SAT Math

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• Answer 50 questions in 15 minutes.
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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. If x(2)=7x+18 - what is the positive value of x?
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.


2. Finding the Missing Number in a Series When You are Given the Average
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


3. Solving a Problem Involving Rates
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.
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.
Use the units to keep things straight - Snowfall inches/hours
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.


4. What are Two Special Pythagorean Triples?

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5. What types of angles are formed when a transversal cross parallel lines?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Four equal acute angles and four equal obtuse angles.
Just add or subtract the coefficients in front of the radicals.
Average the smallest and largest number


6. Multiplying Fractions
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Multiply the numerators and multiply the denominators.
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.


7. If r#t=t(r)-r(t) - then what is 4#3?
-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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime 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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


8. Finding the LCM of Two or More Numbers

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9. Multiplying Monomials
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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
Two relatively prime numbers are integers that have no common factor other than 1.


10. Formula Used to Find Percent
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
Part=Percent x Whole
Slope=change in y/change in x
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


11. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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
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


12. Definition of an Irrational Number
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
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


13. What types of angles are formed when two lines intersect?
-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.
Part=Percent x Whole
Adjacent angles are supplementary - Vertical angles are equal
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


14. Multiplying Expressions with Exponents that Have a Common Base
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
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


15. 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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Cancel factors common to the numerator and denominator.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


16. How do you know if an integer is a multiple of 3 or 9?
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 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.
Multiply the numerators and multiply the denominators.
Put each number in the original ratio over the sum of the numbers.


17. Determining Absolute Value of a 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
Express them with a common denominator.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


18. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
(x1+x2)/2 -(y1+y2)/2
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


19. Dividing Fractions
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
2(pie)r
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


20. Convert From a Fraction to a Decimal - Vice Versa
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.
Use the distributive property then combine the like terms.
Do whatever is necessary to both sides to isolate the variable.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


21. Numbers that are Relatively Prime
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 relatively prime numbers are integers that have no common factor other than 1.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


22. Finding the Surface Area of a Rectangular Solid
Switch the numerator and 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.
Cancel factors common to the numerator and denominator.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


23. Knowing if an Integer is a Multiple of 2 or 4
Average the smallest and largest number
-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)
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


24. Finding the Distance Between Two Points on a Coordinate Graph
Use the units to keep things straight - Snowfall inches/hours
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
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


25. Simplifying Square Roots
The value that appears the most often.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Put the equation into y=mx+b-- in which case b is the y-intercept.


26. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
-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.


27. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Average the smallest and largest number
Use simple numbers like 1 and 2 and see what happens.
Switch the numerator and denominator.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


29. Direct Variation and Inverse Variation
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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
Subtract the smallest from the largest and add 1


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

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31. Knowing if an Integer is a Multiple of 5 or 10
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
-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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


32. General Procedure for Multiplying Polynomials
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
Use the distributive property then combine the like terms.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


33. Finding the Length of an Arc in a Circle

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34. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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


35. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Use the units to keep things straight - Snowfall inches/hours
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


36. Finding the Reciprocal of a Fraction
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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
Switch the numerator and denominator.


37. Converting from an Improper Fraction to a Mixed Number
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.
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.
(pie)r(squared)
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


38. 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.
Slope=change in y/change in x
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Get the absolute value equation by itself. Solve.


39. If (Square Root: x-1)+5=12 - what is the value of x/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.
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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


40. Adding and Subtracting Fractions
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Find a common denominator - then add or subtract the numerators.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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


41. Definition of an Integer
Plug in the given values for the unknowns and calculate according to PEMDAS.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Do whatever is necessary to both sides to isolate the variable.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


42. Setting Up a Ratio
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Find a common denominator - then add or subtract the numerators.


43. Multiply and Divide Positive and Negative Numbers
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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
Average the smallest and largest number
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 Domain and Range of a Function
Factor out and cancel all factors the numerator and denominator have in common.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


45. Converting from part-to-part ratios to part-to-whole ratios
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
The value that falls in the middle of the set.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Put each number in the original ratio over the sum of the numbers.


46. 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
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%
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.


47. Solving a Linear Equation
-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.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Do whatever is necessary to both sides to isolate the variable.


48. Definition of a Rational 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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
FOIL: First - Outer - Inner - Last... Combine Like Terms
-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.


49. Finding the y-intercept When Given an Equation of a Line
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Put the equation into y=mx+b-- in which case b is the y-intercept.


50. Finding the Area of a Sector

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