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. What Does Solving In Terms of Mean?
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
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.


2. Setting Up a Ratio
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


3. Definition of a Rational Number
Combine like terms.
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


4. Converting from an Improper Fraction to a Mixed Number
Put each number in the original ratio over the sum of the numbers.
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


5. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
(pie)r(squared)
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


6. Finding the Length of an Arc in a Circle

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7. Numbers that are Relatively Prime
Combine like terms.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.


8. Factoring a Polynomial ('FOIL in Reverse')
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
-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.


9. Number of Groups - +1 Each Time
-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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


10. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
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.


11. Finding the LCM of Two or More Numbers

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12. 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?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
(x1+x2)/2 -(y1+y2)/2
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


13. Definition of an Irrational Number
Get the absolute value equation by itself. Solve.
Subtract the smallest from the largest and add 1
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.


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

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15. Multiplying Fractions
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
VofaC: (pie)r(2)h
Multiply the numerators and multiply the denominators.
Find a common denominator - then add or subtract the numerators.


16. Determining Absolute Value of a Number
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


17. If x(2)=7x+18 - what is the positive value of x?
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


18. How do you know if an integer is a multiple of 3 or 9?
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The whole number left over after division.
Factor out and cancel all factors the numerator and denominator have in common.


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


20. If 3(3x)=9(x+2) - what is the value of x?
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


21. Finding the Volume of a Cylinder
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Probability: Number of Favorable Outcomes/Total Possible Outcomes
VofaC: (pie)r(2)h


22. 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
Just add or subtract the coefficients in front of the radicals.
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.
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.


23. Solving a Linear Equation
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Do whatever is necessary to both sides to isolate the variable.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


24. An Important Property of a Line Tangent to a Circle
Adjacent angles are supplementary - Vertical angles are equal
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.
Factor out and cancel all factors the numerator and denominator have in common.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


25. Properties of Similar Triangles
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Multiply the numerators and multiply the denominators.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


26. Definition of Remainder
The whole number left over after division.
Part=Percent x Whole
Factor out and cancel all factors the numerator and denominator have in common.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


27. What types of angles are formed when a transversal cross parallel lines?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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.
Four equal acute angles and four equal obtuse angles.
VofaC: (pie)r(2)h


28. 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
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.
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 simple numbers like 1 and 2 and see what happens.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


29. Convert From a Fraction to a Decimal - Vice Versa
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Part=Percent x Whole
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.
-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.


30. If r#t=t(r)-r(t) - then what is 4#3?
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


31. What are Two Special Pythagorean Triples?

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32. Simplifying a Fraction to Lowest Terms
Two relatively prime numbers are integers that have no common factor other than 1.
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
Factor out and cancel all factors the numerator and denominator have in common.


33. Simplifying an Algebraic Equation
Put each number in the original ratio over the sum of the numbers.
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.
Cancel factors common to the numerator and denominator.
Use the units to keep things straight - Snowfall inches/hours


34. Properties of a 30-60-90 Triangle
Use the units to keep things straight - Snowfall inches/hours
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


35. Finding the Area of a Sector

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36. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Multiply the exponents - (x^3)^4=x^3*4=x^12
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.


37. 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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


38. 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?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Do whatever is necessary to both sides to isolate the variable.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Cross multiply.


39. Finding the GCF of Two or More Numbers
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


40. Multiplying and Dividing Roots
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.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


41. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
Subtract the smallest from the largest and add 1
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Cancel factors common to the numerator and denominator.


42. Counting Consecutive Integers
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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Subtract the smallest from the largest and add 1


43. Solving a Proportion
Isolate the radical expression and use the standard rules of algebra.
Cross multiply.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


44. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
VofaC: (pie)r(2)h
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.


45. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
2(pie)r
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


46. Formula Used to Find Percent
(pie)r(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.
Part=Percent x Whole
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


47. Finding the Mode of a Set of Numbers
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Four equal acute angles and four equal obtuse angles.
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
The value that appears the most often.


48. Solving a Radical Equation
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Isolate the radical expression and use the standard rules of algebra.
Just add or subtract the coefficients in front of the radicals.
Use the formula distance=rate*time and its variations to help in this question.


49. Finding the Domain and Range of a 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
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.
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.
Switch the numerator and denominator.


50. Scalene - Isosceles - and Equilateral Triangles
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.
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.
(pie)r(squared)
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.