SAT Math

Instructions:

• Answer 50 questions in 15 minutes.
• If you are not ready to take this test, you can study here.
• 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. Multiplying Binomials
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.
Subtract the smallest from the largest and add 1
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
FOIL: First - Outer - Inner - Last... Combine Like Terms


2. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
Put each number in the original ratio over the sum of the numbers.
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.


3. Raising a Power to a Power
-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.
Slope=change in y/change in x
Multiply the exponents - (x^3)^4=x^3*4=x^12


4. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Do whatever is necessary to both sides to isolate the variable.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
-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.


5. Increasing and Decreasing a Number by a Certain Percentage
Just add or subtract the coefficients in front of the radicals.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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
-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.


6. If r#t=t(r)-r(t) - then what is 4#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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Get the absolute value equation by itself. Solve.


7. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Get the absolute value equation by itself. Solve.
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.


8. Definition of a Rational Number
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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 rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


9. Expressing the Union and Intersection of Sets
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
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.
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.
Average the smallest and largest number


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


11. Difference Between a Factor and a Multiple
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.
-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.
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.
Do whatever is necessary to both sides to isolate the variable.


12. Simplifying Square Roots
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
(x1+x2)/2 -(y1+y2)/2
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


13. If the average of a - b - and 48 is 48 - what is the value of a + b?
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
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


14. Adding a Positive Number to a Negative Number
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
A(2)+b(2)=c(2)
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


15. What types of angles are formed when two lines intersect?
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.
Adjacent angles are supplementary - Vertical angles are equal
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Four equal acute angles and four equal obtuse angles.


16. Convert From a Fraction to a Decimal - Vice Versa
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.
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.
The whole number left over after division.
FOIL: First - Outer - Inner - Last... Combine Like Terms


17. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
-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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


18. 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.
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.
Four equal acute angles and four equal obtuse angles.
Sum: Average x Number of Terms


19. Adding and Subtracting Polynomials
Use the distributive property then combine the like terms.
Combine like terms.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Slope=change in y/change in x


20. Factoring a Polynomial ('FOIL in Reverse')
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
The value that falls in the middle of the set.
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


21. An Important Property of a Line Tangent to a Circle
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
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


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

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23. Finding the Area of a Sector

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24. Finding the y-intercept When Given an Equation of a Line
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Put the equation into y=mx+b-- in which case b is the y-intercept.
Put each number in the original ratio over the sum of the numbers.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


25. Numbers that are Relatively Prime
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Two relatively prime numbers are integers that have no common factor other than 1.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


26. Scalene - Isosceles - and Equilateral Triangles
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)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.


27. 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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Cross multiply.


28. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
VofaC: (pie)r(2)h
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


29. Average Rate and How Do You Find It
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Sum: Average x Number of Terms
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


30. What value of x is not in the domain of the function f(x)=x-2/x-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.
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
Plug in the given values for the unknowns and calculate according to PEMDAS.


31. Counting the Total Number of Possibilities for Several Events to Occur
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
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.


32. 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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Get the absolute value equation by itself. Solve.


33. Prime Factorization of a Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


34. Definition of an Integer
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.
Adjacent angles are supplementary - Vertical angles are equal
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.


35. Finding the Area of a Circle
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
(pie)r(squared)
-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.
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.


36. Factoring the Difference of Two Squares
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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


37. Solving a Proportion
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.
Cross multiply.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.


38. Multiplying Fractions
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.
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.
Multiply the numerators and multiply the denominators.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4


39. Simplifying an Algebraic Equation
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


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

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41. If x(2)=7x+18 - what is the positive value of x?
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.


42. Setting Up a Ratio
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


43. Finding the GCF of Two or More Numbers
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


44. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


45. 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?
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.
Two relatively prime numbers are integers that have no common factor other than 1.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.


46. Finding the Area of a Triangle

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47. Definition of Remainder
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
-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 whole number left over after division.


48. Finding the Slope of a Line When Given Two Points on the Line
Just add or subtract the coefficients in front of the radicals.
Slope=change in y/change in x
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


49. Finding the LCM of Two or More Numbers

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50. Multiply and Divide Positive and Negative Numbers
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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