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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. Properties of a 30-60-90 Triangle
'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
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.

2. Number of Groups - +1 Each Time
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
-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.

3. Definition of an Irrational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

4. Definition of a Rational Number
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
-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.
Average the smallest and largest number

5. If 3(3x)=9(x+2) - what is the value of x?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

6. If x(2)=7x+18 - what is the positive value of x?
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Slope=change in y/change in x
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

7. Solving a Linear Equation
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Do whatever is necessary to both sides to isolate the variable.
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.

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

9. Finding the Domain and Range of a Function
Use the formula distance=rate*time and its variations to help in this question.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Four equal acute angles and four equal obtuse angles.

10. 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.
Use simple numbers like 1 and 2 and see what happens.
Switch the numerator and denominator.
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.

11. 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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Slope=change in y/change in x
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

12. Finding the Circumference of a Circle
Four equal acute angles and four equal obtuse angles.
2(pie)r
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

13. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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
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.
Use simple numbers like 1 and 2 and see what happens.

14. Calculating Negative Exponents and Radical Exponents
Factor out and cancel all factors the numerator and denominator have in common.
Put each number in the original ratio over the sum of the numbers.
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.

15. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

16. Convert From a Fraction to a Decimal - Vice Versa
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.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.

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?
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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
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.

18. 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.
Combine like terms.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

19. Finding the y-intercept When Given an Equation of a Line
Cancel factors common to the numerator and denominator.
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
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 the equation into y=mx+b-- in which case b is the y-intercept.

20. What is the Triangle Inequality Theorem?
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.
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 - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

21. Direct Variation and Inverse Variation
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
Just add or subtract the coefficients in front of the radicals.
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.
Use the distributive property then combine the like terms.

22. Finding the Slope of a Line When Given Two Points on the Line
Probability: Number of Favorable Outcomes/Total Possible Outcomes
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Slope=change in y/change in x
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

23. Dividing Fractions
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Multiply the numerators and multiply the denominators.

24. Finding the GCF of Two or More Numbers
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

25. Solving a System of Equations
The value that appears the most often.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.

26. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Express them with a common denominator.

27. Factoring the Difference of Two Squares
Multiply the exponents - (x^3)^4=x^3*4=x^12
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

28. Numbers that are Relatively Prime
-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.
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.
Two relatively prime numbers are integers that have no common factor other than 1.
-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.

29. 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?
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
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.
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.

30. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
2(pie)r
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.

31. Adding and Subtracting Fractions
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Find a common denominator - then add or subtract the numerators.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

32. Quickly Finding the Average of a Series of Evenly Spaced Numbers
FOIL: First - Outer - Inner - Last... Combine Like Terms
Average the smallest and largest number
The value that appears the most often.
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.

33. Finding the Length of an Arc in a Circle

34. Formula Used to Find Percent
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Combine like terms.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Part=Percent x Whole

35. Counting the Total Number of Possibilities for Several Events to Occur
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
A(2)+b(2)=c(2)
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

36. 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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
(x1+x2)/2 -(y1+y2)/2
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.

37. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Subtract the smallest from the largest and add 1
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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

38. Solving a Proportion
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
-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.
Cross multiply.

39. What Does Solving In Terms of Mean?
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

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

41. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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
-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.

42. Average Rate and How Do You Find It
Cancel factors common to the numerator and denominator.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Just add or subtract the coefficients in front of the radicals.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

43. Simplifying a Fraction to Lowest Terms
Isolate the radical expression and use the standard rules of algebra.
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.
Factor out and cancel all factors the numerator and denominator have in common.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

44. What are Two Special Pythagorean Triples?

45. Simplifying Square Roots
Put each number in the original ratio over the sum of the numbers.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

46. If r#t=t(r)-r(t) - then what is 4#3?
Multiply the exponents - (x^3)^4=x^3*4=x^12
Four equal acute angles and four equal obtuse angles.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Put the equation into y=mx+b-- in which case b is the y-intercept.

47. Multiplying Binomials
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
FOIL: First - Outer - Inner - Last... Combine Like Terms
Average: Sum of the Terms/Number of the Terms

48. 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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute 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.

49. Finding the Sum of the Interior Angles of a Polygon
Find a common denominator - then add or subtract the numerators.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.

50. Determining Absolute Value of a Number
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Multiply the numerators and multiply the denominators.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I