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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. Multiplying and Dividing Roots
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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
Slope=change in y/change in x

2. Simplifying a Fraction to Lowest Terms
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
VofaRS=lwh
Factor out and cancel all factors the numerator and denominator have in common.
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. Solving a Linear Equation
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
-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.
Do whatever is necessary to both sides to isolate the variable.
(pie)r(squared)

4. Finding the Area of a Circle
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
(pie)r(squared)
2(pie)r
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

5. Converting from part-to-part ratios to part-to-whole ratios
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Put each number in the original ratio over the sum of the numbers.
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.

6. Simplifying an Algebraic Equation
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Cancel factors common to the numerator and denominator.
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.

7. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Average the smallest and largest number
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.

8. Finding the GCF of Two or More 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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

9. Properties of a 30-60-90 Triangle
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

10. Adding and Subtracting Fractions
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.
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.
Find a common denominator - then add or subtract the numerators.
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.

11. Finding the Reciprocal of a Fraction
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Switch the numerator and denominator.
Average: Sum of the Terms/Number of the Terms

12. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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 units to keep things straight - Snowfall inches/hours
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

13. 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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Get the absolute value equation by itself. Solve.
The whole number left over after division.

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

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15. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
Factor out and cancel all factors the numerator and denominator have in common.
-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.
-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.

16. If r#t=t(r)-r(t) - then what is 4#3?
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 - substitute for the variable. Then evaluate the expression using the correct order of operations.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

17. What is the Triangle Inequality Theorem?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Put each number in the original ratio over the sum of the numbers.

18. Finding the Sum of the Interior Angles of a Polygon
Use the distributive property then combine the like terms.
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
Subtract the smallest from the largest and add 1
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

19. Adding and Subtracting Roots
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Just add or subtract the coefficients in front of the radicals.
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

20. Average Rate and How Do You Find It
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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
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

21. Knowing if an Integer is a Multiple of 5 or 10
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Isolate the radical expression and use the standard rules of algebra.

22. Finding the Missing Number in a Series When You are Given the Average
Cross multiply.
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.
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.
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.

23. 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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Find a common denominator - then add or subtract the numerators.

24. Finding the Rate of Speed
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Part=Percent x Whole
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use the formula distance=rate*time and its variations to help in this question.

25. 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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Cross multiply.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

26. 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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.

27. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
VofaC: (pie)r(2)h

28. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

29. Scalene - Isosceles - and Equilateral Triangles
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.
Just add or subtract the coefficients in front of the radicals.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Cross multiply.

30. Characteristics of a Rectangle
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

31. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use simple numbers like 1 and 2 and see what happens.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

32. Multiplying Monomials
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

33. Converting From a Mixed Number to an Improper Fraction
Express them with a common denominator.
Do whatever is necessary to both sides to isolate the variable.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.

34. Multiplying Binomials
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
(pie)r(squared)
FOIL: First - Outer - Inner - Last... Combine Like Terms

35. Finding the Slope When Given an Equation of a Line
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
Put each number in the original ratio over the sum of the numbers.

36. Multiplying Fractions
Adjacent angles are supplementary - Vertical angles are equal
Multiply the numerators and multiply the denominators.
-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.
Subtract the smallest from the largest and add 1

37. Solving a Proportion
The value that falls in the middle of the set.
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Cross multiply.

38. Finding the Midpoint Between Two Points
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

39. Setting Up a Ratio
Use the units to keep things straight - Snowfall inches/hours
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
-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.

40. Numbers that are Relatively Prime
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Cross multiply.

41. If (Square Root: x-1)+5=12 - what is the value of x/2?
The value that appears the most often.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

42. Finding the Distance Between Two Points on a Coordinate Graph
(x1+x2)/2 -(y1+y2)/2
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
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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

43. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
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.
VofaC: (pie)r(2)h
Switch the numerator and denominator.

44. Finding the Median of a Set of Numbers
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
The value that falls in the middle of the set.
The value that appears the most often.

45. Finding the Area of a Triangle

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46. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

47. What value of x is not in the domain of the function f(x)=x-2/x-3?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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
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.

48. Finding the Domain and Range of a Function
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
VofaC: (pie)r(2)h
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.

49. Finding the Circumference of a Circle
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
2(pie)r
Switch the numerator and denominator.

50. Finding the Volume of a Rectangular Solid
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 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
VofaRS=lwh
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.