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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. If r#t=t(r)-r(t) - then what is 4#3?
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
-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.

2. If 4(x(2)-10x+25) - then what is the value of x?
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
Four equal acute angles and four equal obtuse angles.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

3. 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.
Switch the numerator and denominator.
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

4. Multiplying Fractions
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the numerators and multiply the denominators.
Do whatever is necessary to both sides to isolate the variable.
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.

5. Multiplying Monomials
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
Slope=change in y/change in x
Put each number in the original ratio over the sum of the numbers.

6. What value of x is not in the domain of the function f(x)=x-2/x-3?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
-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.
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

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

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

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9. Solving a Proportion
A(2)+b(2)=c(2)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Cross multiply.

10. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Sum: Average x Number of Terms
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.

11. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-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.
-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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

13. Prime Factorization of a Number
Multiply the exponents - (x^3)^4=x^3*4=x^12
-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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

14. Dividing Expressions with Exponents that Have a Common Base
(pie)r(squared)
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

15. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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.
Use the units to keep things straight - Snowfall inches/hours
Get the absolute value equation by itself. Solve.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

16. If x(2)=7x+18 - what is the positive value of x?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Part=Percent x Whole
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

17. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.

18. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
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. Setting Up a Ratio
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Cancel factors common to the numerator and denominator.

20. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
FOIL: First - Outer - Inner - Last... Combine Like Terms
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

21. Expressing the Union and Intersection of Sets
Just add or subtract the coefficients in front of the radicals.
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 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
Cancel factors common to the numerator and denominator.

22. Properties of Similar Triangles
Use the units to keep things straight - Snowfall inches/hours
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

23. Finding the Surface Area of a Rectangular Solid
Factor out and cancel all factors the numerator and denominator have in common.
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

24. 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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.

25. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Plug in the given values for the unknowns and calculate according to PEMDAS.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Average the smallest and largest number
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. If (Square Root: x-1)+5=12 - what is the value of x/2?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
Find a common denominator - then add or subtract the numerators.

27. 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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.

28. If the average of a - b - and 48 is 48 - what is the value of a + b?
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
-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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Cross multiply.

29. Multiply and Divide Positive and Negative Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

30. Converting From a Mixed Number to an Improper Fraction
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

31. Adding and Subtracting Polynomials
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Combine like terms.
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.

32. Difference Between a Factor and a Multiple
-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.
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.
Do whatever is necessary to both sides to isolate the variable.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

33. Finding the Area of a Sector

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34. PEMDAS
Switch the numerator and denominator.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
-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.

35. Finding the Volume of a Cylinder
The whole number left over after division.
VofaC: (pie)r(2)h
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.
Slope=change in y/change in x

36. Definition of Remainder
VofaRS=lwh
Find a common denominator - then add or subtract the numerators.
The whole number left over after division.
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

37. Solving a Linear Equation
A(2)+b(2)=c(2)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Do whatever is necessary to both sides to isolate the variable.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

38. Solving a Radical Equation
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Isolate the radical expression and use the standard rules of algebra.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

39. Multiplying Expressions with Exponents that Have a Common Base
The value that appears the most often.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

40. Evaluating an Algebraic Expression
The value that appears the most often.
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
Put the equation into y=mx+b-- in which case b is the y-intercept.

41. Finding a Term in a Geometric Sequence
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Use the formula distance=rate*time and its variations to help in this question.
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.

42. Multiplying Binomials
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Isolate the radical expression and use the standard rules of algebra.
FOIL: First - Outer - Inner - Last... Combine Like Terms

43. Finding the GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
-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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Probability: Number of Favorable Outcomes/Total Possible Outcomes

44. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
-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.
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.
Slope=change in y/change in x

45. If 3(3x)=9(x+2) - what is the value of x?
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
2(pie)r
Cancel factors common to the numerator and denominator.

46. An Important Property of a Line Tangent to a Circle
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
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

47. Multiplying and Dividing Roots
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
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

48. How do you know if an integer is a multiple of 3 or 9?
-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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
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. Adding and Subtracting Monomials
-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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Average: Sum of the Terms/Number of the Terms
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

50. Knowing if an Integer is a Multiple of 2 or 4
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.