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. 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?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


2. PEMDAS
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
Do whatever is necessary to both sides to isolate the variable.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Isolate the radical expression and use the standard rules of algebra.


3. Finding the Domain and Range of a Function
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


4. Characteristics of a Rectangle
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.
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


5. Finding the Reciprocal of a Fraction
FOIL: First - Outer - Inner - Last... Combine Like Terms
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Switch the numerator and denominator.


6. If x(2)=7x+18 - what is the positive value of x?
Cancel factors common to the numerator and denominator.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Put the equation into y=mx+b-- in which case b is the y-intercept.


7. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
Find a common denominator - then add or subtract the numerators.
The value that appears the most often.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


8. Solving a Proportion
Cross multiply.
Use the units to keep things straight - Snowfall inches/hours
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


9. Finding the Circumference of a Circle
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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
2(pie)r
Average the smallest and largest number


10. Scalene - Isosceles - and Equilateral Triangles
-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.
Average the smallest and largest number
Part=Percent x Whole
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.


11. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
Find a common denominator - then add or subtract the numerators.
-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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


12. Finding the y-intercept When Given an Equation of a Line
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.
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
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.


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

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14. What is the Triangle Inequality Theorem?
Subtract the smallest from the largest and add 1
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.
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.
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.


15. If (Square Root: x-1)+5=12 - what is the value of x/2?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
-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 like terms.


16. Dividing Fractions
Cross multiply.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


17. Multiplying and Dividing Roots
The value that falls in the middle of the set.
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.
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 whole number left over after division.


18. Finding the GCF of Two or More Numbers
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Find a common denominator - then add or subtract the numerators.


19. Finding the Area of a Triangle

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

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21. General Procedure for Multiplying Polynomials
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use the distributive property then combine the like terms.


22. If the average of a - b - and 48 is 48 - what is the value of a + b?
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 base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


23. What are Two Special Pythagorean Triples?

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24. Definition of an Irrational Number
Adjacent angles are supplementary - Vertical angles are equal
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Use simple numbers like 1 and 2 and see what happens.


25. If 4(x(2)-10x+25) - then what is the value of x?
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Cancel factors common to the numerator and denominator.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.


26. What Does Solving In Terms of Mean?
VofaRS=lwh
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Do whatever is necessary to both sides to isolate the variable.


27. Raising a Power to a Power
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Use the units to keep things straight - Snowfall inches/hours
Multiply the exponents - (x^3)^4=x^3*4=x^12


28. Characteristics of a Square
Put the equation into y=mx+b-- in which case b is the y-intercept.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Average the smallest and largest number
The value that falls in the middle of the set.


29. If 2+l6-xl=10 and x>0 - what is the value of 2x?
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Get the absolute value equation by itself. Solve.
Switch the numerator and denominator.
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.


30. Solving a Problem Involving Rates
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.
Use the units to keep things straight - Snowfall inches/hours
2(pie)r
-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.


31. Knowing if an Integer is a Multiple of 2 or 4
The value that falls in the middle of the set.
-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.
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


32. What types of angles are formed when a transversal cross parallel lines?
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
-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.
Four equal acute angles and four equal obtuse angles.


33. Counting Consecutive Integers
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Part=Percent x Whole
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Subtract the smallest from the largest and add 1


34. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.


35. Average Rate and How Do You Find It
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


36. Increasing and Decreasing a Number by a Certain Percentage
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the formula distance=rate*time and its variations to help in this question.
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
-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.


37. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
FOIL: First - Outer - Inner - Last... Combine Like Terms
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


38. What value of x is not in the domain of the function f(x)=x-2/x-3?
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


39. Finding the Mode of a Set of Numbers
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
The value that appears the most often.


40. Multiplying Expressions with Exponents that Have a Common Base
-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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


41. Factoring the Difference of Two Squares
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


42. Simplifying Square Roots
Find a common denominator - then add or subtract the numerators.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Factor out and cancel all factors the numerator and denominator have in common.
Use simple numbers like 1 and 2 and see what happens.


43. Finding the Length of an Arc in a Circle

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44. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


45. Multiplying Monomials
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.
A(2)+b(2)=c(2)
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


46. Finding the Sum of the Average of a Series of Numbers
Use the formula distance=rate*time and its variations to help in this question.
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
Sum: Average x Number of Terms
Four equal acute angles and four equal obtuse angles.


47. Setting Up a Ratio
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.
2(pie)r
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


48. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
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.


49. 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?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
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.
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.


50. Converting from an Improper Fraction to a Mixed Number
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.