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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. Converting from an Improper Fraction to a Mixed Number
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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
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 value that appears the most often.

2. Definition of a Rational Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Put each number in the original ratio over the sum of the numbers.

3. Properties of Similar Triangles
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Two relatively prime numbers are integers that have no common factor other than 1.

4. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Part=Percent x Whole
Use simple numbers like 1 and 2 and see what happens.
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.
2(pie)r

5. Setting Up a Ratio
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

6. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Cross multiply.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

7. Finding the Sum of the Interior Angles of a Polygon
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The whole number left over after division.

8. Finding a Term in a Geometric Sequence
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
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

9. Solving a System of Equations
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
(x1+x2)/2 -(y1+y2)/2
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.
Express them with a common denominator.

10. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
VofaC: (pie)r(2)h
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
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.
-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.

11. Formula Used to Find Percent
Part=Percent x Whole
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

12. 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.
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use the distributive property then combine the like terms.

13. Simplifying an Algebraic Equation
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Cancel factors common to the numerator and denominator.

14. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
The value that falls in the middle of the set.
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.
-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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

15. 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
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

16. Properties of a 45-45-90 Triangle
Slope=change in y/change in x
Cancel factors common to the numerator and denominator.
Do whatever is necessary to both sides to isolate the variable.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

17. Raising a Power to a Power
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Probability: Number of Favorable Outcomes/Total Possible Outcomes

18. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Just add or subtract the coefficients in front of the radicals.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

19. Convert From a Fraction to a Decimal - Vice Versa
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.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
(x1+x2)/2 -(y1+y2)/2

20. Finding the Rate of Speed
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 distance=rate*time and its variations to help in this question.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

21. Finding the Volume of a Rectangular Solid
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
-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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
VofaRS=lwh

22. Finding the Mode of a Set of Numbers
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
The value that appears the most often.
Subtract the smallest from the largest and add 1

23. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
The value that appears the most often.
Find a common denominator - then add or subtract the numerators.
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.

24. Finding the Domain and Range of a Function
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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 - substitute for the variable. Then evaluate the expression using the correct order of operations.

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

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26. Properties of the Interior and Exterior Angles of a Triangle
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
(x1+x2)/2 -(y1+y2)/2
-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.

27. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Get the absolute value equation by itself. Solve.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Just add or subtract the coefficients in front of the radicals.

28. Comparing the values of two or more Fractions
2(pie)r
Express them with a common denominator.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

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

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30. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

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

32. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Average: Sum of the Terms/Number of the Terms
-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.

33. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
Sum: Average x Number of Terms
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
-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.

34. Difference Between a Factor and a Multiple
-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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
(x1+x2)/2 -(y1+y2)/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. Finding the Sum of the Average of a Series of Numbers
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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
Sum: Average x Number of Terms

36. Expressing the Union and Intersection of Sets
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Multiply the exponents - (x^3)^4=x^3*4=x^12
-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.
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

37. If x varies directly with y - and the value of x is 12 when y is 11 - what is the value of y when x is 66?
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

38. Finding the Circumference of a Circle
2(pie)r
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.

39. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
FOIL: First - Outer - Inner - Last... 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.

40. Finding the Midpoint Between Two Points
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
(x1+x2)/2 -(y1+y2)/2
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

41. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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
VofaC: (pie)r(2)h
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply the numerators and multiply the denominators.

42. 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.
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

43. Finding the Length of an Arc in a Circle

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44. Adding and Subtracting Polynomials
Combine like terms.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
A(2)+b(2)=c(2)
Factor out and cancel all factors the numerator and denominator have in common.

45. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Slope=change in y/change in x

46. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)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.
Factor out and cancel all factors the numerator and denominator have in common.

47. Characteristics of a Rectangle
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

48. 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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Express them with a common denominator.
Sum: Average x Number of Terms

49. What is the Pythagorean Theorem?
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.
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.
A(2)+b(2)=c(2)
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

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

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