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. Quickly Finding the Average of a Series of Evenly Spaced Numbers
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Two relatively prime numbers are integers that have no common factor other than 1.
Adjacent angles are supplementary - Vertical angles are equal
Average the smallest and largest number


2. Simplifying Square Roots
2(pie)r
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Find a common denominator - then add or subtract the numerators.


3. Determining Absolute Value of a Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


4. Counting Consecutive Integers
Plug in the given values for the unknowns and calculate according to PEMDAS.
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
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.


5. Solving a Proportion
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Cross multiply.
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
(pie)r(squared)


6. Finding the y-intercept When Given an Equation of a Line
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Put the equation into y=mx+b-- in which case b is the y-intercept.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


7. Converting from an Improper Fraction to a Mixed 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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
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.


8. What is the Triangle Inequality Theorem?
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
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.
Multiply the numerators and multiply the denominators.


9. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


10. Difference Between a Factor and a Multiple
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Multiply the numerators and multiply the denominators.
-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.


11. Finding the Mode of a Set of Numbers
Slope=change in y/change in x
The value that appears the most often.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.


12. Definition of an Irrational Number
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
VofaC: (pie)r(2)h


13. Finding the Rate of Speed
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Use the formula distance=rate*time and its variations to help in this question.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


14. 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.
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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


15. 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.
Use the units to keep things straight - Snowfall inches/hours
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
FOIL: First - Outer - Inner - Last... Combine Like Terms


16. Finding the Area of a Sector

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17. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


18. Finding the Circumference of a Circle
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Part=Percent x Whole
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
2(pie)r


19. Evaluating an Algebraic Expression
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
(x1+x2)/2 -(y1+y2)/2
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


20. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
(x1+x2)/2 -(y1+y2)/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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


21. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


22. Finding the Missing Number in a Series When You are Given the Average
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.
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


23. If 3(3x)=9(x+2) - what is the value of x?
-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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


24. What is the positive difference between the answers to the equation 35+x(2)=12x?

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25. Finding a Term in a Geometric Sequence
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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: Sum of the Terms/Number of the Terms
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.


26. Solving a Radical 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.
Isolate the radical expression and use the standard rules of algebra.
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.
Express them with a common denominator.


27. Adding and Subtracting Fractions
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
-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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Find a common denominator - then add or subtract the numerators.


28. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Plug in the given values for the unknowns and calculate according to PEMDAS.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


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

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30. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
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.
-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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


31. Converting From a Mixed Number to an Improper Fraction
Switch the numerator and denominator.
The value that falls in the middle of the set.
Slope=change in y/change in x
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


33. Calculating Negative Exponents and Radical Exponents
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


34. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Subtract the smallest from the largest and add 1
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
-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.
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.


35. 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.
-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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


36. Counting the Total Number of Possibilities for Several Events to Occur
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.
Use simple numbers like 1 and 2 and see what happens.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Subtract the smallest from the largest and add 1


37. Solving a Problem Involving Rates
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use the units to keep things straight - Snowfall inches/hours


38. Finding the Volume of a Rectangular Solid
VofaRS=lwh
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


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

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40. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Plug in the given values for the unknowns and calculate according to PEMDAS.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


41. Adding and Subtracting Polynomials
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Combine like terms.


42. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
(x1+x2)/2 -(y1+y2)/2
Do whatever is necessary to both sides to isolate the variable.
Combine like terms.


43. Properties of the Interior and Exterior Angles of a Triangle
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4


44. Finding the Slope of a Line When Given Two Points on the Line
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Slope=change in y/change in x
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


45. Finding the Sum of the Average of a Series of Numbers
Factor out and cancel all factors the numerator and denominator have in common.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Sum: Average x Number of Terms
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.


46. Formula Used to Find Percent
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
Part=Percent x Whole
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


47. Finding the Area of a Triangle

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48. 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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Probability: Number of Favorable Outcomes/Total Possible Outcomes


49. Finding the Surface Area of a Rectangular Solid
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


50. Finding the Slope When Given an Equation of a Line
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
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Cancel factors common to the numerator and denominator.