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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. Solving a Proportion
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Cross multiply.
Use the units to keep things straight - Snowfall inches/hours

2. Finding the y-intercept When Given an Equation of a Line
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
-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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Put the equation into y=mx+b-- in which case b is the y-intercept.

3. PEMDAS
Four equal acute angles and four equal obtuse angles.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Factor out and cancel all factors the numerator and denominator have in common.

4. Characteristics of a Square
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
-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.

5. General Procedure for Multiplying Polynomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Use the distributive property then combine the like terms.

6. How do you know if an integer is a multiple of 3 or 9?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
Subtract the smallest from the largest and add 1

7. Finding the Area of a Sector

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8. What are Two Special Pythagorean Triples?

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9. Finding the Missing Number in a Series When You are Given the Average
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Express them with a common denominator.
Do whatever is necessary to both sides to isolate the variable.
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.

10. Counting the Total Number of Possibilities for Several Events to Occur
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

11. Expressing the Union and Intersection of Sets
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
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use simple numbers like 1 and 2 and see what happens.

12. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
-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.
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.
Find a common denominator - then add or subtract the numerators.

13. Finding the Area of a Circle
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
(pie)r(squared)
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.
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.

14. 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?
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
The whole number left over after division.

15. Dividing Expressions with Exponents that Have a Common Base
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
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

16. If the average of a - b - and 48 is 48 - what is the value of a + b?
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.

17. Finding the Volume of a Rectangular Solid
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Probability: Number of Favorable Outcomes/Total Possible Outcomes
VofaRS=lwh

18. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

19. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Use the distributive property then combine the like terms.
VofaC: (pie)r(2)h
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

20. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Adjacent angles are supplementary - Vertical angles are equal

21. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
Find a common denominator - then add or subtract the numerators.
(x1+x2)/2 -(y1+y2)/2
Do whatever is necessary to both sides to isolate the variable.

22. Multiplying Monomials
Factor out and cancel all factors the numerator and denominator have in common.
-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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

23. Finding a Term in a Geometric Sequence
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
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Cancel factors common to the numerator and denominator.

24. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Do whatever is necessary to both sides to isolate the variable.
The value that appears the most often.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

25. Increasing and Decreasing a Number by a Certain Percentage
-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.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

26. Determining Absolute Value of a Number
Average: Sum of the Terms/Number of the Terms
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
2(pie)r
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

27. Multiplying and Dividing Roots
Use the units to keep things straight - Snowfall inches/hours
Use the formula distance=rate*time and its variations to help in this question.
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.

28. What value of x is not in the domain of the function f(x)=x-2/x-3?
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.
Do whatever is necessary to both sides to isolate the variable.
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
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.

29. Quickly Finding the Average of a Series of Evenly Spaced Numbers
The value that falls in the middle of the set.
Average: Sum of the Terms/Number of the 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.
Average the smallest and largest number

30. Dividing Fractions
Use the distributive property then combine the like terms.
Find a common denominator - then add or subtract the numerators.
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

31. Raising a Power to a Power
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

32. Counting Consecutive Integers
The whole number left over after division.
Subtract the smallest from the largest and add 1
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

33. Direct Variation and Inverse Variation
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.
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
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.

34. If (Square Root: x-1)+5=12 - what is the value of x/2?
Switch the numerator and denominator.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.

35. 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?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Adjacent angles are supplementary - Vertical angles are equal
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.
Switch the numerator and denominator.

36. Simplifying an Algebraic Equation
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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
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
Cancel factors common to the numerator and denominator.

37. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
VofaRS=lwh

38. What types of angles are formed when two lines intersect?
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Adjacent angles are supplementary - Vertical angles are equal

39. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
(pie)r(squared)
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.

40. 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
Multiply the numerators and multiply the denominators.
VofaC: (pie)r(2)h
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

41. Adding and Subtracting Polynomials
The whole number left over after division.
(x1+x2)/2 -(y1+y2)/2
Sum: Average x Number of Terms
Combine like terms.

42. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Use the units to keep things straight - Snowfall inches/hours
Put the equation into y=mx+b-- in which case b is the y-intercept.

43. Setting Up a Ratio
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

44. If r#t=t(r)-r(t) - then what is 4#3?
Put each number in the original ratio over the sum of the numbers.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Isolate the radical expression and use the standard rules of algebra.
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

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.
Four equal acute angles and four equal obtuse angles.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

46. Formula to Find Average
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
The whole number left over after division.
Average: Sum of the Terms/Number of the Terms

47. Calculating Negative Exponents and Radical Exponents
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Two relatively prime numbers are integers that have no common factor other than 1.

48. Finding the Area of a Triangle

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

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50. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Plug in the given values for the unknowns and calculate according to PEMDAS.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Four equal acute angles and four equal obtuse angles.