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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. Properties of the Interior and Exterior Angles of a Triangle
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

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

3. What Does Solving In Terms of Mean?
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.

4. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
Use simple numbers like 1 and 2 and see what happens.
The value that appears the most often.

5. Dividing Expressions with Exponents that Have a Common Base
Multiply the exponents - (x^3)^4=x^3*4=x^12
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

6. Counting the Total Number of Possibilities for Several Events to Occur
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.
Switch the numerator and denominator.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

7. Finding the Area of a Triangle

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8. Finding the Length of an Arc in a Circle

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9. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Subtract the smallest from the largest and add 1
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

10. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
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.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

11. What is a Function and how do you Evaluate one?

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12. Adding and Subtracting Fractions
Put each number in the original ratio over the sum of the numbers.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.

13. Counting Consecutive Integers
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Subtract the smallest from the largest and add 1

14. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

15. 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
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.

16. Formula to Find Average
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Average: Sum of the Terms/Number of the Terms
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.

17. If the average of a - b - and 48 is 48 - what is the value of a + b?
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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

18. What is the Triangle Inequality Theorem?
Subtract the smallest from the largest and add 1
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.

19. Finding the Mode of a Set of Numbers
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 value that appears the most often.
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.
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.

20. If 3(3x)=9(x+2) - what is the value of x?
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

21. Solving a System of Equations
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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
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.

22. PEMDAS
(x1+x2)/2 -(y1+y2)/2
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Sum: Average x Number of Terms
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

23. Number of Groups - +1 Each Time
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.
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 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.

24. Finding the Volume of a Rectangular Solid
VofaRS=lwh
Just add or subtract the coefficients in front of the radicals.
Switch the numerator and denominator.
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.

25. Multiply and Divide Positive and Negative Numbers
Switch the numerator and denominator.
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
VofaRS=lwh
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

26. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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
Get the absolute value equation by itself. Solve.
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.

27. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
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.
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.

28. Multiplying and Dividing Roots
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

29. 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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

30. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use the units to keep things straight - Snowfall inches/hours
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

31. Difference Between a Factor and a Multiple
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Find a common denominator - then add or subtract the numerators.
-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.

32. Solving a Problem Involving Rates
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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 units to keep things straight - Snowfall inches/hours

33. An Important Property of a Line Tangent to a Circle
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.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the distributive property then combine the like terms.

34. Adding a Positive Number to a Negative Number
Multiply the numerators and multiply the denominators.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

35. Solving a Proportion
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Cross multiply.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
(pie)r(squared)

36. Properties of a 45-45-90 Triangle
Isolate the radical expression and use the standard rules of algebra.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Use the distributive property then combine the like terms.

37. If 4(x(2)-10x+25) - then what is the value of 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.
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
Subtract the smallest from the largest and add 1
A(2)+b(2)=c(2)

38. 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?
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Average the smallest and largest number

39. Converting from an Improper Fraction to a Mixed Number
Subtract the smallest from the largest and add 1
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.
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.
Use the formula distance=rate*time and its variations to help in this question.

40. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Get the absolute value equation by itself. Solve.
Subtract the smallest from the largest and add 1
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.

41. Finding the Reciprocal of a Fraction
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.
Switch the numerator and denominator.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

42. Solving a Linear Equation
Put each number in the original ratio over the sum of the numbers.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Do whatever is necessary to both sides to isolate the variable.
Multiply the numerators and multiply the denominators.

43. Solving a Radical Equation
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.
Isolate the radical expression and use the standard rules of algebra.
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.
Express them with a common denominator.

44. Definition of an Integer
Part=Percent x Whole
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

45. Finding the Distance Between Two Points on a Coordinate Graph
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

46. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
VofaC: (pie)r(2)h
Find a common denominator - then add or subtract the numerators.
Do whatever is necessary to both sides to isolate the variable.

47. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
(x1+x2)/2 -(y1+y2)/2
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

48. Converting from part-to-part ratios to part-to-whole ratios
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
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.

49. Scalene - Isosceles - and Equilateral Triangles
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.
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.
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
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.

50. Definition of an Irrational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
VofaC: (pie)r(2)h
Adjacent angles are supplementary - Vertical angles are equal
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2