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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 5 or 10
Put each number in the original ratio over the sum of the numbers.
-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.
A(2)+b(2)=c(2)
Average the smallest and largest number

2. Solving a Radical Equation
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.
Isolate the radical expression and use the standard rules of algebra.
Do whatever is necessary to both sides to isolate the variable.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

3. Calculating the Probability that an Event will Take Place
Average: Sum of the Terms/Number of the Terms
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
2(pie)r
Probability: Number of Favorable Outcomes/Total Possible Outcomes

4. Average Rate and How Do You Find It
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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

5. What types of angles are formed when two lines intersect?
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Adjacent angles are supplementary - Vertical angles are equal
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Probability: Number of Favorable Outcomes/Total Possible Outcomes

6. If the average of a - b - and 48 is 48 - what is the value of a + b?
The value that appears the most often.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
(pie)r(squared)

7. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
-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.
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.
-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.

8. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

9. Number of Groups - +1 Each Time
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Express them with a common denominator.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

10. 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
Put each number in the original ratio over the sum of the numbers.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
(x1+x2)/2 -(y1+y2)/2

11. Characteristics of a Rectangle
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

12. Multiplying and Dividing Roots
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
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

13. Characteristics of a Parallelogram
Just add or subtract the coefficients in front of the radicals.
-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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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

14. Finding the Circumference of a Circle
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
2(pie)r
(pie)r(squared)
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

15. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use simple numbers like 1 and 2 and see what happens.
-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.
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.

16. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
2(pie)r
-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.
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

17. What Does Solving In Terms of Mean?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Get the absolute value equation by itself. Solve.

18. Determining Absolute Value of a Number
Cancel factors common to the numerator and denominator.
Adjacent angles are supplementary - Vertical angles are equal
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

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

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20. Expressing the Union and Intersection of Sets
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
Use simple numbers like 1 and 2 and see what happens.
Slope=change in y/change in x

21. Finding the Area of a Sector

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22. Finding the Volume of a Rectangular Solid
VofaRS=lwh
(pie)r(squared)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Probability: Number of Favorable Outcomes/Total Possible Outcomes

23. If r#t=t(r)-r(t) - then what is 4#3?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

24. 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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

25. Characteristics of a Square
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Isolate the radical expression and use the standard rules of algebra.

26. Solving a System of Equations
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 numerators and multiply the denominators.
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.
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.

27. Definition of an Irrational Number
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
A(2)+b(2)=c(2)
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

28. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Express them with a common denominator.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Cross multiply.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

29. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of 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.
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.
Just add or subtract the coefficients in front of the radicals.

30. Finding the Area of a Circle
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
(pie)r(squared)
Factor out and cancel all factors the numerator and denominator have in common.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

31. Definition of a Rational Number
Put the equation into y=mx+b-- in which case b is the y-intercept.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Adjacent angles are supplementary - Vertical angles are equal
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

32. Properties of a 30-60-90 Triangle
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Two relatively prime numbers are integers that have no common factor other than 1.
-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.

33. Dividing Fractions
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The whole number left over after division.

34. General Procedure for Multiplying Polynomials
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Get the absolute value equation by itself. Solve.
Isolate the radical expression and use the standard rules of algebra.
Use the distributive property then combine the like terms.

35. An Important Property of a Line Tangent to a Circle
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
Do whatever is necessary to both sides to isolate the variable.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.

36. Definition of Remainder
The whole number left over after division.
Cancel factors common to the numerator and denominator.
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.
Multiply the numerators and multiply the denominators.

37. Comparing the values of two or more Fractions
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
Express them with a common denominator.

38. Finding a Term in a Geometric Sequence
Multiply the numerators and multiply the denominators.
(x1+x2)/2 -(y1+y2)/2
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 - 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.

39. Solving a Problem Involving Rates
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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 units to keep things straight - Snowfall inches/hours
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

40. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

41. Counting Consecutive Integers
Part=Percent x Whole
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Cancel factors common to the numerator and denominator.
Subtract the smallest from the largest and add 1

42. Adding and Subtracting Polynomials
Combine like terms.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
(pie)r(squared)
Use the units to keep things straight - Snowfall inches/hours

43. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply the numerators and multiply the denominators.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.

44. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

45. Prime Factorization of a Number
Isolate the radical expression and use the standard rules of algebra.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

46. Finding the Domain and Range of a Function
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.

47. Adding a Positive Number to a Negative Number
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 coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

48. What is the Pythagorean Theorem?
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.
A(2)+b(2)=c(2)
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.

49. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Multiply the exponents - (x^3)^4=x^3*4=x^12

50. Finding the Mode of a Set of Numbers
The value that appears the most often.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Use the formula distance=rate*time and its variations to help in this question.
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.