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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
The value that appears the most often.
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

2. What are Two Special Pythagorean Triples?

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3. Factoring the Difference of Two Squares
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.
VofaRS=lwh
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
-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.

4. Converting from an Improper Fraction to a Mixed Number
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.

5. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

6. Simplifying Square Roots
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

7. Numbers that are Relatively Prime
-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.
Two relatively prime numbers are integers that have no common factor other than 1.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

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

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9. Direct Variation and Inverse Variation
Use the distributive property then combine the like terms.
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
Express them with a common denominator.
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

10. What types of angles are formed when two lines intersect?
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
The value that appears the most often.
Adjacent angles are supplementary - Vertical angles are equal

11. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.

12. Finding the Reciprocal of a Fraction
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
VofaRS=lwh
Switch the numerator and denominator.
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.

13. Finding the Slope of a Line When Given Two Points on the Line
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the formula distance=rate*time and its variations to help in this question.
Slope=change in y/change in x

14. Evaluating an Algebraic Expression
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Multiply the numerators and multiply the denominators.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Put the equation into y=mx+b-- in which case b is the y-intercept.

15. Adding and Subtracting Polynomials
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
-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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Combine like terms.

16. Properties of the Interior and Exterior Angles of a Triangle
-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 value that falls in the middle of the set.
Multiply the numerators and multiply the denominators.
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.

17. Multiplying Expressions with Exponents that Have a Common Base
Do whatever is necessary to both sides to isolate the variable.
Four equal acute angles and four equal obtuse angles.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Adjacent angles are supplementary - Vertical angles are equal

18. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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
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.

19. Factoring a Polynomial ('FOIL in Reverse')
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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 distributive property then combine the like terms.

20. 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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
-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.

21. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
(x1+x2)/2 -(y1+y2)/2
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

22. Finding the Slope When Given an Equation of a Line
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

23. Finding the Surface Area of a Rectangular Solid
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

24. Solving a Linear Equation
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 find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Do whatever is necessary to both sides to isolate the variable.
Just add or subtract the coefficients in front of the radicals.

25. Finding the Sum of the Average of a Series of Numbers
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Sum: Average x Number of Terms

26. 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
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.
Combine like terms.

27. Finding the Median of a Set of Numbers
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
The value that falls in the middle of the set.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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. Properties of Similar Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Find a common denominator - then add or subtract the numerators.
Do whatever is necessary to both sides to isolate the variable.

29. Prime Factorization of a 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.
Multiply the numerators and multiply the denominators.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Average: Sum of the Terms/Number of the Terms

30. Knowing if an Integer is a Multiple of 5 or 10
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
-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.

31. Number of Groups - +1 Each Time
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 A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

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

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33. Formula Used to Find Percent
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Part=Percent x Whole

34. Definition of Remainder
The whole number left over after division.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Adjacent angles are supplementary - Vertical angles are equal

35. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Put each number in the original ratio over the sum of the numbers.

36. If the average of a - b - and 48 is 48 - what is the value of a + b?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
(pie)r(squared)
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

37. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine 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.
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.
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.

38. Counting the Total Number of Possibilities for Several Events to Occur
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Sum: Average x Number of Terms
Slope=change in y/change in x
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.

39. An Important Property of a Line Tangent to a Circle
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
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.
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. How do you know if an integer is a multiple of 3 or 9?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

41. Finding the LCM of Two or More Numbers

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42. Finding the Missing Number in a Series When You are Given the Average
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Find a common denominator - then add or subtract the numerators.
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.
Cancel factors common to the numerator and denominator.

43. What is the Triangle Inequality Theorem?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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 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.
Express them with a common denominator.

44. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
Average: Sum of the Terms/Number of the Terms
VofaC: (pie)r(2)h
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

45. Average Rate and How Do You Find It
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Plug in the given values for the unknowns and calculate according to PEMDAS.

46. Definition of an Irrational 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.
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

47. Multiplying and Dividing Roots
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%
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.
Express them with a common denominator.

48. Counting Consecutive Integers
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
Subtract the smallest from the largest and add 1
Cross multiply.
-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.

49. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Two relatively prime numbers are integers that have no common factor other than 1.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

50. Properties of a 30-60-90 Triangle
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Do whatever is necessary to both sides to isolate the variable.
-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.