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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 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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

2. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
Subtract the smallest from the largest and add 1
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.

3. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

4. Counting the Total Number of Possibilities for Several Events to Occur
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 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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.

5. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Four equal acute angles and four equal obtuse angles.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.

6. 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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Express them with a common denominator.
Plug in the given values for the unknowns and calculate according to PEMDAS.

7. Finding the Circumference of a Circle
2(pie)r
The whole number left over after division.
Cross multiply.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

8. Finding the Mode of a Set of Numbers
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The value that appears the most often.
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

9. PEMDAS
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Sum: Average x Number of Terms
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

10. Multiplying and Dividing Roots
Just add or subtract the coefficients in front of the radicals.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
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

11. How do you know if an integer is a multiple of 3 or 9?
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.
A(2)+b(2)=c(2)
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
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.

12. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Find a common denominator - then add or subtract the numerators.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
(x1+x2)/2 -(y1+y2)/2

13. Finding the Slope of a Line When Given Two Points on the Line
The value that falls in the middle of the set.
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.
Slope=change in y/change in x
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

14. Adding and Subtracting Roots
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Just add or subtract the coefficients in front of the radicals.
VofaC: (pie)r(2)h
Adjacent angles are supplementary - Vertical angles are equal

15. 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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.

16. Definition of Remainder
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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 whole number left over after division.

17. Solving a Linear Equation
The whole number left over after division.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Do whatever is necessary to both sides to isolate the variable.
VofaRS=lwh

18. Characteristics of a Square
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

19. If r#t=t(r)-r(t) - then what is 4#3?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
VofaC: (pie)r(2)h

20. Finding a Term in a Geometric Sequence
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.

21. Finding the Slope When Given an Equation of a Line
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.

22. Adding a Positive Number to a Negative Number
Use simple numbers like 1 and 2 and see what happens.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Four equal acute angles and four equal obtuse angles.

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

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24. Direct Variation and Inverse Variation
Adjacent angles are supplementary - Vertical angles are equal
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
Get the absolute value equation by itself. 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

25. Finding the Area of a Triangle

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26. Calculating Negative Exponents and Radical Exponents
Use the distributive property then combine the like terms.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

27. Difference Between a Factor and a Multiple
-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.
Sum: Average x Number of Terms
Use the formula distance=rate*time and its variations to help in this question.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

28. Knowing if an Integer is a Multiple of 2 or 4
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
-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.
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 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

29. Solving a System of Equations
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.
Put each number in the original ratio over the sum of the numbers.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.

30. Numbers that are Relatively Prime
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Put each number in the original ratio over the sum of the numbers.
Two relatively prime numbers are integers that have no common factor other than 1.
Part=Percent x Whole

31. Multiplying Expressions with Exponents that Have a Common Base
Switch the numerator and denominator.
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.
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

32. Multiplying Monomials
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
-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 the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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

33. 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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

34. What is the Triangle Inequality Theorem?
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
Subtract the smallest from the largest and add 1
Adjacent angles are supplementary - Vertical angles are equal

35. Finding the Volume of a Rectangular Solid
VofaRS=lwh
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.

36. Multiply and Divide Positive and Negative Numbers
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
VofaRS=lwh
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

37. Definition of a Rational Number
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.

38. What Does Solving In Terms of Mean?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Just add or subtract the coefficients in front of the radicals.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

39. 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
Just add or subtract the coefficients in front of the radicals.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

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

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41. 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.
The whole number left over after division.
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
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

42. If 4(x(2)-10x+25) - then what is the value of x?
VofaC: (pie)r(2)h
-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.
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 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.

43. Solving a Proportion
Average the smallest and largest number
Cross multiply.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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

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

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45. 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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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
Use simple numbers like 1 and 2 and see what happens.

46. Comparing the values of two or more Fractions
Average the smallest and largest number
Express them with a common denominator.
Part=Percent x Whole
Put the equation into y=mx+b-- in which case b is the y-intercept.

47. Multiplying Fractions
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Multiply the numerators and multiply the denominators.

48. Formula Used to Find Percent
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Part=Percent x Whole
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

49. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Factor out and cancel all factors the numerator and denominator 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

50. 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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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