is equal to nine more than twice the second?
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.
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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


47. If x(2)=7x+18 - what is the positive value of x?
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
2(pie)r
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


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

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49. Multiplying Binomials
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.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
FOIL: First - Outer - Inner - Last... Combine Like Terms


50. Factoring the Difference of Two Squares
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
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24