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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. Counting the Total Number of Possibilities for Several Events to Occur
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Slope=change in y/change in x

2. Properties of the Interior and Exterior Angles of a Triangle
-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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
The value that appears the most often.
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.

3. Adding and Subtracting Polynomials
Slope=change in y/change in x
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Combine like terms.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

4. Finding the Reciprocal of a Fraction
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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
Switch the numerator and denominator.

5. Solving a Proportion
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Cross multiply.

6. Difference Between a Factor and a Multiple
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
-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.

7. Numbers that are Relatively Prime
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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
Two relatively prime numbers are integers that have no common factor other than 1.
Slope=change in y/change in x

8. General Procedure for Multiplying Polynomials
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Use the distributive property then combine the like terms.
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.

9. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
-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.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

10. Calculating Negative Exponents and Radical Exponents
Use the formula distance=rate*time and its variations to help in this question.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
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.

11. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

12. Evaluating an Algebraic Expression
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Plug in the given values for the unknowns and calculate according to PEMDAS.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

13. 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?
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
(pie)r(squared)
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.
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.

14. Finding the Volume of a Rectangular Solid
A(2)+b(2)=c(2)
FOIL: First - Outer - Inner - Last... Combine Like Terms
VofaRS=lwh
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. Finding the Length of an Arc in a Circle

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16. Finding the Surface Area of a Rectangular Solid
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.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
VofaRS=lwh

17. Solving a Linear Equation
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Do whatever is necessary to both sides to isolate the variable.
The whole number left over after division.
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

18. Knowing if an Integer is a Multiple of 5 or 10
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
Part=Percent x Whole
-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.
A(2)+b(2)=c(2)

19. Finding the Slope of a Line When Given Two Points on the Line
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Slope=change in y/change in x
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.

20. 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?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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

21. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
Multiply the exponents - (x^3)^4=x^3*4=x^12
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.

22. How do you know if an integer is a multiple of 3 or 9?
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.
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.
Do whatever is necessary to both sides to isolate the variable.

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

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24. Finding the Domain and Range of a Function
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

25. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
Two relatively prime numbers are integers that have no common factor other than 1.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
-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.

26. 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
Subtract the smallest from the largest and add 1
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

27. 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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
2(pie)r
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

28. Increasing and Decreasing a Number by a Certain Percentage
Get the absolute value equation by itself. Solve.
-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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.

29. Finding the GCF of Two or More Numbers
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

30. Characteristics of a Rectangle
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

31. Simplifying Square Roots
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

32. PEMDAS
Cancel factors common to the numerator and denominator.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
VofaC: (pie)r(2)h
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

33. Counting Consecutive Integers
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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Adjacent angles are supplementary - Vertical angles are equal

34. Finding the Missing Number in a Series When You are Given the 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.
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 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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

35. Finding the Median of a Set of Numbers
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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)
The value that falls in the middle of the set.

36. Calculating the Probability that an Event will Take Place
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

37. Properties of a 45-45-90 Triangle
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

38. Adding and Subtracting Roots
VofaC: (pie)r(2)h
Express them with a common denominator.
Just add or subtract the coefficients in front of the radicals.
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.

39. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Switch the numerator and denominator.

40. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
Average: Sum of the Terms/Number of the Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

41. Finding a Term in a Geometric Sequence
(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.
VofaC: (pie)r(2)h
Slope=change in y/change in x

42. 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?
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 value that appears the most often.
-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.
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.

43. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
2(pie)r
Express them with a common denominator.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

44. Properties of Similar Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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
Put each number in the original ratio over the sum of the numbers.
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.

45. Characteristics of a Parallelogram
Use the distributive property then combine the like terms.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
FOIL: First - Outer - Inner - Last... Combine Like Terms

46. Finding the Midpoint Between Two Points
Multiply the numerators and multiply the denominators.
Average the smallest and largest number
(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

47. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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
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.
Do whatever is necessary to both sides to isolate the variable.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

48. 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.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

49. Prime Factorization of a Number
Find a common denominator - then add or subtract the numerators.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
A(2)+b(2)=c(2)

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

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