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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. Factoring a Polynomial ('FOIL in Reverse')
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)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Part=Percent x Whole

2. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Isolate the radical expression and use the standard rules of algebra.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

3. Simplifying Square Roots
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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

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

5. Converting from part-to-part ratios to part-to-whole ratios
VofaC: (pie)r(2)h
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
A(2)+b(2)=c(2)
Put each number in the original ratio over the sum of the numbers.

6. Finding a Term in a Geometric Sequence
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
Do whatever is necessary to both sides to isolate the variable.

7. Determining Absolute Value of a Number
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Isolate the radical expression and use the standard rules of algebra.
Get the absolute value equation by itself. Solve.

8. 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.
The whole number left over after division.
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.
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

9. Properties of Similar Triangles
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
FOIL: First - Outer - Inner - Last... Combine Like Terms
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

10. Quickly Finding the Average of a Series of Evenly Spaced Numbers
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Average the smallest and largest number
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
The whole number left over after division.

11. 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.
Switch the numerator and denominator.
Four equal acute angles and four equal obtuse angles.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

12. Definition of an Irrational Number
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

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

14. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
Slope=change in y/change in x
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

15. Finding the Reciprocal of a Fraction
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Switch the numerator and denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

16. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Subtract the smallest from the largest and add 1
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

17. Solving a System of Equations
(x1+x2)/2 -(y1+y2)/2
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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

18. Finding the Area of a Sector

19. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

20. Finding the LCM of Two or More Numbers

21. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
-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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Do whatever is necessary to both sides to isolate the variable.
Put the equation into y=mx+b-- in which case b is the y-intercept.

22. Convert From a Fraction to a Decimal - Vice Versa
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
Subtract the smallest from the largest and add 1

23. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Do whatever is necessary to both sides to isolate the variable.
The whole number left over after division.

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

25. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

26. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
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.
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.
(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

27. Finding the Mode of a Set of Numbers
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The value that appears the most often.

28. If (Square Root: x-1)+5=12 - what is the value of x/2?
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.

29. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use simple numbers like 1 and 2 and see what happens.
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
Find a common denominator - then add or subtract the numerators.

30. What is the Pythagorean Theorem?
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
FOIL: First - Outer - Inner - Last... Combine Like Terms
Put the equation into y=mx+b-- in which case b is the y-intercept.
A(2)+b(2)=c(2)

31. Knowing if an Integer is a Multiple of 5 or 10
Average: Sum of the Terms/Number of the Terms
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
-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.

32. How do you know if an integer is a multiple of 3 or 9?
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.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

33. Expressing the Union and Intersection of Sets
Four equal acute angles and four equal obtuse angles.
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

34. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
Average the smallest and largest number
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
Use the formula distance=rate*time and its variations to help in this question.

35. Increasing and Decreasing a Number by a Certain Percentage
-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.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

36. Counting Consecutive Integers
Find a common denominator - then add or subtract the numerators.
Subtract the smallest from the largest and add 1
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

37. 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.
The value that appears the most often.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

38. Direct Variation and Inverse Variation
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
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
Put each number in the original ratio over the sum of the numbers.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

39. What Does Solving In Terms of Mean?
Cross multiply.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime 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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

40. Solving a Problem Involving Rates
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
-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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

41. Finding the Length of an Arc in a Circle

42. Multiplying Monomials
-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.
Find a common denominator - then add or subtract the numerators.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

43. Multiply and Divide Positive and Negative Numbers
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
Use simple numbers like 1 and 2 and see what happens.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
FOIL: First - Outer - Inner - Last... Combine Like Terms

44. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Use the distributive property then combine the like terms.
Get the absolute value equation by itself. Solve.
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.
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.

45. Finding the Circumference of a Circle
Part=Percent x Whole
2(pie)r
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 value that appears the most often.

46. If 4(x(2)-10x+25) - then what is the value of x?
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.
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.
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 number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

47. 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?
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 value that appears the most often.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

48. What is the Triangle Inequality Theorem?
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.
Average the smallest and largest number
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.
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.

49. Evaluating an Algebraic Expression
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Adjacent angles are supplementary - Vertical angles are equal
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.

50. Solving a Proportion
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.
The whole number left over after division.
Subtract the smallest from the largest and add 1
Cross multiply.