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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
VofaC: (pie)r(2)h
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Sum: Average x Number of Terms

2. Finding the Domain and Range of a Function
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.
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.
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.
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.

3. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Use simple numbers like 1 and 2 and see what happens.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

4. Evaluating an Algebraic Expression
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Two relatively prime numbers are integers that have no common factor other than 1.
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

5. Finding the Surface Area of a Rectangular Solid
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Sum: Average x Number of Terms
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)

6. Average Rate and How Do You Find It
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

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

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8. Characteristics of a Rectangle
Use the distributive property then combine the like terms.
Isolate the radical expression and use the standard rules of algebra.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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

9. What are Two Special Pythagorean Triples?

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10. 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.
Just add or subtract the coefficients in front of the radicals.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

11. If r#t=t(r)-r(t) - then what is 4#3?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
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.

12. Knowing if an Integer is a Multiple of 2 or 4
-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 numerators and multiply the denominators.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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

13. Setting Up a Ratio
Adjacent angles are supplementary - Vertical angles are equal
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

14. Formula Used to Find Percent
Part=Percent x Whole
-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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Do whatever is necessary to both sides to isolate the variable.

15. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the units to keep things straight - Snowfall inches/hours
The value that falls in the middle of the set.
Switch the numerator and denominator.

16. Simplifying Square Roots
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

17. PEMDAS
-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.
Use the formula distance=rate*time and its variations to help in this question.
Combine like terms.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

18. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
The value that appears the most often.
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.

19. What is the Triangle Inequality Theorem?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
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
Use simple numbers like 1 and 2 and see what happens.

20. Finding the Length of an Arc in a Circle

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21. Adding and Subtracting Fractions
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
-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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Find a common denominator - then add or subtract the numerators.

22. Formula to Find Average
VofaRS=lwh
Average: Sum of the Terms/Number of the Terms
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating 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.

23. Properties of a 30-60-90 Triangle
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 formula distance=rate*time and its variations to help in this question.
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

24. An Important Property of a Line Tangent to a Circle
Adjacent angles are supplementary - Vertical angles are equal
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.
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.

25. Characteristics of a Square
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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

26. 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.
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.
Use the distributive property then combine the like 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.

27. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
Cancel factors common to the numerator and denominator.
Just add or subtract the coefficients in front of the radicals.
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.

28. 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?
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Adjacent angles are supplementary - Vertical angles are equal
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.

29. Knowing if an Integer is a Multiple of 5 or 10
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
Multiply the exponents - (x^3)^4=x^3*4=x^12
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
-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. Increasing and Decreasing a Number by a Certain Percentage
Use the units to keep things straight - Snowfall inches/hours
-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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Find a common denominator - then add or subtract the numerators.

31. Factoring the Difference of Two Squares
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Switch the numerator and denominator.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

32. Finding the y-intercept When Given an Equation of a Line
Four equal acute angles and four equal obtuse angles.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Part=Percent x Whole
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

33. Finding the Slope When Given an Equation of a Line
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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 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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

34. Comparing the values of two or more Fractions
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Express them with a common 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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

35. Finding the Mode of a Set of Numbers
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Put each number in the original ratio over the sum of the numbers.
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
The value that appears the most often.

36. 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
Use simple numbers like 1 and 2 and see what happens.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

37. Finding the Area of a Triangle

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38. Finding the Sum of the Average of a Series of Numbers
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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

39. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Use the units to keep things straight - Snowfall inches/hours
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.
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.

40. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

41. Finding the Circumference of a Circle
Just add or subtract the coefficients in front of the radicals.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
2(pie)r
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

42. Finding the Reciprocal of a Fraction
The whole number left over after division.
Switch the numerator and denominator.
Cross multiply.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

43. Multiplying Monomials
Subtract the smallest from the largest and add 1
Express them with a common denominator.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The value that appears the most often.

44. Raising a Power to a Power
Express them with a common denominator.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Multiply the exponents - (x^3)^4=x^3*4=x^12
-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.

45. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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

46. 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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
-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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

47. Prime Factorization of a Number
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 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.

48. Solving a Radical Equation
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.
Isolate the radical expression and use the standard rules of algebra.
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

49. Finding the Slope of a Line When Given Two Points on the Line
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
Slope=change in y/change in x
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

50. Finding the GCF of Two or More Numbers
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.