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 types of angles are formed when a transversal cross parallel lines?
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Four equal acute angles and four equal obtuse angles.
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.


2. Finding the Reciprocal of a Fraction
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Switch the numerator and denominator.


3. 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?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


4. Finding the Domain and Range of a Function
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Express them with a common denominator.
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
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.


5. Adding and Subtracting Polynomials
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.
Get the absolute value equation by itself. Solve.
Combine like terms.
Just add or subtract the coefficients in front of the radicals.


6. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


7. Converting from part-to-part ratios to part-to-whole ratios
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
-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.
Put each number in the original ratio over the sum of the numbers.
Just add or subtract the coefficients in front of the radicals.


8. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
Multiply the exponents - (x^3)^4=x^3*4=x^12
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Use simple numbers like 1 and 2 and see what happens.


9. Finding the Volume of a Rectangular Solid
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
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.
VofaRS=lwh


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


11. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Switch the numerator and denominator.
(pie)r(squared)
Use simple numbers like 1 and 2 and see what happens.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


12. Solving a Linear Equation
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Do whatever is necessary to both sides to isolate the variable.
Find a common denominator - then add or subtract the numerators.
Sum: Average x Number of Terms


13. Definition of an Irrational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Factor out and cancel all factors the numerator and denominator have in common.
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 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.


14. What Does Solving In Terms of Mean?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
-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.
Average: Sum of the Terms/Number of the Terms


15. Simplifying an Algebraic Equation
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
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.
Cancel factors common to the numerator and denominator.


16. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


17. Finding the Distance Between Two Points on a Coordinate Graph
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Get the absolute value equation by itself. Solve.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


18. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
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.


19. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Plug in the given values for the unknowns and calculate according to PEMDAS.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


20. Solving an Inequality
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.
Use simple numbers like 1 and 2 and see what happens.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


21. Finding a Term in a Geometric Sequence
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.
Use the formula distance=rate*time and its variations to help in this question.
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.


22. Finding the Mode of a Set of Numbers
Part=Percent x Whole
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The value that appears the most often.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


23. Properties of a 45-45-90 Triangle
Put the equation into y=mx+b-- in which case b is the y-intercept.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Get the absolute value equation by itself. Solve.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


24. Counting Consecutive 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.
Subtract the smallest from the largest and add 1
The value that falls in the middle of the set.
Find a common denominator - then add or subtract the numerators.


25. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


26. If (Square Root: x-1)+5=12 - what is the value of x/2?
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
A(2)+b(2)=c(2)
Use the formula distance=rate*time and its variations to help in this question.


27. Finding the Volume of a Cylinder
Slope=change in y/change in x
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating 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.
VofaC: (pie)r(2)h


28. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


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


30. Definition of Remainder
Adjacent angles are supplementary - Vertical angles are equal
The whole number left over after division.
Just add or subtract the coefficients in front of the radicals.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


31. If x(2)=7x+18 - what is the positive value of x?
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


32. Finding the Length of an Arc in a Circle


33. Finding the Area of a Triangle


34. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The whole number left over after division.


35. Characteristics of a Parallelogram
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.
Adjacent angles are supplementary - Vertical angles are equal
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


36. 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?
VofaRS=lwh
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 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
Part=Percent x Whole


37. Solving a Proportion
Cross multiply.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


38. Solving a System of Equations
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
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.
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


39. 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.
Subtract the smallest from the largest and add 1
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.
Adjacent angles are supplementary - Vertical angles are equal


40. What is the Pythagorean Theorem?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
-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.
A(2)+b(2)=c(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.


41. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Average: Sum of the Terms/Number of the Terms


42. If the average of a - b - and 48 is 48 - what is the value of a + b?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Isolate the radical expression and use the standard rules of algebra.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


43. Scalene - Isosceles - and Equilateral Triangles
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Four equal acute angles and four equal obtuse angles.
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.
Isolate the radical expression and use the standard rules of algebra.


44. Solving a Problem Involving Rates
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Use the units to keep things straight - Snowfall inches/hours
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


45. 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.
Sum: Average x Number of Terms
Average: Sum of the Terms/Number of the Terms
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


46. PEMDAS
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
-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.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


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


48. Properties of the Interior and Exterior Angles of a Triangle
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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
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.


49. Knowing if an Integer is a Multiple of 2 or 4
Slope=change in y/change in x
The whole number left over after division.
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.


50. Finding the Median of a Set of Numbers
Average the smallest and largest number
Use the units to keep things straight - Snowfall inches/hours
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The value that falls in the middle of the set.