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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. Finding the Circumference of a Circle
2(pie)r
-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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Two relatively prime numbers are integers that have no common factor other than 1.

2. Solving an Inequality
Use the formula distance=rate*time and its variations to help in this question.
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.
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 variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

3. Finding the Volume of a Cylinder
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
VofaC: (pie)r(2)h
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.

4. Increasing and Decreasing a Number by a Certain Percentage
-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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

5. Solving a Problem Involving Rates
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.
Use the units to keep things straight - Snowfall inches/hours
Multiply the exponents - (x^3)^4=x^3*4=x^12
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

6. If r#t=t(r)-r(t) - then what is 4#3?
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

7. Properties of Similar Triangles
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

8. Average Rate and How Do You Find It
Use the units to keep things straight - Snowfall inches/hours
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 simple numbers like 1 and 2 and see what happens.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

9. 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
Factor out and cancel all factors the numerator and denominator have in common.
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.
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.

10. Raising a Power to a Power
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Multiply the exponents - (x^3)^4=x^3*4=x^12
-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.

11. Adding a Positive Number to a Negative Number
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Just add or subtract the coefficients in front of the radicals.

12. Finding the Sum of the Interior Angles of a Polygon
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
(pie)r(squared)
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

13. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
A(2)+b(2)=c(2)
-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.
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.

14. Setting Up a Ratio
Find a common denominator - then add or subtract the numerators.
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
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

15. Multiplying Fractions
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Multiply the numerators and multiply the denominators.

16. Formula Used to Find Percent
Switch the numerator and denominator.
Part=Percent x Whole
Combine like terms.
-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.

17. What are Two Special Pythagorean Triples?

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18. Characteristics of a Square
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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

19. Adding and Subtracting Monomials
Plug in the given values for the unknowns and calculate according to PEMDAS.
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
Express them with a common denominator.

20. 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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
-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.

21. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
VofaC: (pie)r(2)h
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.

22. Finding the Rate of Speed
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.
Use the formula distance=rate*time and its variations to help in this question.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

23. Finding the Midpoint Between Two Points
Plug in the given values for the unknowns and calculate according to PEMDAS.
(x1+x2)/2 -(y1+y2)/2
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

24. Converting from an Improper Fraction to a Mixed Number
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.
Do whatever is necessary to both sides to isolate the variable.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

25. Knowing if an Integer is a Multiple of 5 or 10
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.
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.
-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.
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.

26. Difference Between a Factor and a Multiple
-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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

27. Adding and Subtracting Roots
-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.
Just add or subtract the coefficients in front of the radicals.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

28. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Plug in the given values for the unknowns and calculate according to PEMDAS.
(pie)r(squared)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Put the equation into y=mx+b-- in which case b is the y-intercept.

29. Characteristics of a Parallelogram
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
-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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

30. Definition of Remainder
Four equal acute angles and four equal obtuse angles.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
The whole number left over after division.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

31. Multiplying Monomials
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
(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

32. Knowing if an Integer is a Multiple of 2 or 4
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Use the distributive property then combine the like terms.
-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.
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

33. Formula to Find Average
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Average: Sum of the Terms/Number of the Terms
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.

34. Prime Factorization of a Number
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

35. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

36. How do you know if an integer is a multiple of 3 or 9?
Put the equation into y=mx+b-- in which case b is the y-intercept.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
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.

37. 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
Put each number in the original ratio over the sum of the numbers.
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

38. Converting From a Mixed Number to an Improper Fraction
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

39. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
A(2)+b(2)=c(2)
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

40. Finding the Missing Number in a Series When You are Given the Average
Express them with a common denominator.
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.
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.
Factor out and cancel all factors the numerator and denominator have in common.

41. 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.
A(2)+b(2)=c(2)
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Put each number in the original ratio over the sum of the numbers.

42. Finding the Slope When Given an Equation of a Line
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Sum: Average x Number of Terms
Slope=change in y/change in x
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

43. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Put the equation into y=mx+b-- in which case b is the y-intercept.
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
-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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

44. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
The whole number left over after division.

45. What types of angles are formed when a transversal cross parallel lines?
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
Four equal acute angles and four equal obtuse angles.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

46. Properties of a 45-45-90 Triangle
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.
Factor out and cancel all factors the numerator and denominator have in common.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

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

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48. What is the Triangle Inequality Theorem?
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.
Combine like 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.
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.

49. Comparing the values of two or more Fractions
VofaRS=lwh
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.
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
Express them with a common denominator.

50. An Important Property of a Line Tangent to a Circle
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Use simple numbers like 1 and 2 and see what happens.
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.