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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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1. Expressing the Union and Intersection of Sets
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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
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

2. Definition of an Integer
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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

3. Finding the Slope When Given an Equation of a Line
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Two relatively prime numbers are integers that have no common factor other than 1.

4. Sale Price of a Jacket Marked Down 30% Each Week for 3 Weeks - What % of the Original Price is the Cost of the Jacket After the 3 Week Sale Period
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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

5. Characteristics of a Rectangle
Just add or subtract the coefficients in front of the radicals.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

6. Finding the GCF of Two or More Numbers
Four equal acute angles and four equal obtuse angles.
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.
Factor out and cancel all factors the numerator and denominator have in common.

7. Multiply and Divide Positive and Negative Numbers
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.
Average: Sum of the Terms/Number of the Terms
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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

8. Finding the Length of an Arc in a Circle

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9. Comparing the values of two or more Fractions
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to 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
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. 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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Use the units to keep things straight - Snowfall inches/hours
Multiply the numerators and multiply the denominators.

11. Formula to Find Average
Four equal acute angles and four equal obtuse angles.
Cancel factors common to the numerator and denominator.
Average: Sum of the Terms/Number of the Terms
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

12. What are Two Special Pythagorean Triples?

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13. If 4(x(2)-10x+25) - then what is the value of x?
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.
(x1+x2)/2 -(y1+y2)/2
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.
Slope=change in y/change in x

14. 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
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.

15. Multiplying Binomials
Two relatively prime numbers are integers that have no common factor other than 1.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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
Use the formula distance=rate*time and its variations to help in this question.

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

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17. Knowing if an Integer is a Multiple of 2 or 4
-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.
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.
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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

18. PEMDAS
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
-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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

19. Simplifying an Algebraic Equation
(x1+x2)/2 -(y1+y2)/2
Cancel factors common to the numerator and denominator.
Cross multiply.
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. Finding the Rate of Speed
Use the distributive property then combine the like 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.
Use the formula distance=rate*time and its variations to help in this question.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

21. Adding and Subtracting Polynomials
2(pie)r
Combine like terms.
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.
(pie)r(squared)

22. Quickly Finding the Average of a Series of Evenly Spaced Numbers
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Average the smallest and largest number
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

23. If (Square Root: x-1)+5=12 - what is the value of x/2?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

24. If r#t=t(r)-r(t) - then what is 4#3?
Sum: Average x Number of Terms
Slope=change in y/change in x
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

25. Knowing if an Integer is a Multiple of 5 or 10
-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.
-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.
Slope=change in y/change in x
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

26. If x(2)=7x+18 - what is the positive value of 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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Part=Percent x Whole

27. Finding the Area of a Triangle

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28. 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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
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.

29. 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?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Just add or subtract the coefficients in front of the radicals.

30. Counting the Total Number of Possibilities for Several Events to Occur
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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
A(2)+b(2)=c(2)

31. 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.
Switch the numerator and denominator.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

32. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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 two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

33. Numbers that are Relatively Prime
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
Cancel factors common to the numerator and denominator.
Two relatively prime numbers are integers that have no common factor other than 1.

34. Finding a Term in a Geometric Sequence
Cancel factors common to the numerator and denominator.
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.
-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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

35. Solving a System of Equations
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.
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
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

36. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Do whatever is necessary to both sides to isolate the variable.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

37. Increasing and Decreasing a Number by a Certain Percentage
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.
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
-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.

38. Setting Up a Ratio
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

39. Finding the Midpoint Between Two Points
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Combine like terms.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
(x1+x2)/2 -(y1+y2)/2

40. Multiplying and Dividing Roots
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
Adjacent angles are supplementary - Vertical angles are equal

41. 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.
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
Put each number in the original ratio over the sum of the numbers.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

42. Multiplying Expressions with Exponents that Have a Common Base
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
-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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Plug in the given values for the unknowns and calculate according to PEMDAS.

43. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Find a common denominator - then add or subtract the numerators.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

44. Evaluating an Algebraic Expression
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.
Factor out and cancel all factors the numerator and denominator have in common.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

45. 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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Average the smallest and largest number

46. Characteristics of a Parallelogram
Two relatively prime numbers are integers that have no common factor other than 1.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Part=Percent x Whole
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

47. Characteristics of a Square
Just add or subtract the coefficients in front of the radicals.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Slope=change in y/change in x
The value that falls in the middle of the set.

48. Solving a Proportion
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Cross multiply.
Put each number in the original ratio over the sum of the numbers.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

49. Finding the Mode of a Set of Numbers
-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.
Slope=change in y/change in x
The value that appears the most often.
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.

50. What is the Pythagorean Theorem?
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 equation into the slope-intercept form: y=mx+b. The slope is m.
A(2)+b(2)=c(2)
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.