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. Definition of a Rational Number
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Subtract the smallest from the largest and add 1


2. Formula to Find Average
-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.
Average: Sum of the Terms/Number of the Terms
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


3. Properties of a 45-45-90 Triangle
The value that appears the most often.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


4. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
2(pie)r
-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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


5. Characteristics of a Rectangle
(pie)r(squared)
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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


6. Finding the Length of an Arc in a Circle

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7. Finding the GCF of Two or More Numbers
Cross multiply.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


8. 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.
Cross multiply.
-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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


9. Simplifying a Fraction to Lowest Terms
Cancel factors common to the numerator and denominator.
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.
Switch the numerator and denominator.


10. Finding the Domain and Range of a Function
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
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.
(pie)r(squared)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


11. Knowing if an Integer is a Multiple of 5 or 10
Plug in the given values for the unknowns and calculate according to PEMDAS.
-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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


12. Converting from an Improper Fraction to a Mixed Number
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
Cross multiply.


13. What types of angles are formed when a transversal cross parallel lines?
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Four equal acute angles and four equal obtuse angles.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


14. 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?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
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 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.


15. Number of Groups - +1 Each Time
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 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 simple numbers like 1 and 2 and see what happens.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


16. Converting from part-to-part ratios to part-to-whole ratios
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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
Put each number in the original ratio over the sum of the numbers.


17. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Sum: Average x Number of Terms
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


18. If x(2)=7x+18 - what is the positive value of x?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
2(pie)r
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


19. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the formula distance=rate*time and its variations to help in this question.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


20. Multiplying and Dividing Roots
FOIL: First - Outer - Inner - Last... Combine Like Terms
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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
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.


21. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
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.
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


22. Difference Between a Factor and a Multiple
Put the equation into y=mx+b-- in which case b is the y-intercept.
The value that appears the most often.
Part=Percent x Whole
-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.


23. Calculating the Probability that an Event will Take Place
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


24. Finding the Surface Area of a Rectangular Solid
FOIL: First - Outer - Inner - Last... Combine Like Terms
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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 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.


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

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26. Finding the Median of a Set of Numbers
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The value that falls in the middle of the set.
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.


27. What is the Triangle Inequality Theorem?
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
Average the smallest and largest number
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.


28. PEMDAS
Factor out and cancel all factors the numerator and denominator 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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


29. What is the Pythagorean Theorem?
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.
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
Do whatever is necessary to both sides to isolate the variable.
A(2)+b(2)=c(2)


30. Converting From a Mixed Number to an Improper Fraction
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Factor out and cancel all factors the numerator and denominator have in common.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


31. Factoring the Difference of Two Squares
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-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.
Slope=change in y/change in x
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


32. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
Put each number in the original ratio over the sum of the numbers.
Average the smallest and largest number
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


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

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34. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
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
Adjacent angles are supplementary - Vertical angles are equal
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


35. What are Two Special Pythagorean Triples?

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36. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Switch the numerator and denominator.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


37. Finding the Slope When Given an Equation of a Line
-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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


38. Increasing and Decreasing a Number by a Certain Percentage
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-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.
Sum: Average x Number of Terms
Factor out and cancel all factors the numerator and denominator have in common.


39. An Important Property of a Line Tangent to a Circle
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.
-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.
Find a common denominator - then add or subtract the numerators.
(pie)r(squared)


40. 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.
Part=Percent x Whole
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
2(pie)r


41. Finding the Area of a Circle
Adjacent angles are supplementary - Vertical angles are equal
Get the absolute value equation by itself. Solve.
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.
(pie)r(squared)


42. Properties of the Interior and Exterior Angles of a Triangle
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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. Raising a Power to a Power
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Get the absolute value equation by itself. Solve.
Multiply the exponents - (x^3)^4=x^3*4=x^12


44. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Part=Percent x Whole
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Cancel factors common to the numerator and denominator.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


45. Finding the Mode of a Set of Numbers
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
-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.
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.
The value that appears the most often.


46. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Just add or subtract the coefficients in front of the radicals.
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.


47. Solving an Inequality
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Four equal acute angles and four equal obtuse angles.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


48. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


49. Determining Absolute Value of a Number
-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.
VofaC: (pie)r(2)h
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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


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

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