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 GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
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.


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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


3. Dividing Fractions
-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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use the distributive property then combine the like terms.
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.


4. Multiplying Monomials
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
Cancel factors common to the numerator and denominator.
(pie)r(squared)
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


5. Simplifying an Algebraic Equation
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Cancel factors common to the numerator and denominator.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Just add or subtract the coefficients in front of the radicals.


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

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7. Comparing the values of two or more Fractions
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
(x1+x2)/2 -(y1+y2)/2
Express them with a common 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.


8. How do you know if an integer is a multiple of 3 or 9?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4


9. 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
-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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


10. 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
Plug in the given values for the unknowns and calculate according to PEMDAS.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)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.


11. Adding and Subtracting Fractions
The whole number left over after division.
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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Find a common denominator - then add or subtract the numerators.


12. Finding the Length of an Arc in a Circle

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13. Finding the Midpoint Between Two Points
Find a common denominator - then add or subtract the numerators.
(x1+x2)/2 -(y1+y2)/2
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


14. If r#t=t(r)-r(t) - then what is 4#3?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
(pie)r(squared)
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use the units to keep things straight - Snowfall inches/hours


15. If 4(x(2)-10x+25) - then what is the value of x?
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.
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.
(pie)r(squared)
Cross multiply.


16. Finding the Area of a Triangle

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17. Finding a Term in a Geometric Sequence
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.


18. What are Two Special Pythagorean Triples?

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19. If x(2)=7x+18 - what is the positive value of x?
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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 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.


20. Average Rate and How Do You Find It
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
VofaC: (pie)r(2)h
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


21. 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.
A(2)+b(2)=c(2)
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.


22. 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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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
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.


23. An Important Property of a Line Tangent to a Circle
Use the units to keep things straight - Snowfall inches/hours
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Average the smallest and largest number


24. Multiplying and Dividing Roots
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Slope=change in y/change in x
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


25. What types of angles are formed when a transversal cross parallel lines?
Two relatively prime numbers are integers that have no common factor other than 1.
Four equal acute angles and four equal obtuse angles.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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


26. Adding and Subtracting Polynomials
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Combine like terms.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Average the smallest and largest number


27. Multiplying Expressions with Exponents that Have a Common Base
Use the units to keep things straight - Snowfall inches/hours
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


28. Finding the y-intercept When Given an Equation of a Line
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.
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
Combine like terms.


29. Factoring a Polynomial ('FOIL in Reverse')
-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.
Subtract the smallest from the largest and add 1
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Probability: Number of Favorable Outcomes/Total Possible Outcomes


30. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
Average the smallest and largest number
Cancel factors common to the numerator and denominator.
Multiply the numerators and multiply the denominators.


31. Properties of the Interior and Exterior Angles of a Triangle
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
Adjacent angles are supplementary - Vertical angles are equal


32. Definition of an Irrational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
The value that appears the most often.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


33. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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 distance=rate*time and its variations to help in this question.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


34. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Four equal acute angles and four equal obtuse angles.
-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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use simple numbers like 1 and 2 and see what happens.


35. If the average of a - b - and 48 is 48 - what is the value of a + b?
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.
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


36. What is the Triangle Inequality Theorem?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Use the units to keep things straight - Snowfall inches/hours
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.
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.


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

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38. Definition of an Integer
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Cancel factors common to the numerator and denominator.


39. Finding the Slope When Given an Equation of a Line
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Use simple numbers like 1 and 2 and see what happens.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
FOIL: First - Outer - Inner - Last... Combine Like Terms


40. Simplifying a Fraction to Lowest Terms
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Factor out and cancel all factors the numerator and denominator have in common.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


41. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
FOIL: First - Outer - Inner - Last... Combine Like Terms
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


42. Adding and Subtracting Monomials
VofaRS=lwh
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Just add or subtract the coefficients in front of the radicals.


43. Converting from part-to-part ratios to part-to-whole ratios
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 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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


44. Formula to Find Average
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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
Average: Sum of the Terms/Number of the Terms
Just add or subtract the coefficients in front of the radicals.


45. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


46. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
Do whatever is necessary to both sides to isolate the variable.
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.


47. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
Cross multiply.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


48. What Does Solving In Terms of Mean?
Express them with a common denominator.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.


49. Finding the Median of a Set of Numbers
Plug in the given values for the unknowns and calculate according to PEMDAS.
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 falls in the middle of the set.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


50. 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
Multiply the exponents - (x^3)^4=x^3*4=x^12
The whole number left over after division.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.