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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. Knowing if an Integer is a Multiple of 2 or 4
-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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

2. Calculating the Probability that an Event will Take Place
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Four equal acute angles and four equal obtuse angles.

3. Finding the Area of a Triangle

4. Solving a Radical Equation
VofaRS=lwh
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Isolate the radical expression and use the standard rules of algebra.
The value that falls in the middle of the set.

5. Determining Absolute Value of a Number
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

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

7. Difference Between a Factor and a Multiple
Use the units to keep things straight - Snowfall inches/hours
-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.
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 exponents - (x^3)^4=x^3*4=x^12

8. 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.
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

9. Setting Up a Ratio
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

10. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Plug in the given values for the unknowns and calculate according to PEMDAS.
Multiply the numerators and multiply the denominators.
VofaC: (pie)r(2)h
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

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

12. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
-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.
Put each number in the original ratio over the sum of the numbers.

13. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
-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.
Put each number in the original ratio over the sum of the numbers.
Use simple numbers like 1 and 2 and see what happens.

14. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Find a common denominator - then add or subtract the numerators.
FOIL: First - Outer - Inner - Last... Combine Like Terms

15. Multiplying Expressions with Exponents that Have a Common Base
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

16. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
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
Part=Percent x Whole
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.

17. Raising a Power to a Power
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
VofaRS=lwh
Multiply the exponents - (x^3)^4=x^3*4=x^12

18. Converting from part-to-part ratios to part-to-whole ratios
Average: Sum of the Terms/Number of the Terms
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The value that falls in the middle of the set.
Put each number in the original ratio over the sum of the numbers.

19. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
Get the absolute value equation by itself. Solve.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

20. An Important Property of a Line Tangent to a Circle
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
-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.
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.

21. 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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
The value that falls in the middle of the set.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

22. Converting from an Improper Fraction to a Mixed Number
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.
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.
The value that appears the most often.

23. Finding the Distance Between Two Points on a Coordinate Graph
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Two relatively prime numbers are integers that have no common factor other than 1.

24. Solving a Problem Involving Rates
A(2)+b(2)=c(2)
Use the units to keep things straight - Snowfall inches/hours
Sum: Average x Number of Terms
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

25. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
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
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 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.

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

27. Multiplying Binomials
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.
Combine like terms.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
FOIL: First - Outer - Inner - Last... Combine Like Terms

28. Simplifying an Algebraic Equation
Cancel factors common to 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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Isolate the radical expression and use the standard rules of algebra.

29. What types of angles are formed when a transversal cross parallel lines?
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Four equal acute angles and four equal obtuse angles.
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

30. General Procedure for Multiplying Polynomials
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use the distributive property then combine the like terms.
(pie)r(squared)
Sum: Average x Number of Terms

31. Counting the Total Number of Possibilities for Several Events to Occur
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

32. Finding the Length of an Arc in a Circle

33. If (Square Root: x-1)+5=12 - what is the value of x/2?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
VofaC: (pie)r(2)h
-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.

34. Properties of the Interior and Exterior Angles of a Triangle
Combine like terms.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
-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.

35. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Switch the numerator and denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
(x1+x2)/2 -(y1+y2)/2

36. Average Rate and How Do You Find It
FOIL: First - Outer - Inner - Last... Combine Like Terms
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
(pie)r(squared)
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

37. What types of angles are formed when two lines intersect?
VofaRS=lwh
Adjacent angles are supplementary - Vertical angles are equal
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

38. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Combine like terms.
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
Get the absolute value equation by itself. Solve.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

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

40. Adding and Subtracting Monomials
VofaC: (pie)r(2)h
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Do whatever is necessary to both sides to isolate the variable.

41. Multiply and Divide Positive and Negative Numbers
A(2)+b(2)=c(2)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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
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

42. Knowing if an Integer is a Multiple of 5 or 10
A(2)+b(2)=c(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.
-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.
2(pie)r

43. Finding the Slope When Given an Equation of a Line
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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
(x1+x2)/2 -(y1+y2)/2

44. If the average of a - b - and 48 is 48 - what is the value of a + b?
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Adjacent angles are supplementary - Vertical angles are equal

45. What are Two Special Pythagorean Triples?

46. Definition of an Integer
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Express them with a common denominator.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

47. Dividing Fractions
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
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.

48. Finding the Reciprocal of a Fraction
Subtract the smallest from the largest and add 1
Switch the numerator and denominator.
The whole number left over after division.
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

49. Finding the LCM of Two or More Numbers

50. Formula Used to Find Percent
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Part=Percent x Whole
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.