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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. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Factor out and cancel all factors the numerator and denominator have in common.
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

2. Finding the Slope of a Line When Given Two Points on the Line
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
Slope=change in y/change in x

3. Characteristics of a Rectangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Slope=change in y/change in x
The whole number left over after division.

4. Finding the Rate of Speed
Plug in the given values for the unknowns and calculate according to PEMDAS.
Use the formula distance=rate*time and its variations to help in this question.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

5. Definition of an Irrational Number
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use simple numbers like 1 and 2 and see what happens.

6. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.

7. 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?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
(x1+x2)/2 -(y1+y2)/2
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

8. Finding the GCF of Two or More Numbers
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Two relatively prime numbers are integers that have no common factor other than 1.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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

9. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

10. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

11. Converting from an Improper Fraction to a Mixed Number
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
Combine like terms.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

12. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

13. What types of angles are formed when two lines intersect?
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Adjacent angles are supplementary - Vertical angles are equal
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
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

14. Dividing Fractions
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.
The whole number left over after division.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.

15. Finding the Midpoint Between Two Points
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
(x1+x2)/2 -(y1+y2)/2
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.

16. Finding the Volume of a Rectangular Solid
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
VofaRS=lwh
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

17. Knowing if an Integer is a Multiple of 5 or 10
Slope=change in y/change in x
-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.
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
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.

18. Definition of an Integer
(x1+x2)/2 -(y1+y2)/2
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
VofaRS=lwh
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

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?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
2(pie)r

20. Characteristics of a Parallelogram
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Switch the numerator and denominator.

21. Solving a System of Equations
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
-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.
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.
Put each number in the original ratio over the sum of the numbers.

22. Counting the Total Number of Possibilities for Several Events to Occur
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
The whole number left over after division.
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.
(x1+x2)/2 -(y1+y2)/2

23. Finding the Domain and Range of a Function
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Isolate the radical expression and use the standard rules of algebra.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

24. Simplifying a Fraction to Lowest Terms
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Factor out and cancel all factors the numerator and denominator have in common.
VofaRS=lwh
Two relatively prime numbers are integers that have no common factor other than 1.

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

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26. Adding and Subtracting Roots
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.
Combine like terms.
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.
Just add or subtract the coefficients in front of the radicals.

27. What types of angles are formed when a transversal cross parallel lines?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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
Four equal acute angles and four equal obtuse angles.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

28. Simplifying an Algebraic Equation
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Slope=change in y/change in x
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Cancel factors common to the numerator and denominator.

29. 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.
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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

30. Properties of a 30-60-90 Triangle
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

31. Convert From a Fraction to a Decimal - Vice Versa
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
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.

32. Dividing Expressions with Exponents that Have a Common Base
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
2(pie)r
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.

33. Multiplying Fractions
Multiply the numerators and multiply the denominators.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.

34. Definition of a Rational Number
The value that falls in the middle of the set.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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 rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

35. Knowing if an Integer is a Multiple of 2 or 4
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Four equal acute angles and four equal obtuse angles.
(x1+x2)/2 -(y1+y2)/2
-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.

36. Multiplying Binomials
Average the smallest and largest number
FOIL: First - Outer - Inner - Last... Combine Like Terms
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Adjacent angles are supplementary - Vertical angles are equal

37. Finding the Area of a Triangle

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38. Finding the Missing Number in a Series When You are Given the Average
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

39. Finding the Sum of the Average of a Series of Numbers
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Sum: Average x Number of 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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

40. What Does Solving In Terms of Mean?
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.
The value that falls in the middle of the set.
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

41. Evaluating an Algebraic Expression
(x1+x2)/2 -(y1+y2)/2
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.

42. Finding the Sum of the Interior Angles of a Polygon
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.
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
Multiply the numerators and multiply the denominators.

43. Raising a Power to a Power
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Switch the numerator and denominator.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

44. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Use the units to keep things straight - Snowfall inches/hours

45. Setting Up a Ratio
Find a common denominator - then add or subtract the numerators.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
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

46. Multiplying Monomials
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Express them with a common denominator.
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 the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

47. Finding a Term in a Geometric Sequence
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.
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.
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.

48. Properties of a 45-45-90 Triangle
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

49. Direct Variation and Inverse Variation
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^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

50. 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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The value that appears the most often.