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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 45-45-90 Triangle
The value that appears the most often.
Four equal acute angles and four equal obtuse angles.
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.

2. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Sum: Average x Number of Terms
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
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.

3. Numbers that are Relatively Prime
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.
Two relatively prime numbers are integers that have no common factor other than 1.
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.
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

4. Multiply and Divide Positive and Negative Numbers
Cross multiply.
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
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 value that falls in the middle of the set.

5. Direct Variation and Inverse Variation
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

6. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Subtract the smallest from the largest and add 1
Get the absolute value equation by itself. Solve.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

7. Converting from part-to-part ratios to part-to-whole ratios
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Put each number in the original ratio over the sum of the numbers.
The value that falls in the middle of the set.

8. Adding and Subtracting Roots
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Use the distributive property then combine the like terms.
Just add or subtract the coefficients in front of the radicals.
Use the units to keep things straight - Snowfall inches/hours

9. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Probability: Number of Favorable Outcomes/Total Possible Outcomes

10. Knowing if an Integer is a Multiple of 2 or 4
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
-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.

11. Properties of Similar Triangles
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

12. How do you know if an integer is a multiple of 3 or 9?
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
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
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.

13. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use simple numbers like 1 and 2 and see what happens.
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.
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

14. 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.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

15. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
Average the smallest and largest number
Sum: Average x Number of Terms
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

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

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17. Factoring the Difference of Two Squares
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.

18. Finding the Missing Number in a Series When You are Given the Average
VofaRS=lwh
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
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.

19. Calculating Negative Exponents and Radical Exponents
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the numerators and multiply the denominators.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

20. Solving a Proportion
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Cross 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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

21. Increasing and Decreasing a Number by a Certain Percentage
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Express them with a common denominator.
-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.

22. Multiplying Fractions
Slope=change in y/change in x
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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 numerators and multiply the denominators.

23. Finding the Domain and Range of a Function
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.

24. Adding and Subtracting Fractions
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Find a common denominator - then add or subtract the numerators.
-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 whole number left over after division.

25. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
Put each number in the original ratio over the sum of the 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
Use the distributive property then combine the like terms.

26. Expressing the Union and Intersection of Sets
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Sum: Average x Number of Terms
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

27. Evaluating an Algebraic Expression
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
Slope=change in y/change in x
Plug in the given values for the unknowns and calculate according to PEMDAS.

28. If 2+l6-xl=10 and x>0 - what is the value of 2x?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Four equal acute angles and four equal obtuse angles.
Get the absolute value equation by itself. Solve.

29. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
-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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

30. Solving a System of Equations
Use the distributive property then combine the like terms.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Get the absolute value equation by itself. Solve.

31. Finding the Volume of a Rectangular Solid
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Cancel factors common to the numerator and denominator.
VofaRS=lwh
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.

32. Finding the Surface Area of a Rectangular Solid
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
Use the formula distance=rate*time and its variations to help in this question.
Combine like terms.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

33. Finding the Median of a Set of Numbers
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Put the equation into y=mx+b-- in which case b is the y-intercept.
The value that falls in the middle of the set.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

34. Characteristics of a Square
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
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Use the distributive property then combine the like terms.

35. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
(x1+x2)/2 -(y1+y2)/2

36. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 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.
Isolate the radical expression and use the standard rules of algebra.

37. 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?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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
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.
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.

38. Definition of Remainder
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
The whole number left over after division.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

39. Knowing if an Integer is a Multiple of 5 or 10
Factor out and cancel all factors the numerator and denominator have in common.
Cross multiply.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
-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.

40. Finding the Reciprocal of a Fraction
Sum: Average x Number of Terms
Combine like terms.
Switch the numerator and denominator.
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.

41. Multiplying Binomials
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
FOIL: First - Outer - Inner - Last... Combine 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.
Part=Percent x Whole

42. Determining Absolute Value of a Number
Find a common denominator - then add or subtract the numerators.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
(x1+x2)/2 -(y1+y2)/2
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

43. Converting From a Mixed Number to an Improper Fraction
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 the whole number part by the denominator - then add the numerator. Keep the same denominator.
Slope=change in y/change in x
Do whatever is necessary to both sides to isolate the variable.

44. Setting Up a Ratio
VofaC: (pie)r(2)h
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

45. 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
Sum: Average x Number of Terms
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Plug in the given values for the unknowns and calculate according to PEMDAS.

46. Finding the y-intercept When Given an Equation of a Line
Part=Percent x Whole
Put the equation into y=mx+b-- in which case b is the y-intercept.
Find a common denominator - then add or subtract the numerators.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

47. Average Rate and How Do You Find It
-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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Multiply the exponents - (x^3)^4=x^3*4=x^12
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

48. Dividing Fractions
VofaRS=lwh
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

49. Finding the Area of a Circle
(pie)r(squared)
Just add or subtract the coefficients in front of the radicals.
2(pie)r
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

50. Definition of a Rational Number
Multiply the exponents - (x^3)^4=x^3*4=x^12
Two relatively prime numbers are integers that have no common factor other than 1.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.