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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. 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.
Combine like terms.
Put each number in the original ratio over the sum of the numbers.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

2. Characteristics of a Parallelogram
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
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

3. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

4. Converting from an Improper Fraction to a Mixed Number
Isolate the radical expression and use the standard rules of algebra.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

5. Adding and Subtracting Monomials
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Two relatively prime numbers are integers that have no common factor other than 1.
Average the smallest and largest number

6. Simplifying an Algebraic Equation
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 one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Cancel factors common to the numerator and denominator.

7. Finding the Reciprocal of a Fraction
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Use the units to keep things straight - Snowfall inches/hours
Switch the numerator and denominator.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

8. Knowing if an Integer is a Multiple of 5 or 10
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
-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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Two relatively prime numbers are integers that have no common factor other than 1.

9. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

10. What Does Solving In Terms of Mean?
Cross 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.
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: Sum of the Terms/Number of the Terms

11. 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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Do whatever is necessary to both sides to isolate the variable.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

12. Finding the Area of a Triangle

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13. 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)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

14. Finding the GCF of Two or More Numbers
Isolate the radical expression and use the standard rules of algebra.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.

15. Finding the Volume of a Rectangular Solid
Find a common denominator - then add or subtract the numerators.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
VofaRS=lwh
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

16. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
(x1+x2)/2 -(y1+y2)/2
Factor out and cancel all factors the numerator and denominator have in common.
Cancel factors common to the numerator and denominator.

17. What is the positive difference between the answers to the equation 35+x(2)=12x?

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18. How do you know if an integer is a multiple of 3 or 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.
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.
Find a common denominator - then add or subtract the numerators.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

19. Properties of Similar Triangles
Combine like terms.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Factor out and cancel all factors the numerator and denominator have in common.
Use simple numbers like 1 and 2 and see what happens.

20. Comparing the values of two or more Fractions
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Express them with a common denominator.

21. What types of angles are formed when two lines intersect?
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
Adjacent angles are supplementary - Vertical angles are equal

22. Setting Up a Ratio
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

23. Finding the Area of a Circle
(pie)r(squared)
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
-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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

24. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

25. 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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

26. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
Sum: Average x Number of Terms
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

27. Definition of an Integer
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

28. 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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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
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.

29. Prime Factorization of a Number
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use simple numbers like 1 and 2 and see what happens.
-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.

30. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
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.
Just add or subtract the coefficients in front of the radicals.
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

31. Knowing if an Integer is a Multiple of 2 or 4
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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
-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.
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.

32. Numbers that are Relatively Prime
Multiply the numerators and multiply the denominators.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Two relatively prime numbers are integers that have no common factor other than 1.
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

33. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Plug in the given values for the unknowns and calculate according to PEMDAS.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Two relatively prime numbers are integers that have no common factor other than 1.

34. Finding the Missing Number in a Series When You are Given the Average
Switch the numerator and denominator.
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.
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.
Two relatively prime numbers are integers that have no common factor other than 1.

35. Characteristics of a Square
Do whatever is necessary to both sides to isolate the variable.
VofaC: (pie)r(2)h
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

36. Finding the Sum of the Average of a Series of Numbers
Multiply the exponents - (x^3)^4=x^3*4=x^12
Sum: Average x Number of Terms
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
(x1+x2)/2 -(y1+y2)/2

37. Factoring the Difference of Two Squares
-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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
The whole number left over after division.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

38. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
VofaRS=lwh
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

39. Finding the Sum of the Interior Angles of a Polygon
Use the units to keep things straight - Snowfall inches/hours
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

40. Properties of a 45-45-90 Triangle
Cancel factors common to the numerator and denominator.
Cross multiply.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

41. If (Square Root: x-1)+5=12 - what is the value of x/2?
Multiply the exponents - (x^3)^4=x^3*4=x^12
(x1+x2)/2 -(y1+y2)/2
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Express them with a common denominator.

42. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Get the absolute value equation by itself. Solve.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

43. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Four equal acute angles and four equal obtuse angles.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

44. Finding the Midpoint Between Two Points
A(2)+b(2)=c(2)
(x1+x2)/2 -(y1+y2)/2
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
2(pie)r

45. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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
Cancel factors common to the numerator and denominator.
Slope=change in y/change in x

46. Converting From a Mixed Number to an Improper Fraction
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Switch the numerator and denominator.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

47. Number of Groups - +1 Each Time
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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. Finding a Term in a Geometric Sequence
Express them with a common denominator.
The whole number left over after division.
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12

49. 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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Sum: Average x Number of Terms
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

50. If 3(3x)=9(x+2) - what is the value of x?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Probability: Number of Favorable Outcomes/Total Possible Outcomes
(pie)r(squared)
Part=Percent x Whole