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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. 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
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 whole number left over after division.
Do whatever is necessary to both sides to isolate the variable.

2. Solving a System of Equations
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.
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

3. Adding and Subtracting Polynomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Combine like terms.
-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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

4. Prime Factorization of a Number
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.
Put each number in the original ratio over the sum of the numbers.
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.

5. 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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

6. Solving a Proportion
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Cross multiply.
Multiply the numerators and multiply the denominators.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

7. Number of Groups - +1 Each Time
Express them with a common denominator.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

8. 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?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: 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.
Average: Sum of the Terms/Number of the Terms

9. Multiplying Binomials
Switch the numerator and denominator.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
FOIL: First - Outer - Inner - Last... Combine Like Terms

10. What value of x is not in the domain of the function f(x)=x-2/x-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.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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

11. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
VofaC: (pie)r(2)h

12. Multiplying Expressions with Exponents that Have a Common Base
The value that appears the most often.
Cross multiply.
The value that falls in the middle of the set.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

13. Multiply and Divide Positive and Negative Numbers
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.
The whole number left over after division.
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

14. Multiplying Fractions
(pie)r(squared)
Get the absolute value equation by itself. Solve.
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.
Multiply the numerators and multiply the denominators.

15. 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.
Slope=change in y/change in x
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
Put each number in the original ratio over the sum of the numbers.

16. What is the Triangle Inequality Theorem?
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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 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.

17. Adding and Subtracting 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.
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
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.

18. Expressing the Union and Intersection of Sets
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
Put each number in the original ratio over the sum of the numbers.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Four equal acute angles and four equal obtuse angles.

19. Raising a Power to a Power
Switch the numerator and denominator.
Four equal acute angles and four equal obtuse angles.
Multiply the exponents - (x^3)^4=x^3*4=x^12
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

20. Comparing the values of two or more Fractions
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)
Express them with a common denominator.
Put each number in the original ratio over the sum of the numbers.

21. Finding the Domain and Range of a Function
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Factor out and cancel all factors the numerator and denominator have in common.
Subtract the smallest from the largest and add 1

22. Adding a Positive Number to a Negative Number
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Switch the numerator and denominator.

23. Properties of the Interior and Exterior Angles of a Triangle
Find a common denominator - then add or subtract the numerators.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.

24. Finding the LCM of Two or More Numbers

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25. If the average of a - b - and 48 is 48 - what is the value of a + b?
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Probability: Number of Favorable Outcomes/Total Possible Outcomes

26. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Factor out and cancel all factors the numerator and denominator have in common.
Use the units to keep things straight - Snowfall inches/hours
Get the absolute value equation by itself. Solve.
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.

27. Finding the Midpoint Between Two Points
Multiply the numerators and multiply the denominators.
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
Put each number in the original ratio over the sum of the numbers.
(x1+x2)/2 -(y1+y2)/2

28. Finding the Median of a Set of Numbers
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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 value that falls in the middle of the set.
Cross multiply.

29. Properties of a 45-45-90 Triangle
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

30. Adding and Subtracting Fractions
A(2)+b(2)=c(2)
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.
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.
Find a common denominator - then add or subtract the numerators.

31. Convert From a Fraction to a Decimal - Vice Versa
Do whatever is necessary to both sides to isolate the variable.
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.
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.

32. Characteristics of a Parallelogram
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
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

33. Knowing if an Integer is a Multiple of 2 or 4
Cross multiply.
-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.
Get the absolute value equation by itself. Solve.

34. Knowing if an Integer is a Multiple of 5 or 10
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Cancel factors common to the numerator and denominator.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
-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.

35. Factoring a Polynomial ('FOIL in Reverse')
-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.
(pie)r(squared)
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

36. Finding the Slope When Given an Equation of a Line
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

37. What are Two Special Pythagorean Triples?

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38. Increasing and Decreasing a Number by a Certain Percentage
(x1+x2)/2 -(y1+y2)/2
-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.
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.
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.

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

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40. Finding the Rate of Speed
Two relatively prime numbers are integers that have no common factor other than 1.
Use the formula distance=rate*time and its variations to help in this question.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
(pie)r(squared)

41. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

42. If 3(3x)=9(x+2) - what is the value of x?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.

43. Average Rate and How Do You Find It
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

44. Simplifying Square Roots
Average: Sum of the Terms/Number of the Terms
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
-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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

45. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
A(2)+b(2)=c(2)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

46. Finding the Sum of the Interior Angles of a Polygon
The value that falls in the middle of the set.
Multiply the numerators and multiply the denominators.
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

47. Counting the Total Number of Possibilities for Several Events to Occur
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.
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 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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

48. Converting from an Improper Fraction to a Mixed Number
Factor out and cancel all factors the numerator and denominator have in common.
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 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.
Find a common denominator - then add or subtract the numerators.

49. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
-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.
Find a common denominator - then add or subtract the numerators.
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.

50. Finding the Mode of a Set of Numbers
The value that appears the most often.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Do whatever is necessary to both sides to isolate the variable.
Two relatively prime numbers are integers that have no common factor other than 1.