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.
• 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. Convert From a Fraction to a Decimal - Vice Versa
-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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
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.


2. Multiplying and Dividing Roots
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
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
-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.


3. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
2(pie)r
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


4. Dividing Expressions with Exponents that Have a Common Base
Switch the numerator and denominator.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.


5. Direct Variation and Inverse Variation
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


6. Adding and Subtracting Roots
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Just add or subtract the coefficients in front of the radicals.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


7. Solving a Problem Involving Rates
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Use the units to keep things straight - Snowfall inches/hours
Two relatively prime numbers are integers that have no common factor other than 1.
Put each number in the original ratio over the sum of the numbers.


8. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Isolate the radical expression and use the standard rules of algebra.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


9. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Get the absolute value equation by itself. 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.
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 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


10. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
FOIL: First - Outer - Inner - Last... Combine Like Terms
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


11. Factoring the Difference of Two Squares
Multiply the numerators and multiply the denominators.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Just add or subtract the coefficients in front of the radicals.


12. Finding the Volume of a Cylinder
Average: Sum of the Terms/Number of the Terms
VofaC: (pie)r(2)h
Use the units to keep things straight - Snowfall inches/hours
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


13. Simplifying an Algebraic Equation
Subtract the smallest from the largest and add 1
Use simple numbers like 1 and 2 and see what happens.
Put each number in the original ratio over the sum of the numbers.
Cancel factors common to the numerator and denominator.


14. Dividing Fractions
Use simple numbers like 1 and 2 and see what happens.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


15. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
VofaRS=lwh
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Multiply the numerators and multiply the denominators.


16. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


17. Finding the Sum of the Average of a Series of Numbers
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.
Sum: Average x Number of Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The whole number left over after division.


18. Numbers that are Relatively Prime
VofaC: (pie)r(2)h
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.
Do whatever is necessary to both sides to isolate the variable.
Two relatively prime numbers are integers that have no common factor other than 1.


19. Prime Factorization of a 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
Just add or subtract the coefficients in front of the radicals.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


20. Simplifying a Fraction to Lowest Terms
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
Factor out and cancel all factors the numerator and denominator have in common.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.


21. Finding the Slope of a Line When Given Two Points on the Line
Find a common denominator - then add or subtract the numerators.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Slope=change in y/change in x
VofaC: (pie)r(2)h


22. Converting From a Mixed Number to an Improper Fraction
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
FOIL: First - Outer - Inner - Last... Combine Like Terms


23. Definition of an Irrational Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


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.
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use the formula distance=rate*time and its variations to help in this question.


25. Finding the Volume of a Rectangular Solid
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
VofaRS=lwh


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

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27. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
Get the absolute value equation by itself. Solve.
2(pie)r


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

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29. Solving a Linear Equation
VofaRS=lwh
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Do whatever is necessary to both sides to isolate the variable.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


30. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Part=Percent x Whole
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
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. Evaluating an Algebraic Expression
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Sum: Average x Number of Terms


32. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


33. Properties of the Interior and Exterior Angles of a Triangle
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


34. Finding the LCM of Two or More Numbers

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35. Solving a Proportion
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Cross multiply.


36. What value of x is not in the domain of the function f(x)=x-2/x-3?
Express them with a common denominator.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
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


37. What types of angles are formed when a transversal cross parallel lines?
Use the distributive property then combine the like terms.
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.
Four equal acute angles and four equal obtuse angles.
Slope=change in y/change in x


38. Raising a Power to a Power
The value that falls in the middle of the set.
2(pie)r
Multiply the exponents - (x^3)^4=x^3*4=x^12
Average the smallest and largest number


39. Counting Consecutive Integers
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Subtract the smallest from the largest and add 1
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.


40. Adding and Subtracting Polynomials
Combine like terms.
Multiply the numerators and multiply the denominators.
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.
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. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Cancel factors common to the numerator and denominator.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Factor out and cancel all factors the numerator and denominator have in common.


42. 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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Get the absolute value equation by itself. Solve.


43. Solving a System of Equations
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.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Use the units to keep things straight - Snowfall inches/hours


44. 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.
-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.
Adjacent angles are supplementary - Vertical angles are equal
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


45. Quickly Finding the Average of a Series of Evenly Spaced Numbers
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.
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
Find a common denominator - then add or subtract the numerators.


46. If the average of a - b - and 48 is 48 - what is the value of a + b?
Switch the numerator and denominator.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


47. Finding the Area of a Triangle

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48. Simplifying Square Roots
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.
Part=Percent x Whole
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


49. Comparing the values of two or more Fractions
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Express them with a common denominator.


50. Finding the Length of an Arc in a Circle

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