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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.
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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. Finding the Mode of a Set of Numbers
Use the distributive property then combine the like terms.
The value that appears the most often.
Find a common denominator - then add or subtract the numerators.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

2. Scalene - Isosceles - and Equilateral Triangles
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
The whole number left over after division.

3. Multiplying and Dividing Roots
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.
Sum: Average x Number of 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
Average the smallest and largest number

4. Properties of a 45-45-90 Triangle
Factor out and cancel all factors the numerator and denominator have in common.
-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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

5. Properties of a 30-60-90 Triangle
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
The value that falls in the middle of the set.
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

6. Multiply and Divide Positive and Negative Numbers
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.
-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.
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

7. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

8. 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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

9. If the average of a - b - and 48 is 48 - what is the value of a + b?
VofaC: (pie)r(2)h
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
A(2)+b(2)=c(2)

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

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11. What value of x is not in the domain of the function f(x)=x-2/x-3?
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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

12. Solving a Linear Equation
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)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
Do whatever is necessary to both sides to isolate the variable.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

13. 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.
Use the distributive property then combine the like terms.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

14. If 3(3x)=9(x+2) - what is the value of x?
2(pie)r
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

15. Calculating the Probability that an Event will Take Place
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
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.

16. Number of Groups - +1 Each Time
Adjacent angles are supplementary - Vertical angles are equal
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.

17. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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
Switch the numerator and denominator.

18. Formula to Find Average
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Average: Sum of the Terms/Number of the Terms
Adjacent angles are supplementary - Vertical angles are equal
VofaC: (pie)r(2)h

19. 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?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
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.

20. 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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Slope=change in y/change in x

21. Comparing the values of two or more Fractions
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.
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
Express them with a common denominator.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

22. If r#t=t(r)-r(t) - then what is 4#3?
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
Multiply the numerators and multiply the denominators.
The value that falls in the middle of the set.
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)?
Two relatively prime numbers are integers that have no common factor other than 1.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

24. Finding the Domain and Range of a Function
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Average the smallest and largest number

25. Finding the Volume of a Rectangular Solid
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
VofaRS=lwh
Plug in the given values for the unknowns and calculate according to PEMDAS.
Get the absolute value equation by itself. Solve.

26. Counting Consecutive Integers
Average: Sum of the Terms/Number of the Terms
Subtract the smallest from the largest and add 1
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use the units to keep things straight - Snowfall inches/hours

27. Finding the Slope When Given an Equation of a Line
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
-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 the equation into the slope-intercept form: y=mx+b. The slope is m.
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

28. Definition of an Irrational Number
The value that appears the most often.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

29. Difference Between a Factor and a Multiple
The whole number left over after division.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
-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.
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. Properties of Similar Triangles
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
A(2)+b(2)=c(2)

31. Raising a Power to a Power
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime 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.
Multiply the exponents - (x^3)^4=x^3*4=x^12

32. Multiplying Fractions
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.
Multiply the numerators and multiply the denominators.
Get the absolute value equation by itself. Solve.
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

33. 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?
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Put the equation into y=mx+b-- in which case b is the y-intercept.

34. Finding the Sum of the Interior Angles of a Polygon
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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

35. Finding the Distance Between Two Points on a Coordinate Graph
Cross multiply.
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)
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. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.

37. Finding the Length of an Arc in a Circle

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38. Definition of Remainder
The whole number left over after division.
Use the distributive property then combine the like terms.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

39. Numbers that are Relatively Prime
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
VofaC: (pie)r(2)h
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
Two relatively prime numbers are integers that have no common factor other than 1.

40. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use the distributive property then combine the like 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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

41. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
VofaRS=lwh
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.
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.

42. Finding the LCM of Two or More Numbers

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43. If x(2)=7x+18 - what is the positive value of x?
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

44. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
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.
Slope=change in y/change in x
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

45. Solving an Inequality
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
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.
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

46. Solving a Problem Involving Rates
Part=Percent x Whole
Average the smallest and largest number
Combine like terms.
Use the units to keep things straight - Snowfall inches/hours

47. Finding the Rate of Speed
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use the formula distance=rate*time and its variations to help in this question.
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

48. If 4(x(2)-10x+25) - then what is the value of x?
Put the equation into y=mx+b-- in which case b is the y-intercept.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use simple numbers like 1 and 2 and see what happens.
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.

49. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Cross multiply.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Use simple numbers like 1 and 2 and see what happens.

50. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Adjacent angles are supplementary - Vertical angles are equal
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.