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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 a Term in a Geometric Sequence
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.
Subtract the smallest from the largest and add 1
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use the formula distance=rate*time and its variations to help in this question.

2. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
-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.

3. Finding the Volume of a Cylinder
-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.
VofaC: (pie)r(2)h
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Cancel factors common to the numerator and denominator.

4. If 4(x(2)-10x+25) - then what is the value of x?
Multiply the numerators and multiply the denominators.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

5. 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.
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Four equal acute angles and four equal obtuse angles.

6. Adding and Subtracting Polynomials
(x1+x2)/2 -(y1+y2)/2
Combine 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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

7. If x(2)=7x+18 - what is the positive value of x?
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.
2(pie)r
Part=Percent x Whole
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

8. Finding the Mode of a Set of Numbers
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
The value that appears the most often.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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

9. Finding the Area of a Triangle

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10. Adding and Subtracting Roots
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Just add or subtract the coefficients in front of the radicals.
A(2)+b(2)=c(2)
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

11. Finding the Midpoint Between Two Points
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.
(x1+x2)/2 -(y1+y2)/2
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Get the absolute value equation by itself. Solve.

12. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

13. Prime Factorization of a Number
Just add or subtract the coefficients in front of the radicals.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
FOIL: First - Outer - Inner - Last... Combine Like Terms
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

14. 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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Multiply the numerators and multiply the denominators.
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

15. Factoring a Polynomial ('FOIL in Reverse')
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
(pie)r(squared)
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

16. Multiplying Monomials
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

17. Average Rate and How Do You Find It
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Put each number in the original ratio over the sum of the numbers.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

18. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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
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
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.
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.

19. Formula Used to Find Percent
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
VofaC: (pie)r(2)h
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.
Part=Percent x Whole

20. Convert From a Fraction to a Decimal - Vice Versa
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
(x1+x2)/2 -(y1+y2)/2
VofaC: (pie)r(2)h

21. 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
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Just add or subtract the coefficients in front of the radicals.
The value that falls in the middle of the set.

22. Properties of Similar Triangles
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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
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.

23. Multiplying and Dividing Roots
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

24. What types of angles are formed when a transversal cross parallel lines?
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the numerators and multiply the denominators.
Four equal acute angles and four equal obtuse angles.
The value that appears the most often.

25. Comparing the values of two or more Fractions
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
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Express them with a common denominator.

26. Finding the Missing Number in a Series When You are Given the Average
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.
Subtract the smallest from the largest and add 1
Isolate the radical expression and use the standard rules of algebra.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

27. Properties of a 30-60-90 Triangle
Use the distributive property then combine the 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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

28. Determining Absolute Value of a Number
Adjacent angles are supplementary - Vertical angles are equal
Put each number in the original ratio over the sum of the numbers.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

29. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
The value that appears the most often.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
VofaRS=lwh

30. Finding the y-intercept When Given an Equation of a Line
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Put the equation into y=mx+b-- in which case b is the y-intercept.
(x1+x2)/2 -(y1+y2)/2

31. 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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Factor out and cancel all factors the numerator and denominator have in common.
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. Properties of a 45-45-90 Triangle
(x1+x2)/2 -(y1+y2)/2
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

33. Difference Between a Factor and a Multiple
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.

34. What is the Pythagorean Theorem?
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
A(2)+b(2)=c(2)

35. Increasing and Decreasing a Number by a Certain Percentage
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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
-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.
2(pie)r

36. Converting from an Improper Fraction to a Mixed Number
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Factor out and cancel all factors the numerator and denominator have in common.
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

37. Multiplying Fractions
Factor out and cancel all factors the numerator and denominator have in common.
Multiply the numerators and multiply the denominators.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

38. Dividing Fractions
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Put the equation into y=mx+b-- in which case b is the y-intercept.

39. Finding the Median of a Set of Numbers
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Cross multiply.
The value that falls in the middle of the set.
Adjacent angles are supplementary - Vertical angles are equal

40. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
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.
Use simple numbers like 1 and 2 and see what happens.
Multiply the numerators and multiply the denominators.

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

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42. Counting the Total Number of Possibilities for Several Events to Occur
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.
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.
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. Finding the Volume of a Rectangular Solid
VofaRS=lwh
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Four equal acute angles and four equal obtuse angles.
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

44. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Average: Sum of the Terms/Number of the Terms
(x1+x2)/2 -(y1+y2)/2
-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.

45. Finding the Area of a Sector

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46. Finding the Slope When Given an Equation of a Line
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.
Find a common denominator - then add or subtract the numerators.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

47. Simplifying Square Roots
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
(x1+x2)/2 -(y1+y2)/2
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Cross multiply.

48. How do you know if an integer is a multiple of 3 or 9?
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

49. What Does Solving In Terms of Mean?
Two relatively prime numbers are integers that have no common factor other than 1.
Do whatever is necessary to both sides to isolate the variable.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

50. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
VofaC: (pie)r(2)h
Express them with a common denominator.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value