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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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1. If the average of a - b - and 48 is 48 - what is the value of a + b?
Two relatively prime numbers are integers that have no common factor other than 1.
Use the formula distance=rate*time and its variations to help in this question.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

2. Finding the Volume of a Rectangular Solid
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Express them with a common denominator.
VofaRS=lwh

3. Properties of a 45-45-90 Triangle
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Part=Percent x Whole
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

4. Finding the Distance Between Two Points on a Coordinate Graph
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Express them with a common denominator.
Isolate the radical expression and use the standard rules of algebra.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

5. Knowing if an Integer is a Multiple of 2 or 4
The value that falls in the middle of the set.
-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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

6. Knowing if an Integer is a Multiple of 5 or 10
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The value that falls in the middle of the set.
-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.

7. 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?
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Express them with a common denominator.

8. What are Two Special Pythagorean Triples?

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9. Finding the Sum of the Average of a Series of Numbers
A(2)+b(2)=c(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
Sum: Average x Number of Terms
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

10. Counting the Total Number of Possibilities for Several Events to Occur
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Use the formula distance=rate*time and its variations to help in this question.

11. What types of angles are formed when a transversal cross parallel lines?
Use the formula distance=rate*time and its variations to help in this question.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Four equal acute angles and four equal obtuse angles.

12. Converting From a Mixed Number to an Improper Fraction
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Adjacent angles are supplementary - Vertical angles are equal

13. Comparing the values of two or more Fractions
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Express them with a common denominator.

14. Finding the Midpoint Between Two Points
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
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.
(x1+x2)/2 -(y1+y2)/2
Do whatever is necessary to both sides to isolate the variable.

15. 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.
Use the formula distance=rate*time and its variations to help in this question.
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.
VofaC: (pie)r(2)h

16. Formula to Find Average
Adjacent angles are supplementary - Vertical angles are equal
VofaC: (pie)r(2)h
Average: Sum of the Terms/Number of the Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.

17. Finding the Slope of a Line When Given Two Points on the Line
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 group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Slope=change in y/change in x

18. Definition of Remainder
-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.
The whole number left over after division.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

19. Increasing and Decreasing a Number by a Certain Percentage
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Average the smallest and largest number
-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.
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.

20. Characteristics of a Square
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.
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.
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

21. If 4(x(2)-10x+25) - then what is the value of x?
Get the absolute value equation by itself. Solve.
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.
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12

22. Finding the Area of a Circle
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
(pie)r(squared)
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

23. Multiplying Fractions
Multiply the numerators and multiply the denominators.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use the distributive property then combine the like terms.

24. If 3(3x)=9(x+2) - what is the value of x?
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
Sum: Average x Number of Terms
Find a common denominator - then add or subtract the numerators.

25. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Put the equation into y=mx+b-- in which case b is the y-intercept.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.

26. Simplifying an Algebraic Equation
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Cancel factors common to the numerator and denominator.
-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.

27. 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
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

28. Finding the Reciprocal of a Fraction
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Switch the numerator and denominator.
Put each number in the original ratio over the sum of the numbers.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

29. Factoring a Polynomial ('FOIL in Reverse')
Switch the numerator and denominator.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

30. Scalene - Isosceles - and Equilateral Triangles
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
Factor out and cancel all factors the numerator and denominator have in common.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

31. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
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
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.
Average the smallest and largest number

32. Numbers that are Relatively Prime
The whole number left over after division.
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.
Two relatively prime numbers are integers that have no common factor other than 1.

33. Expressing the Union and Intersection of Sets
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 variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Part=Percent x Whole
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

34. 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
Cross multiply.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
-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.

35. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.

36. Finding the Area of a Sector

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37. 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
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

38. Converting from part-to-part ratios to part-to-whole ratios
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Put each number in the original ratio over the sum of the numbers.
Get the absolute value equation by itself. Solve.

39. Finding the Median of a Set of 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.
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

40. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Find a common denominator - then add or subtract the numerators.
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

41. Characteristics of a Parallelogram
-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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Average the smallest and largest number
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

42. Finding the Domain and Range of a Function
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

43. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

44. Finding a Term in a Geometric Sequence
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
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.

45. Solving an Inequality
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply the exponents - (x^3)^4=x^3*4=x^12
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Four equal acute angles and four equal obtuse angles.

46. Simplifying Square Roots
Use simple numbers like 1 and 2 and see what happens.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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

47. How do you know if an integer is a multiple of 3 or 9?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Average the smallest and largest number
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.

48. Properties of a 30-60-90 Triangle
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

49. Definition of a Rational Number
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

50. Finding the Circumference of a Circle
2(pie)r
Express them with a common denominator.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.