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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. Simplifying Square Roots
Find a common denominator - then add or subtract the numerators.
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.
Two relatively prime numbers are integers that have no common factor other than 1.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

2. Multiplying Monomials
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

3. Finding the Area of a Triangle

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4. Finding the Missing Number in a Series When You are Given the Average
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.
Factor out and cancel all factors the numerator and denominator have in common.
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.

5. Finding the Mode of a Set of Numbers
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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 value that appears the most often.
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.

6. Simplifying a Fraction to Lowest Terms
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.
Factor out and cancel all factors the numerator and denominator have in common.
Slope=change in y/change in x
Combine like terms.

7. Number of Groups - +1 Each Time
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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 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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

8. Scalene - Isosceles - and Equilateral Triangles
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Substitute r=4 and t=3 and evaluate the exponents before subtracting 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.

9. How do you know if an integer is a multiple of 3 or 9?
Adjacent angles are supplementary - Vertical angles are equal
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

10. Properties of a 30-60-90 Triangle
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

11. Characteristics of a Rectangle
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
Express them with a common denominator.

12. Counting Consecutive Integers
Slope=change in y/change in x
Subtract the smallest from the largest and add 1
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.

13. Comparing the values of two or more Fractions
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

14. Finding the LCM of Two or More Numbers

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15. Finding the Rate of Speed
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.
Combine like terms.
VofaRS=lwh

16. 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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

17. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Two relatively prime numbers are integers that have no common factor other than 1.
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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

18. 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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Put each number in the original ratio over the sum of the numbers.
Use the units to keep things straight - Snowfall inches/hours

19. Setting Up a Ratio
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.
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.
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.

20. Finding the Sum of the Average of a Series of Numbers
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Cancel factors common to the numerator and denominator.
Sum: Average x Number of Terms

21. Multiplying Binomials
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

22. Converting from part-to-part ratios to part-to-whole ratios
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Put each number in the original ratio over the sum of the numbers.
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

23. Dividing Fractions
Part=Percent x Whole
Factor out and cancel all factors the numerator and denominator have in common.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.

24. If r#t=t(r)-r(t) - then what is 4#3?
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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 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.

25. 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
Use the distributive property then combine the like terms.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Cross multiply.

26. Finding the Circumference of a Circle
2(pie)r
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Four equal acute angles and four equal obtuse angles.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

27. What value of x is not in the domain of the function f(x)=x-2/x-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
Put each number in the original ratio over the sum of the numbers.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Part=Percent x Whole

28. Calculating the Probability that an Event will Take Place
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Probability: Number of Favorable Outcomes/Total Possible Outcomes

29. Finding the Area of a Sector

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30. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

31. Convert From a Fraction to a Decimal - Vice Versa
Express them with a common denominator.
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.
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.

32. Raising a Power to a Power
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.
Cancel factors common to the numerator and denominator.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

33. What is the Triangle Inequality Theorem?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the 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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.

34. Finding the GCF of Two or More 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
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.

35. Counting the Total Number of Possibilities for Several Events to Occur
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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.
Combine like terms.

36. If 4(x(2)-10x+25) - then what is the value of x?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Cross multiply.
Slope=change in y/change in x
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.

37. If x(2)=7x+18 - what is the positive value of x?
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

38. Solving a Radical Equation
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.
Isolate the radical expression and use the standard rules of algebra.
Cross multiply.
Switch the numerator and denominator.

39. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Switch the numerator and denominator.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

40. Finding the Volume of a Cylinder
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
VofaC: (pie)r(2)h
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Do whatever is necessary to both sides to isolate the variable.

41. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
Sum: Average x Number of Terms

42. What types of angles are formed when a transversal cross parallel lines?
Cancel factors common to the numerator and denominator.
Use the formula distance=rate*time and its variations to help in this question.
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.
Four equal acute angles and four equal obtuse angles.

43. Finding the Sum of the Interior Angles of a Polygon
Put each number in the original ratio over the sum of the numbers.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

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

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45. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
A(2)+b(2)=c(2)

46. Characteristics of a Parallelogram
Slope=change in y/change in x
FOIL: First - Outer - Inner - Last... Combine Like Terms
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the formula distance=rate*time and its variations to help in this question.

47. What types of angles are formed when two lines intersect?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Adjacent angles are supplementary - Vertical angles are equal
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.
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

48. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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
The value that appears the most often.
FOIL: First - Outer - Inner - Last... Combine Like Terms

49. 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
Plug in the given values for the unknowns and calculate according to PEMDAS.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Sum: Average x Number of Terms
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.

50. Dividing Expressions with Exponents that Have a Common Base
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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 each number in the original ratio over the sum of the numbers.