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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 GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
-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.
-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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

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

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3. Finding the Reciprocal of a Fraction
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Switch the numerator and denominator.

4. Finding the Area of a Circle
Express them with a common denominator.
(pie)r(squared)
Factor out and cancel all factors the numerator and denominator have in common.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

5. If (Square Root: x-1)+5=12 - what is the value of x/2?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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

6. Finding the y-intercept When Given an Equation of a Line
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Put the equation into y=mx+b-- in which case b is the y-intercept.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
VofaC: (pie)r(2)h

7. What value of x is not in the domain of the function f(x)=x-2/x-3?
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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

8. Evaluating an Algebraic Expression
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Plug in the given values for the unknowns and calculate according to PEMDAS.

9. Finding the Surface Area of a Rectangular Solid
Four equal acute angles and four equal obtuse angles.
The value that appears the most often.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

10. Convert From a Fraction to a Decimal - Vice Versa
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.
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
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.

11. Multiply and Divide Positive and Negative Numbers
2(pie)r
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

12. Multiplying Expressions with Exponents that Have a Common Base
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

13. Multiplying and Dividing Roots
FOIL: First - Outer - Inner - Last... Combine Like Terms
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.

14. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Get the absolute value equation by itself. Solve.
Cancel factors common to the numerator and denominator.
Multiply the numerators and multiply the denominators.

15. 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?
Put each number in the original ratio over the sum of the numbers.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
Multiply the numerators and multiply the denominators.

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

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17. Direct Variation and Inverse Variation
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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
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

18. Scalene - Isosceles - and Equilateral Triangles
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
Subtract the smallest from the largest and add 1
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.

19. Characteristics of a Parallelogram
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 pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

20. What types of angles are formed when two lines intersect?
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Adjacent angles are supplementary - Vertical angles are equal

21. 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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Part=Percent x Whole

22. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Average the smallest and largest number
The whole number left over after division.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

23. 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
The value that falls in the middle of the set.
(x1+x2)/2 -(y1+y2)/2
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

24. Definition of an Irrational Number
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.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

25. If r#t=t(r)-r(t) - then what is 4#3?
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use simple numbers like 1 and 2 and see what happens.

26. Finding the Slope When Given an Equation of a Line
Use the formula distance=rate*time and its variations to help in this question.
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

27. Formula Used to Find Percent
Get the absolute value equation by itself. Solve.
Part=Percent x Whole
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
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

28. Converting from an Improper Fraction to a Mixed Number
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.
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.
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
(x1+x2)/2 -(y1+y2)/2

29. Knowing if an Integer is a Multiple of 2 or 4
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
-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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

30. Finding the Area of a Sector

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31. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Use simple numbers like 1 and 2 and see what happens.
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.
-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.

32. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

33. Finding the Circumference of a Circle
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.
2(pie)r
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
FOIL: First - Outer - Inner - Last... Combine Like Terms

34. Definition of an Integer
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

35. Expressing the Union and Intersection of Sets
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
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
-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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

36. Finding the Missing Number in a Series When You are Given the Average
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

37. Multiplying Monomials
2(pie)r
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.
-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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

38. Counting Consecutive Integers
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.
Subtract the smallest from the largest and add 1
Use simple numbers like 1 and 2 and see what happens.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

39. Simplifying an Algebraic Equation
Use the units to keep things straight - Snowfall inches/hours
Cancel factors common to the numerator and denominator.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
(x1+x2)/2 -(y1+y2)/2

40. If 4(x(2)-10x+25) - then what is the value of x?
A(2)+b(2)=c(2)
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
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.

41. Finding the Mode of a Set of Numbers
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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
The value that appears the most often.

42. Simplifying a Fraction to Lowest Terms
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
Factor out and cancel all factors the numerator and denominator have in common.
Adjacent angles are supplementary - Vertical angles are equal

43. 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?
Find a common denominator - then add or subtract the numerators.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply the exponents - (x^3)^4=x^3*4=x^12

44. Solving a Radical Equation
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
A(2)+b(2)=c(2)
Isolate the radical expression and use the standard rules of algebra.
The whole number left over after division.

45. Factoring the Difference of Two Squares
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.
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.
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

46. Finding a Term in a Geometric Sequence
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
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.

47. Converting From a Mixed Number to an Improper Fraction
Find a common denominator - then add or subtract the numerators.
A(2)+b(2)=c(2)
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

48. Solving a Problem Involving Rates
(pie)r(squared)
The value that falls in the middle of the set.
Use the units to keep things straight - Snowfall inches/hours
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

49. Multiplying Fractions
Multiply the numerators and multiply the denominators.
-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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Isolate the radical expression and use the standard rules of algebra.

50. What Does Solving In Terms of Mean?
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 the distance formula: d=(square root over) (x2-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.
Cancel factors common to the numerator and denominator.