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

2. Dividing Fractions
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

3. An Important Property of a Line Tangent to a Circle
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

4. Increasing and Decreasing a Number by a Certain Percentage
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
-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.
Cross multiply.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

5. If the average of a - b - and 48 is 48 - what is the value of a + b?
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.
2(pie)r
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

6. 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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
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.

7. PEMDAS
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Subtract the smallest from the largest and add 1
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

8. Knowing if an Integer is a Multiple of 5 or 10
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
-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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

9. Knowing if an Integer is a Multiple of 2 or 4
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
-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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

10. Raising a Power to a Power
-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
Isolate the radical expression and use the standard rules of algebra.
Multiply the exponents - (x^3)^4=x^3*4=x^12

11. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

12. What types of angles are formed when two lines intersect?
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
Get the absolute value equation by itself. Solve.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

13. Definition of Remainder
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
The whole number left over after division.
Switch the numerator and denominator.

14. Finding the Missing Number in a Series When You are Given the 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.
Use the units to keep things straight - Snowfall inches/hours
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.

15. Adding and Subtracting Fractions
Isolate the radical expression and use the standard rules of algebra.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Find a common denominator - then add or subtract the numerators.
2(pie)r

16. Scalene - Isosceles - and Equilateral Triangles
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.
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.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

17. Factoring a Polynomial ('FOIL in Reverse')
Sum: Average x Number of Terms
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Adjacent angles are supplementary - Vertical angles are equal
A(2)+b(2)=c(2)

18. Finding the Rate of Speed
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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 formula distance=rate*time and its variations to help in this question.
Get the absolute value equation by itself. Solve.

19. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
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.
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Cancel factors common to the numerator and denominator.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

21. Finding the Area of a Triangle

22. What are Two Special Pythagorean Triples?

23. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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
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.
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.

24. Finding the GCF of Two or More Numbers
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

25. If r#t=t(r)-r(t) - then what is 4#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.
Average: Sum of the Terms/Number of the Terms
Four equal acute angles and four equal obtuse angles.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

26. Evaluating an Algebraic 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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.

27. Direct Variation and Inverse Variation
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.
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 relatively prime numbers are integers that have no common factor other than 1.

28. Solving a Proportion
Use the formula distance=rate*time and its variations to help in this question.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Subtract the smallest from the largest and add 1
Cross multiply.

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

30. Multiplying Fractions
Cancel factors common to the numerator and denominator.
Multiply the numerators and multiply the denominators.
Part=Percent x Whole
Two relatively prime numbers are integers that have no common factor other than 1.

31. Finding the Midpoint Between Two Points
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
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.
(x1+x2)/2 -(y1+y2)/2

32. Calculating the Probability that an Event will Take Place
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

33. 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.
-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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

34. Number of Groups - +1 Each Time
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Factor out and cancel all factors the numerator and denominator have in common.
Two relatively prime numbers are integers that have no common factor other than 1.

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

36. Converting From a Mixed Number to an Improper Fraction
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.
A(2)+b(2)=c(2)
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

37. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Part=Percent x Whole
Plug in the given values for the unknowns and calculate according to PEMDAS.
Get the absolute value equation by itself. Solve.

38. Converting from part-to-part ratios to part-to-whole ratios
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.
-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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

39. General Procedure for Multiplying Polynomials
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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

40. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Just add or subtract the coefficients in front of the radicals.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Average: Sum of the Terms/Number of the Terms
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

41. 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?
Multiply the exponents - (x^3)^4=x^3*4=x^12
-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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

42. If 3(3x)=9(x+2) - what is the value of x?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Use simple numbers like 1 and 2 and see what happens.
The whole number left over after division.

43. Finding the Slope When Given an Equation of a Line
Part=Percent x Whole
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Just add or subtract the coefficients in front of the radicals.

44. Finding the Sum of the Interior Angles of a Polygon
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.
Find a common denominator - then add or subtract the numerators.
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

45. Multiplying and Dividing Roots
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.
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.
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.
Just add or subtract the coefficients in front of the radicals.

46. Average Rate and How Do You Find It
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

47. Solving a Problem Involving Rates
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Use the units to keep things straight - Snowfall inches/hours
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

48. Definition of an Irrational Number
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The value that falls in the middle of the set.

49. If (Square Root: x-1)+5=12 - what is the value of x/2?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

50. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
VofaRS=lwh
Slope=change in y/change in x
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24