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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. Calculating Negative Exponents and Radical Exponents
-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.
-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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Put the equation into y=mx+b-- in which case b is the y-intercept.

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

3. Finding the Missing Number in a Series When You are Given the Average
Find a common denominator - then add or subtract the numerators.
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.
-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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

4. Solving an Inequality
A(2)+b(2)=c(2)
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
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.

5. 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
Cross multiply.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
-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. Prime Factorization of a Number
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Slope=change in y/change in x
Put the equation into y=mx+b-- in which case b is the y-intercept.

7. Convert From a Fraction to a Decimal - Vice Versa
Do whatever is necessary to both sides to isolate the variable.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
A(2)+b(2)=c(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.

8. Finding the Area of a Sector

9. Characteristics of a Square
A(2)+b(2)=c(2)
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.
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.

10. What is the Triangle Inequality Theorem?
Use the units to keep things straight - Snowfall inches/hours
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.
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.

11. Finding the Rate of Speed
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.
Average the smallest and largest number
Four equal acute angles and four equal obtuse angles.
Use the formula distance=rate*time and its variations to help in this question.

12. 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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
VofaRS=lwh

13. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
Express them with a common 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.
-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.

14. Formula to Find Average
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.
Average: Sum of the Terms/Number of the Terms
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

15. If 4(x(2)-10x+25) - then what is the value of x?
Cross multiply.
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

16. 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?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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 the units to keep things straight - Snowfall inches/hours

17. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

18. Finding the LCM of Two or More Numbers

19. Multiplying Binomials
Part=Percent x Whole
FOIL: First - Outer - Inner - Last... Combine Like Terms
Express them with a common denominator.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

20. How do you know if an integer is a multiple of 3 or 9?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
A(2)+b(2)=c(2)
The value that appears the most often.

21. 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
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Switch the numerator and denominator.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

22. Finding the Slope When Given an Equation of a Line
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.
The whole number left over after division.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

23. Finding the Surface Area of a Rectangular Solid
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Use simple numbers like 1 and 2 and see what happens.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

24. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
(pie)r(squared)
Average the smallest and largest number
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.

25. Formula Used to Find Percent
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
Part=Percent x Whole

26. Evaluating an Algebraic Expression
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

27. Average Rate and How Do You Find It
Sum: Average x Number of Terms
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
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

28. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
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
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
VofaC: (pie)r(2)h

29. If the average of a - b - and 48 is 48 - what is the value of a + b?
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

30. Characteristics of a Rectangle
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Put the equation into y=mx+b-- in which case b is the y-intercept.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

31. 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
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.
VofaC: (pie)r(2)h
Do whatever is necessary to both sides to isolate the variable.

32. If r#t=t(r)-r(t) - then what is 4#3?
The whole number left over after division.
Combine like terms.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

33. Multiplying Monomials
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
The value that appears the most often.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

34. Multiply and Divide Positive and Negative Numbers
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Get the absolute value equation by itself. Solve.
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

35. Finding the Reciprocal of a Fraction
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Switch the numerator and denominator.

36. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

37. Properties of the Interior and Exterior Angles of a Triangle
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.
Use the distributive property then combine the like terms.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

38. Converting From a Mixed Number to an Improper Fraction
2(pie)r
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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 the whole number part by the denominator - then add the numerator. Keep the same denominator.

39. Counting the Total Number of Possibilities for Several Events to Occur
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.
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.
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 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.

40. Solving a Problem Involving Rates
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Use the units to keep things straight - Snowfall inches/hours
Use simple numbers like 1 and 2 and see what happens.
Part=Percent x Whole

41. Finding a Term in a Geometric Sequence
(pie)r(squared)
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.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

42. Characteristics of a Parallelogram
Isolate the radical expression and use the standard rules of algebra.
Adjacent angles are supplementary - Vertical angles are equal
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

43. Solving a System of Equations
Slope=change in y/change in x
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

44. Expressing the Union and Intersection of Sets
Express them with a common denominator.
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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

45. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Two relatively prime numbers are integers that have no common factor other than 1.
Combine like terms.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

46. Finding the Circumference of a Circle
Get the absolute value equation by itself. Solve.
Cancel factors common to the numerator and denominator.
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.
2(pie)r

47. 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.
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.
Put each number in the original ratio over the sum of the numbers.

48. 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?
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Sum: Average x Number of Terms
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

49. Adding and Subtracting Polynomials
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Combine like terms.

50. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
2(pie)r
Use simple numbers like 1 and 2 and see what happens.
Subtract the smallest from the largest and add 1
Put the equation into y=mx+b-- in which case b is the y-intercept.