SAT Math

Instructions:

• Answer 50 questions in 15 minutes.
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• Match each statement with the correct term.
• Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Converting from an Improper Fraction to a Mixed Number
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
Subtract the smallest from the largest and add 1
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.


2. Determining Absolute Value of a Number
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the units to keep things straight - Snowfall inches/hours
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


3. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
A(2)+b(2)=c(2)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


4. Properties of Similar Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


5. Finding the Slope of a Line When Given Two Points on the Line
VofaRS=lwh
Slope=change in y/change in x
Do whatever is necessary to both sides to isolate the variable.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


6. Finding the Volume of a Rectangular Solid
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
VofaRS=lwh
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.


7. Finding the Length of an Arc in a Circle

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8. Multiplying Expressions with Exponents that Have a Common Base
Cancel factors common to the numerator and denominator.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.


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

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10. Finding the Area of a Triangle

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11. Multiplying Monomials
The value that falls in the middle of the set.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Slope=change in y/change in x
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


12. Quickly Finding the Average of a Series of Evenly Spaced Numbers
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Average the smallest and largest number
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


13. Finding the y-intercept When Given an Equation of a Line
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.


14. Prime Factorization of a Number
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


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

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16. What types of angles are formed when a transversal cross parallel lines?
Two relatively prime numbers are integers that have no common factor other than 1.
Four equal acute angles and four equal obtuse angles.
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.
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.


17. Finding the Midpoint Between Two Points
The value that falls in the middle of the set.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
FOIL: First - Outer - Inner - Last... Combine Like Terms
(x1+x2)/2 -(y1+y2)/2


18. Converting from part-to-part ratios to part-to-whole ratios
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.
Put each number in the original ratio over the sum of the numbers.
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


19. Solving a Proportion
-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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Cross multiply.
Use the distributive property then combine the like terms.


20. Finding the Area of a Sector

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21. Finding the Surface Area of a Rectangular Solid
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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
(pie)r(squared)


22. What is the Pythagorean Theorem?
Isolate the radical expression and use the standard rules of algebra.
FOIL: First - Outer - Inner - Last... Combine Like Terms
A(2)+b(2)=c(2)
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


23. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Average: Sum of the Terms/Number of the Terms
Find a common denominator - then add or subtract the numerators.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


24. 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.
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 distributive property then combine the like terms.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


25. What are Two Special Pythagorean Triples?

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26. Scalene - Isosceles - and Equilateral Triangles
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.
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 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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


27. Difference Between a Factor and a Multiple
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


28. Converting From a Mixed Number to an Improper Fraction
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


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

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30. Finding the Area of a Circle
Part=Percent x Whole
The value that falls in the middle of the set.
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.
(pie)r(squared)


31. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.


32. Solving a Problem Involving Rates
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Use the units to keep things straight - Snowfall inches/hours
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.


33. Finding the Domain and Range of a Function
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Just add or subtract the coefficients in front of the radicals.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


34. Definition of an Integer
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Cross multiply.
VofaC: (pie)r(2)h
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


35. Definition of a Rational Number
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


36. What is the Triangle Inequality Theorem?
-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.
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 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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


37. Factoring the Difference of Two Squares
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


38. What types of angles are formed when two lines intersect?
Cross multiply.
Adjacent angles are supplementary - Vertical angles are equal
Do whatever is necessary to both sides to isolate the variable.
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


39. Finding the Circumference of a Circle
Average: Sum of the Terms/Number of the Terms
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Cancel factors common to the numerator and denominator.
2(pie)r


40. Finding the Median of a Set of Numbers
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.
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The value that falls in the middle of the set.


41. Simplifying an Algebraic Equation
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Cancel factors common to the numerator and denominator.
Multiply the numerators and multiply the denominators.


42. Finding the Mode of a Set of Numbers
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
The value that appears the most often.
Part=Percent x Whole
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.


43. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
VofaRS=lwh
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


44. Solving a System of Equations
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


45. Adding and Subtracting Monomials
Cancel factors common to the numerator and denominator.
-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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


46. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
-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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


47. Adding and Subtracting Fractions
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Isolate the radical expression and use the standard rules of algebra.
Find a common denominator - then add or subtract the numerators.
Use the units to keep things straight - Snowfall inches/hours


48. How do you know if an integer is a multiple of 3 or 9?
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Isolate the radical expression and use the standard rules of algebra.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


49. If (Square Root: x-1)+5=12 - what is the value of x/2?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Use simple numbers like 1 and 2 and see what happens.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


50. If 4(x(2)-10x+25) - then what is the value of x?
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.
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.
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.
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.