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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. Adding and Subtracting Roots
Multiply the numerators and multiply the denominators.
Just add or subtract the coefficients in front of the radicals.
Average: Sum of the Terms/Number of the Terms
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

2. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

3. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use the distributive property then combine the like terms.

4. Finding the Area of a Circle
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Four equal acute angles and four equal obtuse angles.
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.
(pie)r(squared)

5. Finding the Length of an Arc in a Circle

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6. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
-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.
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
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

7. Multiplying Fractions
Multiply the numerators and multiply the denominators.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.

8. Formula to Find Average
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Average: Sum of the Terms/Number of the Terms
Find a common denominator - then add or subtract the numerators.

9. 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.
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.
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

10. Scalene - Isosceles - and Equilateral Triangles
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
Express them with a common denominator.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

11. If x(2)=7x+18 - what is the positive value of x?
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.
Express them with a common denominator.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

12. Sale Price of a Jacket Marked Down 30% Each Week for 3 Weeks - What % of the Original Price is the Cost of the Jacket After the 3 Week Sale Period
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Switch the numerator and denominator.
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
Factor out and cancel all factors the numerator and denominator have in common.

13. Numbers that are Relatively Prime
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.
Two relatively prime numbers are integers that have no common factor other than 1.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Isolate the radical expression and use the standard rules of algebra.

14. Converting from an Improper Fraction to a Mixed Number
FOIL: First - Outer - Inner - Last... Combine Like Terms
(x1+x2)/2 -(y1+y2)/2
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.
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.

15. Convert From a Fraction to a Decimal - Vice Versa
Switch the numerator and 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.
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 value that falls in the middle of the set.

16. 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.
Cross multiply.
VofaC: (pie)r(2)h
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

17. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
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.

18. What value of x is not in the domain of the function f(x)=x-2/x-3?
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use the distributive property then combine the like terms.
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

19. Finding the Surface Area of a Rectangular Solid
Use simple numbers like 1 and 2 and see what happens.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.

20. Knowing if an Integer is a Multiple of 2 or 4
-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.
-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.
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

21. Evaluating an Algebraic Expression
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Plug in the given values for the unknowns and calculate according to PEMDAS.

22. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Use simple numbers like 1 and 2 and see what happens.
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.

23. Adding and Subtracting Monomials
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The value that falls in the middle of the set.
FOIL: First - Outer - Inner - Last... Combine Like Terms

24. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Combine like terms.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

25. Multiplying and Dividing Roots
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
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.

26. Finding a Term in a Geometric Sequence
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.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
The value that appears the most often.

27. Finding the y-intercept When Given an Equation of a Line
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.
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
Sum: Average x Number of Terms

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

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29. Knowing if an Integer is a Multiple of 5 or 10
(pie)r(squared)
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.
-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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

30. Prime Factorization of a Number
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
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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

31. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Just add or subtract the coefficients in front of the radicals.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

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.
Sum: Average x Number of Terms
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
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.

33. Simplifying a Fraction to Lowest Terms
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.
A(2)+b(2)=c(2)
Factor out and cancel all factors the numerator and denominator have in common.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

34. Finding the Slope When Given an Equation of a Line
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
Do whatever is necessary to both sides to isolate the variable.

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?
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.
Slope=change in y/change in x
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

36. Finding the Rate of Speed
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Use the formula distance=rate*time and its variations to help in this question.
-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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

37. Finding the Missing Number in a Series When You are Given the Average
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.
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.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

38. Comparing the values of two or more Fractions
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Get the absolute value equation by itself. Solve.
Express them with a common denominator.
Put the equation into y=mx+b-- in which case b is the y-intercept.

39. Solving a Radical Equation
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Average the smallest and largest number
Isolate the radical expression and use the standard rules of algebra.

40. Finding the Median of a Set of Numbers
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
The value that falls in the middle of the set.
Get the absolute value equation by itself. Solve.

41. If the average of a - b - and 48 is 48 - what is the value of a + b?
The value that appears the most often.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Use simple numbers like 1 and 2 and see what happens.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

42. Dividing Fractions
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Four equal acute angles and four equal obtuse angles.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Express them with a common denominator.

43. Solving an Inequality
Four equal acute angles and four equal obtuse angles.
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

44. Finding the Volume of a Rectangular Solid
Isolate the radical expression and use the standard rules of algebra.
VofaRS=lwh
Use the distributive property then combine the like terms.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

45. Finding the Circumference of a Circle
(pie)r(squared)
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.
2(pie)r
Average the smallest and largest number

46. Adding and Subtracting Polynomials
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Combine like terms.

47. Finding the Sum of the Average of a Series 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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.

48. What types of angles are formed when two lines intersect?
Use the units to keep things straight - Snowfall inches/hours
Adjacent angles are supplementary - Vertical angles are equal
The whole number left over after division.
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.

49. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

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

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