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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. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Use the distributive property then combine the like terms.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.

2. Average Rate and How Do You Find It
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.
VofaC: (pie)r(2)h
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Put the equation into y=mx+b-- in which case b is the y-intercept.

3. Difference Between a Factor and a Multiple
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.
-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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

4. Adding and Subtracting Fractions
Plug in the given values for the unknowns and calculate according to PEMDAS.
Find a common denominator - then add or subtract the numerators.
Four equal acute angles and four equal obtuse angles.
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

5. Counting the Total Number of Possibilities for Several Events to Occur
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
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.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

6. Finding a Term in a Geometric Sequence
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
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.

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

8. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Use the formula distance=rate*time and its variations to help in this question.

9. Counting Consecutive Integers
Part=Percent x Whole
Adjacent angles are supplementary - Vertical angles are equal
Subtract the smallest from the largest and add 1
-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.

10. 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
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
Sum: Average x Number of Terms
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

11. Factoring the Difference of Two Squares
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
-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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

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

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13. Converting from part-to-part ratios to part-to-whole ratios
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Put each number in the original ratio over the sum of the numbers.

14. 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?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

15. Solving a Proportion
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Get the absolute value equation by itself. Solve.
Cross multiply.

16. 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?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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
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.
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.

17. How do you know if an integer is a multiple of 3 or 9?
Cancel factors common to the numerator and denominator.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Just add or subtract the coefficients in front of the radicals.
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.

18. Finding the LCM of Two or More Numbers

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19. Prime Factorization of a Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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 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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

20. Setting Up a Ratio
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
The whole number left over after division.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
2(pie)r

21. Finding the Midpoint Between Two Points
-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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
2(pie)r
(x1+x2)/2 -(y1+y2)/2

22. Dividing Fractions
-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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The value that falls in the middle of the set.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

23. Formula to Find Average
Multiply the exponents - (x^3)^4=x^3*4=x^12
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
VofaRS=lwh
Average: Sum of the Terms/Number of the Terms

24. Direct Variation and Inverse Variation
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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 base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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. What types of angles are formed when two lines intersect?
Use the distributive property then combine the like terms.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Adjacent angles are supplementary - Vertical angles are equal

26. What Does Solving In Terms of Mean?
-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.
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 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.
Isolate the radical expression and use the standard rules of algebra.

27. Converting from an Improper Fraction to a Mixed Number
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 units to keep things straight - Snowfall inches/hours
Use the distributive property then combine the like terms.
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.

28. Properties of the Interior and Exterior Angles of a Triangle
Slope=change in y/change in x
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
-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.

29. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Find a common denominator - then add or subtract the numerators.
Use simple numbers like 1 and 2 and see what happens.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

30. Solving a System of Equations
Use the distributive property then combine the like terms.
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.
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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

31. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
Multiply the numerators and multiply the denominators.
Four equal acute angles and four equal obtuse angles.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

32. Solving a Problem Involving Rates
-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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Use the units to keep things straight - Snowfall inches/hours
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

33. Finding the Rate of Speed
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.
The value that falls in the middle of the set.
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.

34. Adding and Subtracting Monomials
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.
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 one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

35. Multiplying Expressions with Exponents that Have a Common Base
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.
Get the absolute value equation by itself. Solve.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

36. Finding the Surface Area of a Rectangular Solid
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use the distributive property then combine the like terms.
Multiply the exponents - (x^3)^4=x^3*4=x^12

37. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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
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.
Put each number in the original ratio over the sum of the numbers.

38. Evaluating an Algebraic Expression
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Isolate the radical expression and use the standard rules of algebra.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

39. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
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
Get the absolute value equation by itself. Solve.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

40. If 3(3x)=9(x+2) - what is the value of x?
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 number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.

41. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Get the absolute value equation by itself. Solve.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

42. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
Multiply the numerators and multiply the denominators.
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes

43. Multiplying Monomials
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Put the equation into y=mx+b-- in which case b is the y-intercept.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

44. Formula Used to Find Percent
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Part=Percent x Whole
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

45. Finding the Slope When Given an Equation of a Line
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Four equal acute angles and four equal obtuse angles.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

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

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47. Number of Groups - +1 Each Time
Part=Percent x Whole
Just add or subtract the coefficients in front of the radicals.
Subtract the smallest from the largest and add 1
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

48. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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
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.
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.

49. Adding and Subtracting Polynomials
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
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.
Combine like terms.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

50. Knowing if an Integer is a Multiple of 2 or 4
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.
-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.