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SAT Math

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. Difference Between a Factor and a Multiple
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Use the units to keep things straight - Snowfall inches/hours
-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.

2. Solving a Proportion
Do whatever is necessary to both sides to isolate the variable.
Switch the numerator and denominator.
Cross multiply.
Just add or subtract the coefficients in front of the radicals.

3. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Use the units to keep things straight - Snowfall inches/hours
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.

4. General Procedure for Multiplying Polynomials
Sum: Average x Number of Terms
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Use the distributive property then combine the like terms.

5. 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?
(pie)r(squared)
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Adjacent angles are supplementary - Vertical angles are equal
-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.

6. Simplifying an Algebraic Equation
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Cancel factors common to the numerator and denominator.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.

7. 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
2(pie)r
Adjacent angles are supplementary - Vertical angles are equal
Multiply the exponents - (x^3)^4=x^3*4=x^12

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

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9. Finding the Slope of a Line When Given Two Points on the Line
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Slope=change in y/change in x
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

10. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Combine like terms.
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

11. Multiplying Binomials
Subtract the smallest from the largest and add 1
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

12. What is the Pythagorean Theorem?
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
A(2)+b(2)=c(2)
2(pie)r
Use the distributive property then combine the like terms.

13. Formula to Find Average
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Average: Sum of the Terms/Number of the Terms

14. Adding and Subtracting Fractions
Multiply the exponents - (x^3)^4=x^3*4=x^12
Find a common denominator - then add or subtract the numerators.
Multiply the numerators and multiply the denominators.
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 Midpoint Between Two Points
-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.
(x1+x2)/2 -(y1+y2)/2
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

16. If x(2)=7x+18 - what is the positive value of x?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

17. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
-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.
Subtract the smallest from the largest and add 1
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

18. Definition of Remainder
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The whole number left over after division.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

19. Comparing the values of two or more Fractions
Express them with a common denominator.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Four equal acute angles and four equal obtuse angles.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

20. Properties of the Interior and Exterior Angles of a Triangle
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
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.

21. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Find a common denominator - then add or subtract the numerators.
Get the absolute value equation by itself. Solve.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

22. Finding the Mode of a Set of Numbers
The value that appears the most often.
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.
Two relatively prime numbers are integers that have no common factor other than 1.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

23. Definition of an Irrational Number
-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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

24. Adding and Subtracting Polynomials
Use the distributive property then combine the like terms.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Combine like terms.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

25. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Average: Sum of the Terms/Number of the Terms
-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.
VofaRS=lwh
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

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

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27. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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 radical expression and use the standard rules of algebra.

28. Finding the Area of a Triangle

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29. If the average of a - b - and 48 is 48 - what is the value of a + b?
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

30. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Sum: Average x Number of Terms
Use the formula distance=rate*time and its variations to help in this question.

31. Solving a Radical Equation
Multiply the exponents - (x^3)^4=x^3*4=x^12
Two relatively prime numbers are integers that have no common factor other than 1.
Isolate the radical expression and use the standard rules of algebra.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

32. 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.
Part=Percent x Whole
Plug in the given values for the unknowns and calculate according to PEMDAS.
Combine like terms.

33. Simplifying Square Roots
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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 out the perfect squares under the radical - take their square roots - and put the result in front.

34. Converting From a Mixed Number to an Improper Fraction
Switch the numerator and denominator.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Use the units to keep things straight - Snowfall inches/hours

35. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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.
Just add or subtract the coefficients in front of the radicals.
Two relatively prime numbers are integers that have no common factor other than 1.

36. Finding the Circumference of a Circle
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
2(pie)r
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Subtract the smallest from the largest and add 1

37. Finding the Volume of a Cylinder
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
VofaC: (pie)r(2)h

38. Finding the Length of an Arc in a Circle

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39. Number of Groups - +1 Each Time
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
(pie)r(squared)
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

40. Calculating Negative Exponents and Radical Exponents
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

41. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

42. Properties of a 45-45-90 Triangle
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
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Two relatively prime numbers are integers that have no common factor other than 1.

43. An Important Property of a Line Tangent to a Circle
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
-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.

44. 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
-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.
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

45. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

46. If 4(x(2)-10x+25) - then 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
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.

47. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

48. Convert From a Fraction to a Decimal - Vice Versa
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.

49. Sale Price of a Jacket Marked Down 30% Each Week for 3 Weeks - What % of the Original Price is the Cost of the Jacket After the 3 Week Sale Period
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.
Use the formula distance=rate*time and its variations to help in this question.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Just add or subtract the coefficients in front of the radicals.

50. How do you know if an integer is a multiple of 3 or 9?
-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.
Get the absolute value equation by itself. Solve.
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.
Part=Percent x Whole