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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. Properties of Similar Triangles
Sum: Average x Number of Terms
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
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

2. Expressing the Union and Intersection of Sets
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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
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
Switch the numerator and denominator.

3. If 3(3x)=9(x+2) - what is the value of x?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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
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

4. Comparing the values of two or more Fractions
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Express them with a common denominator.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

5. 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.
Switch the numerator and denominator.
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

6. Convert From a Fraction to a Decimal - Vice Versa
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
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^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.

7. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
VofaRS=lwh
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Two relatively prime numbers are integers that have no common factor other than 1.
Use simple numbers like 1 and 2 and see what happens.

8. 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?
(pie)r(squared)
Average the smallest and largest number
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.
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.

9. Finding the Volume of a Rectangular Solid
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
VofaRS=lwh
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

10. Finding the Rate of Speed
Part=Percent x Whole
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.
Use the formula distance=rate*time and its variations to help in this question.
Isolate the radical expression and use the standard rules of algebra.

11. If (Square Root: x-1)+5=12 - what is the value of x/2?
-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.
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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
The value that falls in the middle of the set.

12. If 4(x(2)-10x+25) - then what is the value of x?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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
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
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.

13. Finding the Circumference of a Circle
2(pie)r
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.
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.

14. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

15. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
Average the smallest and largest number
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

16. Formula Used to Find Percent
Part=Percent x Whole
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The value that appears the most often.

17. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

18. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
(pie)r(squared)
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 simple numbers like 1 and 2 and see what happens.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

19. Dividing Fractions
-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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
VofaC: (pie)r(2)h

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

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

22. Finding the Midpoint Between Two Points
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 the smallest and largest number
A(2)+b(2)=c(2)
(x1+x2)/2 -(y1+y2)/2

23. Prime Factorization of a Number
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use the units to keep things straight - Snowfall inches/hours
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

24. Finding the Mode of a Set of Numbers
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The value that appears the most often.
Four equal acute angles and four equal obtuse angles.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

25. Counting Consecutive Integers
-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.
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

26. 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
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

27. Finding the Median of a Set of Numbers
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.
The value that falls in the middle of the set.
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

28. Converting from part-to-part ratios to part-to-whole ratios
Cancel factors common to the numerator and denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Put each number in the original ratio over the sum of the numbers.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

29. What is the Triangle Inequality Theorem?
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.
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.
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

30. Simplifying Square Roots
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.
-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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

31. Number of Groups - +1 Each Time
Adjacent angles are supplementary - Vertical angles are equal
Express them with a common denominator.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

32. Quickly Finding the Average of a Series of Evenly Spaced Numbers
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Average the smallest and largest number
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

33. Finding the Area of a Circle
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
(pie)r(squared)
Multiply the exponents - (x^3)^4=x^3*4=x^12
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

34. 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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

35. Finding a Term in a Geometric Sequence
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use simple numbers like 1 and 2 and see what happens.
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

36. Definition of Remainder
Sum: Average x Number of Terms
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The whole number left over after division.

37. 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
-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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

38. Finding the Length of an Arc in a Circle

39. Factoring a Polynomial ('FOIL in Reverse')
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
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the numerators and multiply the denominators.

40. How do you know if an integer is a multiple of 3 or 9?
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.
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

41. Scalene - Isosceles - and Equilateral Triangles
Express them with a common denominator.
The value that appears the most often.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.

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

43. Adding and Subtracting Monomials
Use the units to keep things straight - Snowfall inches/hours
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
(x1+x2)/2 -(y1+y2)/2
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

44. If x(2)=7x+18 - what is the positive value of x?
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Subtract the smallest from the largest and add 1
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Factor out and cancel all factors the numerator and denominator have in common.

45. Converting from an Improper Fraction to a Mixed Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
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 - 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.

46. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Use simple numbers like 1 and 2 and see what happens.

47. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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

48. Definition of an Irrational Number
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

49. 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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Express them with a common denominator.
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

50. Multiply and Divide Positive and Negative Numbers
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
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