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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. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Sum: Average x Number of Terms
The value that falls in the middle of the set.
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.

2. 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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

3. Solving a System of Equations
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.
Use the distributive property then combine the like terms.
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.
Get the absolute value equation by itself. Solve.

4. Simplifying Square 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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

5. Knowing if an Integer is a Multiple of 5 or 10
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
-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.

6. Dividing Expressions with Exponents that Have a Common Base
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.
Sum: Average x Number of Terms
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

7. Number of Groups - +1 Each Time
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Isolate the radical expression and use the standard rules of algebra.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

8. Solving a Radical Equation
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Isolate the radical expression and use the standard rules of algebra.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

9. What are Two Special Pythagorean Triples?

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10. Finding the Median of a Set of Numbers
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Do whatever is necessary to both sides to isolate the variable.
The value that falls in the middle of the set.
(pie)r(squared)

11. Convert From a Fraction to a Decimal - Vice Versa
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Average: Sum of the Terms/Number of the Terms
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

12. Finding the GCF of Two or More Numbers
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

13. Counting Consecutive Integers
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Subtract the smallest from the largest and add 1

14. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
A(2)+b(2)=c(2)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

15. An Important Property of a Line Tangent to a Circle
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.
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.
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.
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.

16. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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.
Slope=change in y/change in 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.

17. Definition of an Irrational Number
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.
Adjacent angles are supplementary - Vertical angles are equal
Slope=change in y/change in x
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

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

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19. 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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

20. 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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms

21. If the average of a - b - and 48 is 48 - what is the value of a + b?
-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.
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
Subtract the smallest from the largest and add 1
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

22. Knowing if an Integer is a Multiple of 2 or 4
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
-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.
Use the distributive property then combine the like terms.
Isolate the radical expression and use the standard rules of algebra.

23. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
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.

24. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

25. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
Express them with a common denominator.
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
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.

26. How do you know if an integer is a multiple of 3 or 9?
-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.
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 two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

27. Multiplying and Dividing Roots
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.
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.
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.

28. Expressing the Union and Intersection of Sets
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
A(2)+b(2)=c(2)
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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

29. Multiplying Expressions with Exponents that Have a Common Base
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.
Part=Percent x Whole
-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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

30. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
(x1+x2)/2 -(y1+y2)/2
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Get the absolute value equation by itself. Solve.

31. Properties of Similar Triangles
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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
Average: Sum of the Terms/Number of the Terms

32. Solving a Proportion
Cross multiply.
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
-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.
Use the formula distance=rate*time and its variations to help in this question.

33. Characteristics of a Rectangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
-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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
A(2)+b(2)=c(2)

34. 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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

35. Scalene - Isosceles - and Equilateral Triangles
Use simple numbers like 1 and 2 and see what happens.
Part=Percent x Whole
The whole number left over after division.
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.

36. What is the Triangle Inequality Theorem?
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.
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.
A(2)+b(2)=c(2)
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

37. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
VofaRS=lwh
The whole number left over after division.
Use the units to keep things straight - Snowfall inches/hours
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

38. Dividing Fractions
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
A(2)+b(2)=c(2)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

39. Finding the Area of a Circle
(pie)r(squared)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

40. Multiply and Divide Positive and Negative Numbers
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.
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
Two relatively prime numbers are integers that have no common factor other than 1.

41. 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?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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 value that appears the most often.

42. Finding the Length of an Arc in a Circle

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43. Properties of a 45-45-90 Triangle
Use simple numbers like 1 and 2 and see what happens.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
Four equal acute angles and four equal obtuse angles.

44. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.

45. Converting from part-to-part ratios to part-to-whole ratios
Switch the numerator and denominator.
2(pie)r
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Put each number in the original ratio over the sum of the numbers.

46. Finding a Term in a Geometric Sequence
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
VofaRS=lwh
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.
Factor out and cancel all factors the numerator and denominator have in common.

47. Evaluating an Algebraic Expression
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use the distributive property then combine the like terms.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Plug in the given values for the unknowns and calculate according to PEMDAS.

48. Finding the Area of a Triangle

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49. Solving an Inequality
Just add or subtract the coefficients in front of the radicals.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

50. PEMDAS
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.