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SAT Math

Subjects : 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 is the Pythagorean Theorem?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
A(2)+b(2)=c(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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

2. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

3. Quickly Finding the Average of a Series of Evenly Spaced Numbers
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.
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.
Sum: Average x Number of Terms
Average the smallest and largest number

4. Number of Groups - +1 Each Time
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
(pie)r(squared)
Switch the numerator and denominator.
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.

5. What types of angles are formed when a transversal cross parallel lines?
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
-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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Four equal acute angles and four equal obtuse angles.

6. Solving a Problem Involving Rates
VofaRS=lwh
Use the units to keep things straight - Snowfall inches/hours
Put each number in the original ratio over the sum of the numbers.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

7. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

8. Definition of an Irrational Number
Slope=change in y/change in x
Use simple numbers like 1 and 2 and see what happens.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

9. Knowing if an Integer is a Multiple of 2 or 4
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.
-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.
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.
VofaRS=lwh

10. What value of x is not in the domain of the function f(x)=x-2/x-3?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

11. 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.
Just add or subtract the coefficients in front of the radicals.
-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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

12. Knowing if an Integer is a Multiple of 5 or 10
-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.
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

13. What types of angles are formed when two lines intersect?
Use the distributive property then combine the like terms.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
VofaRS=lwh
Adjacent angles are supplementary - Vertical angles are equal

14. Counting the Total Number of Possibilities for Several Events to Occur
Put the equation into y=mx+b-- in which case b is the y-intercept.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
-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 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.

15. Solving an Inequality
A(2)+b(2)=c(2)
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The value that appears the most often.
Just add or subtract the coefficients in front of the radicals.

16. Simplifying an Algebraic Equation
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.
Cancel factors common to the numerator and denominator.
Subtract the smallest from the largest and add 1
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

17. Raising a Power to a Power
Average: Sum of the Terms/Number of the Terms
VofaC: (pie)r(2)h
Multiply the exponents - (x^3)^4=x^3*4=x^12
The value that appears the most often.

18. Simplifying Square Roots
Cross multiply.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.

19. If the average of a - b - and 48 is 48 - what is the value of a + b?
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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

20. Properties of a 45-45-90 Triangle
Average: Sum of the Terms/Number of the Terms
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
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.

21. Adding and Subtracting Monomials
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use the formula distance=rate*time and its variations to help in this question.
Switch the numerator and denominator.

22. Multiplying Fractions
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Multiply the numerators and multiply the denominators.
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.

23. Finding the Midpoint Between Two Points
Average the smallest and largest number
(x1+x2)/2 -(y1+y2)/2
Switch the numerator and denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

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

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25. Finding the Volume of a Rectangular Solid
VofaRS=lwh
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Use the formula distance=rate*time and its variations to help in this question.
Isolate the radical expression and use the standard rules of algebra.

26. Evaluating an Algebraic Expression
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.

27. Dividing Expressions with Exponents that Have a Common Base
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

28. What are Two Special Pythagorean Triples?

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29. Calculating Negative Exponents and Radical Exponents
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Find a common denominator - then add or subtract the numerators.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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

30. 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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

31. How do you know if an integer is a multiple of 3 or 9?
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Isolate the radical expression and use the standard rules of algebra.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

32. 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?
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

33. Adding and Subtracting Polynomials
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
Four equal acute angles and four equal obtuse angles.
Two relatively prime numbers are integers that have no common factor other than 1.

34. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Subtract the smallest from the largest and add 1
Use the units to keep things straight - Snowfall inches/hours
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

35. Definition of Remainder
The whole number left over after division.
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.
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

36. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
The whole number left over after division.

37. Adding and Subtracting Roots
VofaRS=lwh
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Just add or subtract the coefficients in front of the radicals.

38. Finding the Area of a Circle
(pie)r(squared)
(x1+x2)/2 -(y1+y2)/2
FOIL: First - Outer - Inner - Last... Combine Like Terms
Sum: Average x Number of Terms

39. Counting Consecutive Integers
Two relatively prime numbers are integers that have no common factor other than 1.
Subtract the smallest from the largest and add 1
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Just add or subtract the coefficients in front of the radicals.

40. Finding the Volume of a Cylinder
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.
VofaC: (pie)r(2)h
Plug in the given values for the unknowns and calculate according to PEMDAS.
(pie)r(squared)

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

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42. Formula Used to Find Percent
The value that appears the most often.
Cancel factors common to the numerator and denominator.
Part=Percent x Whole
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

43. General Procedure for Multiplying Polynomials
Use the distributive property then combine the 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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Two relatively prime numbers are integers that have no common factor other than 1.

44. Finding the LCM of Two or More Numbers

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45. Calculating the Probability that an Event will Take Place
Combine like terms.
Just add or subtract the coefficients in front of the radicals.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

46. Adding and Subtracting Fractions
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Put the equation into y=mx+b-- in which case b is the y-intercept.
Find a common denominator - then add or subtract the numerators.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

47. 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.
Get the absolute value equation by itself. 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)

48. 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.
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

49. Converting From a Mixed Number to an Improper Fraction
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
A(2)+b(2)=c(2)
Use simple numbers like 1 and 2 and see what happens.

50. Multiply and Divide Positive and Negative Numbers
A(2)+b(2)=c(2)
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
Use the distributive property then combine the like terms.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.