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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. Definition of an Integer
Subtract the smallest from the largest and add 1
Use simple numbers like 1 and 2 and see what happens.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.

2. Adding and Subtracting Monomials
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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(pie)r

3. How do you know if an integer is a multiple of 3 or 9?
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Do whatever is necessary to both sides to isolate the variable.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

4. Factoring the Difference of Two Squares
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Put the equation into y=mx+b-- in which case b is the y-intercept.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

5. Solving an Inequality
Subtract the smallest from the largest and add 1
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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

6. Determining Absolute Value of a Number
Put each number in the original ratio over the sum of the numbers.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

7. What value of x is not in the domain of the function f(x)=x-2/x-3?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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

8. If 4(x(2)-10x+25) - then what is the value of x?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Four equal acute angles and four equal obtuse angles.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.

9. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.

10. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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
Do whatever is necessary to both sides to isolate the variable.

11. Finding the Slope of a Line When Given Two Points on the Line
Subtract the smallest from the largest and add 1
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Slope=change in y/change in x

12. Dividing Expressions with Exponents that Have a Common Base
Use the units to keep things straight - Snowfall inches/hours
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

13. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Multiply the numerators and multiply the denominators.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.

14. Finding the Missing Number in a Series When You are Given the Average
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.
2(pie)r
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
Get the absolute value equation by itself. Solve.

15. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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 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.
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.
Use the formula distance=rate*time and its variations to help in this question.

16. Finding the Area of a Circle
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.
-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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
(pie)r(squared)

17. Multiply and Divide Positive and Negative Numbers
2(pie)r
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
Do whatever is necessary to both sides to isolate the variable.
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

18. Adding and Subtracting Fractions
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.

19. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

20. Calculating the Probability that an Event will Take Place
Isolate the radical expression and use the standard rules of algebra.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Use the formula distance=rate*time and its variations to help in this question.
(x1+x2)/2 -(y1+y2)/2

21. 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.
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.
Average: Sum of the Terms/Number of the Terms
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

22. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
The value that falls in the middle of the set.

23. What types of angles are formed when two lines intersect?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Adjacent angles are supplementary - Vertical angles are equal
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
2(pie)r

24. Finding a Term in a Geometric Sequence
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

25. Formula to Find Average
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Average: Sum of the Terms/Number of the Terms
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

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

27. Finding the Midpoint Between Two Points
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.
-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.
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
(x1+x2)/2 -(y1+y2)/2

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

29. Characteristics of a Parallelogram
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.
Multiply the numerators and multiply the denominators.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

30. 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%
FOIL: First - Outer - Inner - Last... Combine Like Terms
VofaC: (pie)r(2)h
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

31. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Average the smallest and largest number
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

32. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

33. Finding the Surface Area of a Rectangular Solid
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

34. Dividing Fractions
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

35. An Important Property of a Line Tangent to a Circle
Use the distributive property then combine the like terms.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
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

36. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

37. Definition of Remainder
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
The whole number left over after division.
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
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

38. Characteristics of a Square
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Isolate the radical expression and use the standard rules of algebra.

39. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The value that falls in the middle of the set.
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.

40. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

41. Solving a Linear Equation
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Do whatever is necessary to both sides to isolate the variable.

42. Multiplying Fractions
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the numerators and multiply the denominators.
-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.

43. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like 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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

44. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Do whatever is necessary to both sides to isolate the variable.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

45. Definition of an Irrational Number
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

46. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
Four equal acute angles and four equal obtuse angles.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

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

48. Difference Between a Factor and a Multiple
Do whatever is necessary to both sides to isolate the variable.
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.
-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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

49. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
Use the distributive property then combine the like terms.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Cancel factors common to the numerator and denominator.

50. Converting from part-to-part ratios to part-to-whole ratios
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 each number in the original ratio over the sum of the numbers.
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.
(pie)r(squared)