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. Finding the Length of an Arc in a Circle

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2. 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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)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.
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.


3. Average Rate and How Do You Find It
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


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

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5. If r#t=t(r)-r(t) - then what is 4#3?
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


6. 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?
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.
Average: Sum of the Terms/Number of the Terms
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.


7. Finding a Term in a Geometric Sequence
Switch the numerator and denominator.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
The value that falls in the middle of the set.
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. Determining Absolute Value of a Number
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.
Get the absolute value equation by itself. Solve.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


9. What are Two Special Pythagorean Triples?

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10. Adding a Positive Number to a Negative 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.
-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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Cross multiply.


11. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
Average: Sum of the Terms/Number of the Terms
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Cancel factors common to the numerator and denominator.


12. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


13. Simplifying an Algebraic Equation
Express them with a common denominator.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
Cancel factors common to the numerator and denominator.


14. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
Two relatively prime numbers are integers that have no common factor other than 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.
Slope=change in y/change in x


15. Definition of an Irrational Number
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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


16. Calculating the Probability that an Event will Take Place
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


17. Dividing Expressions with Exponents that Have a Common Base
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.


18. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
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.
(pie)r(squared)


19. An Important Property of a Line Tangent to a Circle
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
Do whatever is necessary to both sides to isolate the variable.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


20. If (Square Root: x-1)+5=12 - what is the value of x/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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Use the distributive property then combine the like terms.


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


22. Characteristics of a Parallelogram
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


23. Expressing the Union and Intersection of Sets
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


24. Finding the Slope of a Line When Given Two Points on the Line
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.
Slope=change in y/change in x
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.


25. Finding the LCM of Two or More Numbers

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26. Finding the Domain and Range of a Function
The value that falls in the middle of the set.
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.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


27. Finding the GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Subtract the smallest from the largest and add 1


28. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.


29. If x(2)=7x+18 - what is the positive value of x?
Plug in the given values for the unknowns and calculate according to PEMDAS.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


30. Number of Groups - +1 Each Time
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.
Get the absolute value equation by itself. Solve.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Switch the numerator and denominator.


31. Adding and Subtracting Roots
VofaRS=lwh
Express them with a common denominator.
Just add or subtract the coefficients in front of the radicals.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


32. 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.
Combine like terms.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


33. Finding the Area of a Triangle

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34. Finding the y-intercept When Given an Equation of a Line
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Use the formula distance=rate*time and its variations to help in this question.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Do whatever is necessary to both sides to isolate the variable.


35. Converting From a Mixed Number to an Improper Fraction
Sum: Average x Number of Terms
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


36. Finding the Rate of Speed
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
A(2)+b(2)=c(2)
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


37. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


38. Adding and Subtracting Fractions
Two relatively prime numbers are integers that have no common factor other than 1.
Find a common denominator - then add or subtract the numerators.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Part=Percent x Whole


39. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Just add or subtract the coefficients in front of the radicals.
Multiply the numerators and multiply the denominators.


40. Finding the Surface Area of a Rectangular Solid
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.
Two relatively prime numbers are integers that have no common factor other than 1.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


41. Evaluating an Algebraic Expression
Use the formula distance=rate*time and its variations to help in this question.
The value that appears the most often.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Adjacent angles are supplementary - Vertical angles are equal


42. Simplifying Square Roots
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.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


43. Solving a System of Equations
Just add or subtract the coefficients in front of the radicals.
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 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
-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.


44. Finding the Area of a Sector

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45. Finding the Volume of a Rectangular Solid
VofaRS=lwh
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
The value that appears the most often.


46. Sale Price of a Jacket Marked Down 30% Each Week for 3 Weeks - What % of the Original Price is the Cost of the Jacket After the 3 Week Sale Period
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Express them with a common denominator.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


47. 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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Use the distributive property then combine the like terms.


48. Setting Up a Ratio
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


49. If 4(x(2)-10x+25) - then what is the value of x?
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


50. Definition of Remainder
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
The whole number left over after division.
-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.
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.