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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. Properties of a 30-60-90 Triangle
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Plug in the given values for the unknowns and calculate according to PEMDAS.

2. Determining Absolute Value of a Number
The whole number left over after division.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

3. Counting Consecutive Integers
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.
Subtract the smallest from the largest and add 1
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

4. Converting from part-to-part ratios to part-to-whole ratios
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Put each number in the original ratio over the sum of the numbers.
The value that falls in the middle of the set.

5. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Average the smallest and largest number
Subtract the smallest from the largest and add 1
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

6. Formula to Find Average
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)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
Average: Sum of the Terms/Number of the Terms
Use simple numbers like 1 and 2 and see what happens.

7. Properties of the Interior and Exterior Angles of a Triangle
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
-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.

8. If the average of a - b - and 48 is 48 - what is the value of a + b?
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

9. Finding the Sum of the Average of a Series of Numbers
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Sum: Average x Number of Terms
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

10. Average Rate and How Do You Find It
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
A(2)+b(2)=c(2)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

11. Definition of an Irrational Number
Do whatever is necessary to both sides to isolate the variable.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Use simple numbers like 1 and 2 and see what happens.

12. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Cross multiply.

13. Knowing if an Integer is a Multiple of 5 or 10
Sum: Average x Number of 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.
Factor out and cancel all factors the numerator and denominator have in common.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

14. How do you know if an integer is a multiple of 3 or 9?
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
-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.
The value that falls in the middle of the set.

15. Adding a Positive Number to a Negative Number
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Two relatively prime numbers are integers that have no common factor other than 1.

16. Characteristics of a Rectangle
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

17. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Slope=change in y/change in x
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Adjacent angles are supplementary - Vertical angles are equal

18. Adding and Subtracting Fractions
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Find a common denominator - then add or subtract the numerators.
Adjacent angles are supplementary - Vertical angles are equal

19. Finding the y-intercept When Given an Equation of a Line
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 the equation into y=mx+b-- in which case b is the y-intercept.
2(pie)r
Use the formula distance=rate*time and its variations to help in this question.

20. Finding the Rate of Speed
Cross multiply.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Use the formula distance=rate*time and its variations to help in this question.

21. What are Two Special Pythagorean Triples?

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22. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Combine like terms.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

23. Finding the Area of a Circle
(pie)r(squared)
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Just add or subtract the coefficients in front of the radicals.

24. Adding and Subtracting Polynomials
Put the equation into y=mx+b-- in which case b is the y-intercept.
VofaC: (pie)r(2)h
Combine like terms.
Multiply the numerators and multiply the denominators.

25. Finding the Missing Number in a Series When You are Given the Average
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
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

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

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27. Finding the Volume of a Rectangular Solid
Four equal acute angles and four equal obtuse angles.
Combine like terms.
VofaRS=lwh
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

28. Convert From a Fraction to a Decimal - Vice Versa
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
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.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

29. Setting Up a Ratio
-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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

30. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The value that falls in the middle of the set.
Slope=change in y/change in x

31. If (Square Root: x-1)+5=12 - what is the value of x/2?
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
The whole number left over after division.

32. Finding the Slope of a Line When Given Two Points on the Line
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
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.
Just add or subtract the coefficients in front of the radicals.
Slope=change in y/change in x

33. 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.
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
Cross multiply.
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

34. Solving an Inequality
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Factor out and cancel all factors the numerator and denominator have in common.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

35. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

36. 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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

37. Simplifying Square Roots
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use simple numbers like 1 and 2 and see what happens.

38. 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?
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
VofaC: (pie)r(2)h
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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

39. Expressing the Union and Intersection of Sets
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.
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.
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 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

40. Finding the Circumference of a Circle
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
-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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
2(pie)r

41. Finding a Term in a Geometric Sequence
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

42. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

43. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Average: Sum of the Terms/Number of the Terms
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

44. Raising a Power to a Power
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

45. Prime Factorization of a Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Average: Sum of the Terms/Number of the Terms
Part=Percent x Whole
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

46. Definition of an Integer
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Do whatever is necessary to both sides to isolate the variable.
Just add or subtract the coefficients in front of the radicals.

47. Adding and Subtracting Roots
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Just add or subtract the coefficients in front of the radicals.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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

48. Comparing the values of two or more Fractions
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

49. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Slope=change in y/change in x
Four equal acute angles and four equal obtuse angles.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

50. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
The value that appears the most often.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Cross multiply.
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.