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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. Comparing the values of two or more Fractions
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Express them with a common denominator.
The value that appears the most often.

2. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.

3. 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?
Plug in the given values for the unknowns and calculate according to PEMDAS.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

4. Multiplying Binomials
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

5. Finding the Missing Number in a Series When You are Given the Average
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
VofaRS=lwh
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

6. What are Two Special Pythagorean Triples?

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7. If 3(3x)=9(x+2) - what is the value of x?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

8. Finding the Area of a Sector

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9. Properties of the Interior and Exterior Angles of a Triangle
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.
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.
Use the distributive property then combine the like terms.

10. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
-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.

11. Adding and Subtracting Fractions
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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
-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.
Find a common denominator - then add or subtract the numerators.

12. Characteristics of a Rectangle
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use the distributive property then combine the like terms.
Combine like terms.

13. Expressing the Union and Intersection of Sets
Cross multiply.
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
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

14. Solving a Linear Equation
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Do whatever is necessary to both sides to isolate the variable.
Factor out and cancel all factors the numerator and denominator have in common.

15. Definition of an Irrational Number
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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

16. What is the Triangle Inequality Theorem?
FOIL: First - Outer - Inner - Last... Combine Like Terms
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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 Circumference of a Circle
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
2(pie)r
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.

18. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Four equal acute angles and four equal obtuse angles.
Cancel factors common to the numerator and denominator.

19. 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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Adjacent angles are supplementary - Vertical angles are equal

20. 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.
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Average: Sum of the Terms/Number of the Terms

21. If (Square Root: x-1)+5=12 - what is the value of x/2?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

22. Finding the Volume of a Rectangular Solid
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Isolate the radical expression and use the standard rules of algebra.
VofaRS=lwh
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.

23. If the average of a - b - and 48 is 48 - what is the value of a + b?
The value that falls in the middle of the set.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

24. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
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.
(x1+x2)/2 -(y1+y2)/2
Use the distributive property then combine the like terms.

25. Solving a Problem Involving Rates
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.
Use the units to keep things straight - Snowfall inches/hours
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.

26. Adding and Subtracting Roots
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use simple numbers like 1 and 2 and see what happens.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Just add or subtract the coefficients in front of the radicals.

27. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
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.
VofaRS=lwh
Part=Percent x Whole

28. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Multiply the numerators and multiply the denominators.
Sum: Average x Number of Terms

29. Finding the Rate of Speed
Put the equation into y=mx+b-- in which case b is the y-intercept.
Use the formula distance=rate*time and its variations to help in this question.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

30. 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?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use the units to keep things straight - Snowfall inches/hours
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.

31. What Does Solving In Terms of Mean?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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)
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.

32. Determining Absolute Value of a Number
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
-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.

33. Definition of Remainder
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Combine like terms.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
The whole number left over after division.

34. Counting the Total Number of Possibilities for Several Events to Occur
Two relatively prime numbers are integers that have no common factor other than 1.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
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.

35. Factoring the Difference of Two Squares
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Slope=change in y/change in x
The whole number left over after division.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

36. Finding the Slope of a Line When Given Two Points on the Line
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Average the smallest and largest number
Get the absolute value equation by itself. Solve.
Slope=change in y/change in x

37. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Put each number in the original ratio over the sum of the numbers.
Use simple numbers like 1 and 2 and see what happens.
Use the units to keep things straight - Snowfall inches/hours
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

38. Evaluating an Algebraic Expression
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
The value that falls in the middle of the set.
Multiply the exponents - (x^3)^4=x^3*4=x^12

39. Finding the Median of a Set of Numbers
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 falls in the middle of the set.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

40. 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
Use the units to keep things straight - Snowfall inches/hours
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

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

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42. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Multiply the numerators and multiply the denominators.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Subtract the smallest from the largest and add 1

43. Definition of an Integer
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.

44. Simplifying Square Roots
Use the distributive property then combine the like terms.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

45. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Cancel factors common to the numerator and denominator.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Put the equation into y=mx+b-- in which case b is the y-intercept.

46. Direct Variation and Inverse Variation
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Adjacent angles are supplementary - Vertical angles are equal
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

47. Factoring a Polynomial ('FOIL in Reverse')
Average: Sum of the Terms/Number of the Terms
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use the formula distance=rate*time and its variations to help in this question.

48. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
VofaRS=lwh
A(2)+b(2)=c(2)
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.

49. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

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50. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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
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
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.