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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. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

2. Scalene - Isosceles - and Equilateral Triangles
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 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
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.
Four equal acute angles and four equal obtuse angles.

3. Multiplying and Dividing Roots
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

4. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Probability: Number of Favorable Outcomes/Total Possible Outcomes
VofaRS=lwh

5. 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.
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Cross multiply.

6. Determining Absolute Value of a Number
Combine like terms.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The value that falls in the middle of the set.

7. Factoring a Polynomial ('FOIL in Reverse')
Use simple numbers like 1 and 2 and see what happens.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

8. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
Combine like terms.
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.

9. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
-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.
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

10. What value of x is not in the domain of the function f(x)=x-2/x-3?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)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
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.
2(pie)r

11. Finding the Volume of a Rectangular Solid
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
VofaRS=lwh
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

12. Properties of Similar Triangles
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.
Use simple numbers like 1 and 2 and see what happens.
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

13. Characteristics of a Square
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.
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

14. Finding the Area of a Triangle

15. Definition of a Rational Number
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

16. Finding the Midpoint Between Two Points
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Four equal acute angles and four equal obtuse angles.
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.
(x1+x2)/2 -(y1+y2)/2

17. Dividing Expressions with Exponents that Have a Common Base
Slope=change in y/change in x
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Sum: Average x Number of Terms

18. Numbers that are Relatively Prime
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Two relatively prime numbers are integers that have no common factor other than 1.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

19. If x(2)=7x+18 - what is the positive 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
Two relatively prime numbers are integers that have no common factor other than 1.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

20. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
Slope=change in y/change in x
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.

21. Properties of a 30-60-90 Triangle
Express them with a common denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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

22. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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 equal acute angles and four equal obtuse angles.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

23. What are Two Special Pythagorean Triples?

24. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
FOIL: First - Outer - Inner - Last... Combine 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.
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.

25. Finding the Missing Number in a Series When You are Given the Average
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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 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.
2(pie)r

26. Finding the Area of a Circle
The whole number left over after division.
Four equal acute angles and four equal obtuse angles.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
(pie)r(squared)

27. If 4(x(2)-10x+25) - then what is the value of x?
The value that appears the most often.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.

28. Solving a Proportion
Adjacent angles are supplementary - Vertical angles are equal
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Cross multiply.

29. General Procedure for Multiplying Polynomials
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Use the distributive property then combine the like terms.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Four equal acute angles and four equal obtuse angles.

30. Increasing and Decreasing a Number by a Certain Percentage
Two relatively prime numbers are integers that have no common factor other than 1.
-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 exponents and keep the same base.y^13/y^8=y^13-8=y^5
Combine like terms.

31. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
-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.

32. Calculating Negative Exponents and Radical Exponents
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.
Combine like terms.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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

33. What is the Pythagorean Theorem?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Find a common denominator - then add or subtract the numerators.
Cancel factors common to the numerator and denominator.
A(2)+b(2)=c(2)

34. Definition of Remainder
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 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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

35. Finding the Volume of a Cylinder
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
VofaC: (pie)r(2)h

36. What is the Triangle Inequality Theorem?
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.
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.

37. Counting the Total Number of Possibilities for Several Events to Occur
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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 whole number left over after division.

38. Counting Consecutive Integers
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
-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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

39. 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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Sum: Average x Number of Terms

40. Multiply and Divide Positive and Negative Numbers
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.
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
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

41. Definition of an Integer
Use the distance formula: d=(square root over) (x2-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.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

42. Adding and Subtracting Roots
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Just add or subtract the coefficients in front of the radicals.

43. Multiplying Expressions with Exponents that Have a Common Base
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
-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. Factoring the Difference of Two Squares
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Slope=change in y/change in x
A(2)+b(2)=c(2)

45. 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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

46. Direct Variation and Inverse Variation
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.
Use simple numbers like 1 and 2 and see what happens.
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
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

47. Finding the Domain and Range of a Function
Four equal acute angles and four equal obtuse angles.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
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.

48. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
-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.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

49. Converting From a Mixed Number to an Improper Fraction
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

50. Finding the Slope When Given an Equation of a Line
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
(pie)r(squared)
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
The value that falls in the middle of the set.