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?

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2. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


3. Average Rate and How Do You Find It
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Adjacent angles are supplementary - Vertical angles are equal
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


4. What types of angles are formed when a transversal cross parallel lines?
VofaRS=lwh
Four equal acute angles and four equal obtuse angles.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


5. Finding the Circumference of a Circle
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.
A(2)+b(2)=c(2)
2(pie)r
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.


6. 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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Isolate the radical expression and use the standard rules of algebra.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


7. Comparing the values of two or more Fractions
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.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


8. Dividing Expressions with Exponents that Have a Common Base
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


9. Finding the Domain and Range of a Function
Use simple numbers like 1 and 2 and see what happens.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Use the units to keep things straight - Snowfall inches/hours
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.


10. Number of Groups - +1 Each Time
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Adjacent angles are supplementary - Vertical angles are equal
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


11. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
VofaRS=lwh
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.


12. Finding the Distance Between Two Points on a Coordinate Graph
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Just add or subtract the coefficients in front of the radicals.
-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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


13. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Find a common denominator - then add or subtract the numerators.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.


14. Prime Factorization of a Number
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.


15. Setting Up a Ratio
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.


16. Adding and Subtracting Fractions
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Use the distributive property then combine the like terms.
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.
Find a common denominator - then add or subtract the numerators.


17. An Important Property of a Line Tangent to a Circle
-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.
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


18. Finding the Mode of a Set of 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
The value that falls in the middle of the set.
Put each number in the original ratio over the sum of the numbers.
The value that appears the most often.


19. Finding the Surface Area of a Rectangular Solid
Use simple numbers like 1 and 2 and see what happens.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Find a common denominator - then add or subtract the numerators.


20. Finding the GCF of Two or More Numbers
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.


21. Finding the LCM of Two or More Numbers

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22. Characteristics of a Rectangle
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
(x1+x2)/2 -(y1+y2)/2
Four equal acute angles and four equal obtuse angles.


23. Multiply and Divide Positive and Negative Numbers
Put the equation into y=mx+b-- in which case b is the y-intercept.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Average the smallest and largest number
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


24. Multiplying Binomials
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
A(2)+b(2)=c(2)
Multiply the exponents - (x^3)^4=x^3*4=x^12
FOIL: First - Outer - Inner - Last... Combine Like Terms


25. Finding the Missing Number in a Series When You are Given the Average
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.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.


26. Finding the Area of a Sector

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27. Scalene - Isosceles - and Equilateral Triangles
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
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


28. 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?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.


29. Finding the Length of an Arc in a Circle

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30. Factoring a Polynomial ('FOIL in Reverse')
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
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
FOIL: First - Outer - Inner - Last... Combine Like Terms


31. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
-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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


32. Solving a Radical Equation
Part=Percent x Whole
Isolate the radical expression and use the standard rules of algebra.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.


33. 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
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


34. Dividing Fractions
Cancel factors common to the numerator and denominator.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


35. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same 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.
Just add or subtract the coefficients in front of the radicals.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


36. If r#t=t(r)-r(t) - then what is 4#3?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


37. PEMDAS
A(2)+b(2)=c(2)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.


38. What is the Pythagorean Theorem?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
A(2)+b(2)=c(2)
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.


39. Calculating the Probability that an Event will Take Place
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
FOIL: First - Outer - Inner - Last... Combine Like Terms
Probability: Number of Favorable Outcomes/Total Possible Outcomes


40. Finding the Slope When Given an Equation of a Line
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


41. What Does Solving In Terms of Mean?
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.
Cross multiply.
(x1+x2)/2 -(y1+y2)/2


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

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43. Solving a System of Equations
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


44. 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
-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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


45. 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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Multiply the numerators and multiply the denominators.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


46. If x(2)=7x+18 - what is the positive value of x?
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.
-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.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


47. Finding the Slope of a Line When Given Two Points on the Line
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Slope=change in y/change in x
-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.


48. Multiplying Fractions
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Four equal acute angles and four equal obtuse angles.
Multiply the numerators and multiply the denominators.


49. Finding the Sum of the Interior Angles of a Polygon
Use the formula distance=rate*time and its variations to help in this question.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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


50. Finding the Sum of the Average of a Series of Numbers
Slope=change in y/change in x
(pie)r(squared)
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Sum: Average x Number of Terms