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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. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Find a common denominator - then add or subtract the numerators.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

2. Number of Groups - +1 Each Time
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Average: Sum of the Terms/Number of the Terms

3. What types of angles are formed when two lines intersect?
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Adjacent angles are supplementary - Vertical angles are equal
Find a common denominator - then add or subtract the numerators.
The value that appears the most often.

4. 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?
Cancel factors common to the numerator and denominator.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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 two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

5. If the average of a - b - and 48 is 48 - what is the value of a + b?
-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.
-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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

6. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

7. Definition of Remainder
Subtract the smallest from the largest and add 1
The whole number left over after division.
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 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.

8. Expressing the Union and Intersection of Sets
Plug in the given values for the unknowns and calculate according to PEMDAS.
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
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

9. Multiplying Monomials
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

10. How do you know if an integer is a multiple of 3 or 9?
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
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.
Do whatever is necessary to both sides to isolate the variable.

11. PEMDAS
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
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

12. If (Square Root: x-1)+5=12 - what is the value of x/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
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 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.
Switch the numerator and denominator.

13. Finding the Reciprocal of a Fraction
-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.
Switch the numerator and 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.
-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.

14. Solving a Proportion
Just add or subtract the coefficients in front of the radicals.
Cross multiply.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Two relatively prime numbers are integers that have no common factor other than 1.

15. Finding the Length of an Arc in a Circle
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.
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
Factor out and cancel all factors the numerator and denominator have in common.

16. Finding the Slope of a Line When Given Two Points on the Line
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Slope=change in y/change in x
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.
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

17. Simplifying an Algebraic Equation
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Cancel factors common to the numerator and denominator.
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

18. Solving a Linear Equation
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.
-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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Do whatever is necessary to both sides to isolate the variable.

19. Direct Variation and Inverse Variation
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Average the smallest and largest number
Subtract the smallest from the largest and add 1
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

20. Factoring the Difference of Two Squares
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
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

21. Finding the LCM of Two or More Numbers
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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

22. What is the Pythagorean Theorem?
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
A(2)+b(2)=c(2)
Express them with a common denominator.
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.

23. Finding the Distance Between Two Points on a Coordinate Graph
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Plug in the given values for the unknowns and calculate according to PEMDAS.

24. 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.
Cross multiply.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

25. Dividing Fractions
Two relatively prime numbers are integers that have no common factor other than 1.
Switch the numerator and denominator.
Use the distributive property then combine the like terms.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

26. Finding the Volume of a Rectangular Solid
Switch the numerator and denominator.
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.
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
VofaRS=lwh

27. What are Two Special Pythagorean Triples?
Cross multiply.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use the formula distance=rate*time and its variations to help in this question.
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.

28. Adding and Subtracting Roots
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Subtract the smallest from the largest and add 1
Just add or subtract the coefficients in front of the radicals.
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

29. Converting from an Improper Fraction to a Mixed Number
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
Just add or subtract the coefficients in front of the radicals.
Four equal acute angles and four equal obtuse angles.

30. Finding the y-intercept When Given an Equation of a Line
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 equation into y=mx+b-- in which case b is the y-intercept.
The value that falls in the middle of the set.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

31. 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?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

32. Increasing and Decreasing a Number by a Certain Percentage
-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)
Two relatively prime numbers are integers that have no common factor other than 1.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

33. 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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Do whatever is necessary to both sides to isolate the variable.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

34. What Does Solving In Terms of Mean?
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Average: Sum of the Terms/Number of the Terms

35. Dividing Expressions with Exponents that Have a Common Base
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.

36. Solving an Inequality
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.
The value that falls in the middle of the set.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.

37. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Average: Sum of the Terms/Number of the Terms
(x1+x2)/2 -(y1+y2)/2
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

38. Finding the Area of a Triangle
Plug in the given values for the unknowns and calculate according to PEMDAS.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.

39. Finding the Volume of a Cylinder
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
VofaC: (pie)r(2)h
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Plug in the given values for the unknowns and calculate according to PEMDAS.

40. Finding the Surface Area of a Rectangular Solid
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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
(x1+x2)/2 -(y1+y2)/2

41. Difference Between a Factor and a Multiple
-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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

42. Convert From a Fraction to a Decimal - Vice Versa
Average: Sum of the Terms/Number of the Terms
Switch the numerator and denominator.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

43. If 4(x(2)-10x+25) - then what is the value of x?
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
The whole number left over after division.
VofaRS=lwh

44. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Use simple numbers like 1 and 2 and see what happens.

45. 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
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 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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

46. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Part=Percent x Whole
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

47. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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
Get the absolute value equation by itself. Solve.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

48. If r#t=t(r)-r(t) - then what is 4#3?
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%
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
FOIL: First - Outer - Inner - Last... Combine Like Terms

49. Knowing if an Integer is a Multiple of 2 or 4
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.
-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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
The value that falls in the middle of the set.

50. Finding the GCF of Two or More Numbers
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
-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.

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