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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. 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?
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Sum: Average x Number of Terms
Adjacent angles are supplementary - Vertical angles are equal
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. Definition of a Rational Number
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.
Factor out and cancel all factors the numerator and denominator have in common.
Adjacent angles are supplementary - Vertical angles are equal
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

3. Increasing and Decreasing a Number by a Certain Percentage
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
VofaRS=lwh
-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.
-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.

4. Formula Used to Find Percent
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Slope=change in y/change in x
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.
Part=Percent x Whole

5. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Plug in the given values for the unknowns and calculate according to PEMDAS.
Average the smallest and largest number
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
(pie)r(squared)

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

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7. Characteristics of a Square
Factor out and cancel all factors the numerator and denominator 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.
The value that appears the most often.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

8. Properties of Similar Triangles
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.
Just add or subtract the coefficients in front of the radicals.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

9. Finding the GCF of Two or More Numbers
A(2)+b(2)=c(2)
Do whatever is necessary to both sides to isolate the variable.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

10. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Part=Percent x Whole
Put each number in the original ratio over the sum of the numbers.

11. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
Subtract the smallest from the largest and add 1
Factor out and cancel all factors the numerator and denominator have in common.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

12. If (Square Root: x-1)+5=12 - what is the value of x/2?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Switch the numerator and denominator.
Average: Sum of the Terms/Number of the Terms

13. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

14. PEMDAS
The value that appears the most often.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Put each number in the original ratio over the sum of the numbers.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

15. Properties of a 45-45-90 Triangle
Use the distributive property then combine the like terms.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

16. Scalene - Isosceles - and Equilateral Triangles
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

17. Properties of a 30-60-90 Triangle
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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

18. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Part=Percent x Whole
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.

19. 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?
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.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Do whatever is necessary to both sides to isolate the variable.

20. Finding the Mode of a Set of 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.
The value that appears the most often.
(pie)r(squared)
Four equal acute angles and four equal obtuse angles.

21. If 3(3x)=9(x+2) - what is the value of x?
Slope=change in y/change in x
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

22. Difference Between a Factor and a Multiple
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
-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.
Subtract the smallest from the largest and add 1
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

23. Counting Consecutive Integers
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
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.

24. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
(x1+x2)/2 -(y1+y2)/2
The whole number left over after division.

25. Simplifying a Fraction to Lowest Terms
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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
Factor out and cancel all factors the numerator and denominator have in common.
Use the units to keep things straight - Snowfall inches/hours

26. What value of x is not in the domain of the function f(x)=x-2/x-3?
Factor out and cancel all factors the numerator and denominator have in common.
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
Cancel factors common to the numerator and denominator.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

27. Finding the Sum of the Interior Angles of a Polygon
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.
Find a common denominator - then add or subtract the numerators.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

28. 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.
(pie)r(squared)
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

29. Finding the Surface Area of a Rectangular Solid
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
(pie)r(squared)
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

30. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply the numerators and multiply the denominators.
Use the distributive property then combine the like terms.

31. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Use the units to keep things straight - Snowfall inches/hours
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

32. Finding the Circumference of a Circle
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.
(x1+x2)/2 -(y1+y2)/2
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
2(pie)r

33. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Combine like 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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

34. Finding the Volume of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
VofaRS=lwh
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

35. Converting from an Improper Fraction to a Mixed Number
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
(pie)r(squared)

36. If 4(x(2)-10x+25) - then what is the value of x?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Sum: Average x Number of Terms
Multiply the exponents - (x^3)^4=x^3*4=x^12

37. Solving a Proportion
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Cross multiply.
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.
Sum: Average x Number of Terms

38. 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.
Cancel factors common to the numerator and denominator.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

39. Adding a Positive Number to a Negative Number
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

40. Finding the LCM of Two or More Numbers

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41. Knowing if an Integer is a Multiple of 5 or 10
-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.
(x1+x2)/2 -(y1+y2)/2
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Switch the numerator and denominator.

42. Calculating the Probability that an Event will Take Place
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
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.

43. Dividing Expressions with Exponents that Have a Common Base
Plug in the given values for the unknowns and calculate according to PEMDAS.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Get the absolute value equation by itself. Solve.

44. Counting the Total Number of Possibilities for Several Events to Occur
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
The whole number left over after division.

45. Finding the Area of a Sector

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46. Adding and Subtracting Roots
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
(pie)r(squared)
Just add or subtract the coefficients in front of the radicals.
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

47. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use the distributive property then combine the like terms.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

48. Number of Groups - +1 Each Time
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Isolate the radical expression and use the standard rules of algebra.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

49. What is the Triangle Inequality Theorem?
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

50. Finding the Rate of Speed
Plug in the given values for the unknowns and calculate according to PEMDAS.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Use the formula distance=rate*time and its variations to help in this question.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.