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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. What Does Solving In Terms of Mean?
Isolate the radical expression and use the standard rules of algebra.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

2. If 2+l6-xl=10 and x>0 - what is the value of 2x?
-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.
Get the absolute value equation by itself. Solve.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

3. Finding the Area of a Triangle

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4. Finding the Median of a Set of 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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The value that falls in the middle of the set.
Slope=change in y/change in x

5. Finding the y-intercept When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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 variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

6. 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?
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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 units to keep things straight - Snowfall inches/hours
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

7. Solving a Proportion
Cross multiply.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
The value that falls in the middle of the set.

8. An Important Property of a Line Tangent to a Circle
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Change the division sign to a multiplication sign - invert the second fraction - 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.
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.

9. Converting From a Mixed Number to an Improper Fraction
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
-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.
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.

10. Solving an Inequality
-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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.

11. Properties of the Interior and Exterior Angles of a Triangle
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 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.
2(pie)r
VofaC: (pie)r(2)h

12. Formula to Find Average
Average: Sum of the Terms/Number of 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.
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.

13. Definition of a Rational Number
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 formula distance=rate*time and its variations to help in this question.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Four equal acute angles and four equal obtuse angles.

14. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

15. Determining Absolute Value of a Number
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

16. Characteristics of a Parallelogram
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

17. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Two relatively prime numbers are integers that have no common factor other than 1.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
-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.

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

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19. Multiplying Expressions with Exponents that Have a Common Base
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

20. Direct Variation and Inverse Variation
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
The value that appears the most often.
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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

21. Finding the Area of a Sector

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22. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Do whatever is necessary to both sides to isolate the variable.
Use simple numbers like 1 and 2 and see what happens.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

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

24. Finding the Slope When Given an Equation of a Line
Part=Percent x Whole
Two relatively prime numbers are integers that have no common factor other than 1.
Switch the numerator and denominator.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

25. Prime Factorization of a Number
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

26. Comparing the values of two or more Fractions
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Express them with a common denominator.
-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.

27. Characteristics of a Square
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
-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.

28. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.

29. Convert From a Fraction to a Decimal - Vice Versa
Subtract the smallest from the largest and add 1
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.
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.
-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.

30. Adding and Subtracting Fractions
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Find a common denominator - then add or subtract the numerators.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

31. Adding and Subtracting Polynomials
VofaRS=lwh
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Combine like terms.

32. 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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

33. Counting the Total Number of Possibilities for Several Events to Occur
Use simple numbers like 1 and 2 and see what happens.
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

34. Finding the Volume of a Rectangular Solid
Part=Percent x Whole
VofaRS=lwh
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.

35. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
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.
Find a common denominator - then add or subtract the numerators.
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

36. If x(2)=7x+18 - what is the positive value of x?
Average the smallest and largest number
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
(x1+x2)/2 -(y1+y2)/2

37. 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
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
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. Counting Consecutive Integers
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Subtract the smallest from the largest and add 1
The value that falls in the middle of the set.

39. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
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.
Find a common denominator - then add or subtract the numerators.
-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.

40. Finding a Term in a Geometric Sequence
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
2(pie)r
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.

41. Simplifying an Algebraic Equation
2(pie)r
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Cancel factors common to the numerator and denominator.
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.

42. What is the Pythagorean Theorem?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
A(2)+b(2)=c(2)
Subtract the smallest from the largest and add 1

43. Finding the GCF of Two or More Numbers
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Do whatever is necessary to both sides to isolate the variable.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

44. Evaluating an Algebraic Expression
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Plug in the given values for the unknowns and calculate according to PEMDAS.

45. Finding the Sum of the Average of a Series of Numbers
Just add or subtract the coefficients in front of the radicals.
Sum: Average x Number of Terms
Isolate the radical expression and use the standard rules of algebra.
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.

46. Finding the Distance Between Two Points on a Coordinate Graph
-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.
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
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

47. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Just add or subtract the coefficients in front of the radicals.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.

48. Expressing the Union and Intersection of Sets
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

49. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
A(2)+b(2)=c(2)
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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 of the Angles of a Polygon: (n-2)*180 - n is the number of sides

50. Finding the Volume of a Cylinder
Cancel factors common to the numerator and denominator.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
VofaC: (pie)r(2)h