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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?
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.

2. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Four equal acute angles and four equal obtuse angles.

3. Finding the Rate of Speed
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: Sum of the Terms/Number of the Terms
Use the formula distance=rate*time and its variations to help in this question.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

4. Formula Used to Find Percent
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Part=Percent x Whole
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

5. Solving an Inequality
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

6. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
(x1+x2)/2 -(y1+y2)/2
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

7. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Average the smallest and largest number
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.
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.

8. Properties of a 30-60-90 Triangle
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

9. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
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.
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
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

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

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11. 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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
VofaC: (pie)r(2)h

12. Finding a Term in a Geometric Sequence
Slope=change in y/change in x
Put each number in the original ratio over the sum of the numbers.
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.
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.

13. Factoring the Difference of Two Squares
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 the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
-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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

14. Multiplying and Dividing Roots
Average the smallest and largest number
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.
Switch the numerator and denominator.

15. Finding the Volume of a Rectangular Solid
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
VofaRS=lwh
Just add or subtract the coefficients in front of the radicals.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

16. Definition of an Irrational Number
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Use the units to keep things straight - Snowfall inches/hours

17. Determining Absolute Value of a Number
Use simple numbers like 1 and 2 and see what happens.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

18. Properties of Similar Triangles
Cancel factors common to the numerator and denominator.
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.

19. Solving a Proportion
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.
Use the units to keep things straight - Snowfall inches/hours
Cross multiply.
2(pie)r

20. Solving a System of Equations
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

21. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
A(2)+b(2)=c(2)
Two relatively prime numbers are integers that have no common factor other than 1.

22. Finding the y-intercept When Given an Equation of a Line
Average: Sum of the Terms/Number of the Terms
Put the equation into y=mx+b-- in which case b is the y-intercept.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Four equal acute angles and four equal obtuse angles.

23. Raising a Power to a Power
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.

24. What is the Pythagorean Theorem?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Part=Percent x Whole
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.
A(2)+b(2)=c(2)

25. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
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.

26. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/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.
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.

27. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

28. Finding the Sum of the Interior Angles of a Polygon
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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

29. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
Use the distributive property then combine the like terms.

30. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.

31. Finding the Slope When Given an Equation of a Line
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
Slope=change in y/change in x
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Multiply the numerators and multiply the denominators.

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

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33. Direct Variation and Inverse Variation
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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
VofaC: (pie)r(2)h
Sum: Average x Number of Terms

34. Finding the Surface Area of a Rectangular Solid
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

35. What Does Solving In Terms of Mean?
Plug in the given values for the unknowns and calculate according to PEMDAS.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
(pie)r(squared)

36. General Procedure for Multiplying Polynomials
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Use the distributive property then combine the like terms.
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 value that appears the most often.

37. Properties of the Interior and Exterior Angles of a Triangle
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 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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

38. 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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
(pie)r(squared)

39. Finding the Length of an Arc in a Circle

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40. Finding the Mode of a Set of Numbers
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The value that appears the most often.
(x1+x2)/2 -(y1+y2)/2
Use the distributive property then combine the like terms.

41. Multiply and Divide Positive and Negative Numbers
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
-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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

42. 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.
(pie)r(squared)
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.
The value that appears the most often.

43. Adding a Positive Number to a Negative Number
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Average: Sum of the Terms/Number of the Terms
Two relatively prime numbers are integers that have no common factor other than 1.

44. Finding the Median of a Set of Numbers
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
The value that falls in the middle of the set.
Put the equation into y=mx+b-- in which case b is the y-intercept.

45. 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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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

46. Finding the GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
VofaC: (pie)r(2)h
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
Slope=change in y/change in x

47. What value of x is not in the domain of the function f(x)=x-2/x-3?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime 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

48. Multiplying Fractions
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Average the smallest and largest number
Multiply the numerators and multiply the denominators.

49. Comparing the values of two or more Fractions
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Express them with a common denominator.

50. Finding the LCM of Two or More Numbers

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