SAT Math

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• Answer 50 questions in 15 minutes.
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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 positive difference between the answers to the equation 35+x(2)=12x?

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2. Finding a Term in a Geometric Sequence
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.


3. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Switch the numerator and denominator.
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.
-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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


4. Finding the Midpoint Between Two Points
Four equal acute angles and four equal obtuse angles.
The whole number left over after division.
(x1+x2)/2 -(y1+y2)/2
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


5. Finding the Area of a Triangle

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6. Factoring the Difference of Two Squares
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
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.


7. If 3(3x)=9(x+2) - what is the value of x?
Cross multiply.
Express them with a common denominator.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
The whole number left over after division.


8. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
(pie)r(squared)


9. PEMDAS
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
FOIL: First - Outer - Inner - Last... Combine Like Terms


10. 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.
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.


11. Quickly Finding the Average of a Series of Evenly Spaced Numbers
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Average the smallest and largest number
-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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


12. Knowing if an Integer is a Multiple of 2 or 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.
2(pie)r
Do whatever is necessary to both sides to isolate the variable.
FOIL: First - Outer - Inner - Last... Combine Like Terms


13. 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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to 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.
Isolate the radical expression and use the standard rules of algebra.


14. Counting the Total Number of Possibilities for Several Events to Occur
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.


15. Finding the Area of a Sector

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16. Finding the Mode of a Set of Numbers
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The value that appears the most often.
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
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


17. Calculating the Probability that an Event will Take Place
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Part=Percent x Whole
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Slope=change in y/change in x


18. Finding the Sum of the Interior Angles of a Polygon
Subtract the smallest from the largest and add 1
Sum: Average x Number of Terms
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


19. Characteristics of a Rectangle
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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


20. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
Use the formula distance=rate*time and its variations to help in this question.


21. Finding the Median of a Set of Numbers
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
The value that falls in the middle of the set.
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.
The value that appears the most often.


22. What is the Triangle Inequality Theorem?
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.
Isolate the radical expression and use the standard rules of algebra.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.


23. Finding the LCM of Two or More Numbers

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24. Finding the Volume of a Cylinder
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.
Cancel factors common to the numerator and denominator.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
VofaC: (pie)r(2)h


25. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
Part=Percent x Whole
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 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


26. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


27. Converting from part-to-part ratios to part-to-whole ratios
Average: Sum of the Terms/Number of the Terms
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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 each number in the original ratio over the sum of the numbers.


28. General Procedure for Multiplying Polynomials
Sum: Average x Number of Terms
Use the distributive property then combine the like terms.
Slope=change in y/change in x
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


29. Finding the Missing Number in a Series When You are Given the Average
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
Find a common denominator - then add or subtract the numerators.


30. If the average of a - b - and 48 is 48 - what is the value of a + b?
(x1+x2)/2 -(y1+y2)/2
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


31. Properties of the Interior and Exterior Angles of a Triangle
Slope=change in y/change in x
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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 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.


32. If r#t=t(r)-r(t) - then what is 4#3?
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.
Use the units to keep things straight - Snowfall inches/hours
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


33. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
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.


34. 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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.


35. Solving a Linear Equation
A(2)+b(2)=c(2)
The whole number left over after division.
Do whatever is necessary to both sides to isolate the variable.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


36. 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.
Put each number in the original ratio over the sum of the numbers.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use the formula distance=rate*time and its variations to help in this question.


37. Multiplying Expressions with Exponents that Have a Common Base
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Get the absolute value equation by itself. Solve.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


38. 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?
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.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


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

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40. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
Slope=change in y/change in x
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


41. Formula Used to Find Percent
(pie)r(squared)
Part=Percent x Whole
Use simple numbers like 1 and 2 and see what happens.
Do whatever is necessary to both sides to isolate the variable.


42. Adding and Subtracting Fractions
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Find a common denominator - then add or subtract the numerators.


43. Determining Absolute Value of a Number
2(pie)r
VofaRS=lwh
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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


44. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Slope=change in y/change in x
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.


45. Converting from an Improper Fraction to a Mixed Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
(x1+x2)/2 -(y1+y2)/2
(pie)r(squared)
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.


46. Multiplying Fractions
Part=Percent x Whole
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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 numerators and multiply the denominators.


47. Properties of Similar Triangles
Isolate the radical expression and use the standard rules of algebra.
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
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


48. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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
The value that falls in the middle of the set.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


49. Definition of a Rational Number
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 square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Just add or subtract the coefficients in front of the radicals.
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. 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%
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
(x1+x2)/2 -(y1+y2)/2
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.