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SAT Math

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
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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. Properties of a 30-60-90 Triangle
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Four equal acute angles and four equal obtuse angles.

2. 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
Subtract the smallest from the largest and add 1
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

3. 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?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

4. What is the Triangle Inequality Theorem?
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
2(pie)r
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

5. Solving a System of Equations
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.
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.
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.

6. Properties of Similar Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Multiply the numerators and multiply the denominators.
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.

7. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
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.
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
Sum: Average x Number of Terms

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

9. Knowing if an Integer is a Multiple of 5 or 10
VofaRS=lwh
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 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

10. Finding the Median of a Set of Numbers
(pie)r(squared)
The value that falls in the middle of the set.
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
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.

11. Finding the Volume of a Rectangular Solid
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
2(pie)r
VofaRS=lwh
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.

12. Finding the Surface Area of a Rectangular Solid
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

13. Finding the Length of an Arc in a Circle

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14. Finding the Reciprocal of a Fraction
Switch the numerator and 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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

15. Solving an Inequality
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
2(pie)r
VofaRS=lwh

16. Average Rate and How Do You Find It
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Put each number in the original ratio over the sum of the numbers.
Multiply the numerators and multiply the denominators.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

17. Properties of a 45-45-90 Triangle
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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

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

19. Prime Factorization of a Number
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

20. Counting the Total Number of Possibilities for Several Events to Occur
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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 distance=rate*time and its variations to help in this question.
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.

21. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Switch the numerator and denominator.
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
Two relatively prime numbers are integers that have no common factor other than 1.

22. Adding and Subtracting Roots
VofaC: (pie)r(2)h
Subtract the smallest from the largest and add 1
Just add or subtract the coefficients in front of the radicals.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

23. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 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.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Do whatever is necessary to both sides to isolate the variable.

24. Formula Used to Find Percent
Average: Sum of the Terms/Number of the Terms
Part=Percent x Whole
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 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 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?
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
2(pie)r
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

26. 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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Four equal acute angles and four equal obtuse angles.
Slope=change in y/change in x

27. Adding and Subtracting Polynomials
Adjacent angles are supplementary - Vertical angles are equal
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.
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.
Combine like terms.

28. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Multiply the numerators and multiply the denominators.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

29. Finding the Area of a Triangle

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30. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.

31. Finding the Missing Number in a Series When You are Given the Average
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
Average the smallest and largest number

32. Simplifying an Algebraic Equation
Cross multiply.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Adjacent angles are supplementary - Vertical angles are equal
Cancel factors common to the numerator and denominator.

33. Factoring the Difference of Two Squares
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

34. Multiplying Monomials
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 value that falls in the middle of the set.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.

35. If r#t=t(r)-r(t) - then what is 4#3?
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.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.

36. If 2+l6-xl=10 and x>0 - what is the value of 2x?
VofaC: (pie)r(2)h
The whole number left over after division.
Do whatever is necessary to both sides to isolate the variable.
Get the absolute value equation by itself. Solve.

37. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
Use the distributive property then combine the like terms.
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
Put each number in the original ratio over the sum of the numbers.

38. Definition of a Rational Number
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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 appears the most often.
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.

39. How do you know if an integer is a multiple of 3 or 9?
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Combine like terms.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

40. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
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.

41. Properties of the Interior and Exterior Angles of a Triangle
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.
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.
Sum: Average x Number of Terms
Combine like terms.

42. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
-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.

43. Simplifying Square Roots
Multiply the numerators and multiply the denominators.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
-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. Multiply and Divide Positive and Negative Numbers
The value that appears the most often.
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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

45. Finding the Circumference of a Circle
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
2(pie)r
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
(x1+x2)/2 -(y1+y2)/2

46. Determining Absolute Value of a Number
-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.
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.

47. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
-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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
A(2)+b(2)=c(2)

48. Converting From a Mixed Number to an Improper Fraction
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

49. Direct Variation and Inverse Variation
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Find a common denominator - then add or subtract the numerators.
Average: Sum of the Terms/Number of the Terms

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
Part=Percent x Whole
VofaC: (pie)r(2)h
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24