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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. Finding the Length of an Arc in a Circle

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2. Finding the Reciprocal of a Fraction
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
Use the distributive property then combine the like terms.
Switch the numerator and denominator.

3. Finding the Median of a Set of Numbers
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
The value that falls in the middle of the set.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

4. Dividing Expressions with Exponents that Have a Common Base
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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

5. Properties of a 45-45-90 Triangle
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Two relatively prime numbers are integers that have no common factor other than 1.

6. Characteristics of a Square
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

7. Multiplying Fractions
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply the numerators and multiply the denominators.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

8. Converting from part-to-part ratios to part-to-whole ratios
Do whatever is necessary to both sides to isolate the variable.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put each number in the original ratio over the sum of the numbers.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

9. Multiplying Binomials
-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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
The value that falls in the middle of the set.
FOIL: First - Outer - Inner - Last... Combine Like Terms

10. If the average of a - b - and 48 is 48 - what is the value of a + b?
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

11. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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
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.

12. Convert From a Fraction to a Decimal - Vice Versa
Use the units to keep things straight - Snowfall inches/hours
-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.
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 pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

13. Finding the Sum of the Average of a Series of Numbers
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Sum: Average x Number of Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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. Number of Groups - +1 Each Time
Find a common denominator - then add or subtract the numerators.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.

15. If (Square Root: x-1)+5=12 - what is the value of x/2?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Four equal acute angles and four equal obtuse angles.
Isolate the radical expression and use the standard rules of algebra.
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.

16. Finding the Surface Area of a Rectangular Solid
Average the smallest and largest number
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

17. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Cancel factors common to the numerator and denominator.
Multiply the numerators and multiply the denominators.
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
Use the units to keep things straight - Snowfall inches/hours

18. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

19. Solving a Radical Equation
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute 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
Isolate the radical expression and use the standard rules of algebra.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

20. Multiplying Monomials
A(2)+b(2)=c(2)
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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
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.

21. How do you know if an integer is a multiple of 3 or 9?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
VofaRS=lwh
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.

22. If 3(3x)=9(x+2) - what is the value of x?
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
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

23. Finding the Domain and Range of a Function
Put each number in the original ratio over the sum of the numbers.
Get the absolute value equation by itself. 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.
Cancel factors common to the numerator and denominator.

24. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
The value that falls in the middle of the set.

25. Calculating Negative Exponents and Radical Exponents
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
A(2)+b(2)=c(2)
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

26. Finding the y-intercept When Given an Equation of a Line
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Put the equation into y=mx+b-- in which case b is the y-intercept.

27. Setting Up a Ratio
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.
Find a common denominator - then add or subtract the numerators.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

28. 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.
Use the formula distance=rate*time and its variations to help in this question.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.

29. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
VofaC: (pie)r(2)h

30. Multiplying and Dividing Roots
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.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.

31. Formula to Find Average
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.
Average: Sum of the Terms/Number of the Terms
Just add or subtract the coefficients in front of the radicals.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

32. 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?
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.
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.
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.
Find a common denominator - then add or subtract the numerators.

33. Finding a Term in a Geometric Sequence
Isolate the radical expression and use the standard rules of algebra.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

34. 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?
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Plug in the given values for the unknowns and calculate according to PEMDAS.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

35. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The value that appears the most often.
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.
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.

36. If x varies directly with y - and the value of x is 12 when y is 11 - what is the value of y when x is 66?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Subtract the smallest from the largest and add 1
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.

37. Scalene - Isosceles - and Equilateral Triangles
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

38. Solving a Linear Equation
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Do whatever is necessary to both sides to isolate the variable.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

39. What Does Solving In Terms of Mean?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Four equal acute angles and four equal obtuse angles.

40. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
-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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.

41. What are Two Special Pythagorean Triples?

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42. An Important Property of a Line Tangent to a Circle
Two relatively prime numbers are integers that have no common factor other than 1.
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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
(pie)r(squared)

43. Definition of an Irrational Number
(pie)r(squared)
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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

44. 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
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
(x1+x2)/2 -(y1+y2)/2

45. Expressing the Union and Intersection of Sets
-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.
A(2)+b(2)=c(2)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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

46. Finding the LCM of Two or More Numbers

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47. Finding the Rate of Speed
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.
Switch the numerator and denominator.
Use the formula distance=rate*time and its variations to help in this question.
-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.

48. Evaluating an Algebraic Expression
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Plug in the given values for the unknowns and calculate according to PEMDAS.

49. Finding the Sum of the Interior Angles of a Polygon
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
2(pie)r

50. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use the formula distance=rate*time and its variations to help in this question.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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

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