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

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2. Scalene - Isosceles - and Equilateral Triangles
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
VofaRS=lwh
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


3. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
The whole number left over after division.


4. Simplifying an Algebraic Equation
Put the equation into y=mx+b-- in which case b is the y-intercept.
Multiply the numerators and multiply the denominators.
Cancel factors common to the numerator and denominator.
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.


5. Properties of the Interior and Exterior Angles of a Triangle
The value that falls in the middle of the set.
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.
Get the absolute value equation by itself. Solve.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


6. Solving a Problem Involving Rates
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
2(pie)r
Use the units to keep things straight - Snowfall inches/hours
Factor out and cancel all factors the numerator and denominator have in common.


7. Solving a Radical Equation
Plug in the given values for the unknowns and calculate according to PEMDAS.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Isolate the radical expression and use the standard rules of algebra.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


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

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9. Dividing Fractions
Factor out and cancel all factors the numerator and denominator have in common.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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


10. Properties of Similar Triangles
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


11. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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.
2(pie)r


12. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
Adjacent angles are supplementary - Vertical angles are equal
Use the distributive property then combine the like terms.
Use simple numbers like 1 and 2 and see what happens.


13. Quickly Finding the Average of a Series of Evenly Spaced Numbers
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Average the smallest and largest number
Combine like terms.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


14. 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
Use the formula distance=rate*time and its variations to help in this question.
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%
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


15. Characteristics of a Parallelogram
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.
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 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.


16. Adding and Subtracting Monomials
Put the equation into y=mx+b-- in which case b is the y-intercept.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
-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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


17. Definition of an Integer
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
2(pie)r
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Plug in the given values for the unknowns and calculate according to PEMDAS.


18. Finding the Area of a Sector

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19. Expressing the Union and Intersection of Sets
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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
Cross multiply.
-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.


20. Increasing and Decreasing a Number by a Certain Percentage
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Put each number in the original ratio over the sum of the numbers.
-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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


21. Counting the Total Number of Possibilities for Several Events to Occur
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
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.
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.


22. 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
Just add or subtract the coefficients in front of the radicals.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Switch the numerator and denominator.


23. Solving a System of Equations
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
-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.
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.


24. Formula to Find Average
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Multiply the exponents - (x^3)^4=x^3*4=x^12
Average: Sum of the Terms/Number of the 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


25. Finding the Area of a Triangle

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26. What Does Solving In Terms of Mean?
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.


27. Finding the LCM of Two or More Numbers

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28. Finding the Length of an Arc in a Circle

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29. Let N represent the smallest positive integer that is a multiple of 6 and 8 - but leaves a remainder of 2 when divided by 7. What is the value of N?
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


30. What value of x is not in the domain of the function f(x)=x-2/x-3?
VofaC: (pie)r(2)h
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
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


31. Difference Between a Factor and a Multiple
-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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


32. Converting from part-to-part ratios to part-to-whole ratios
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Average: Sum of the Terms/Number of the Terms
Put each number in the original ratio over the sum of the numbers.
Use the distributive property then combine the like terms.


33. 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.
Slope=change in y/change in x
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The value that falls in the middle of the set.


34. 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.
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Slope=change in y/change in x


35. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Switch the numerator and denominator.


36. 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.
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.
Do whatever is necessary to both sides to isolate the variable.
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.


37. If the average of a - b - and 48 is 48 - what is the value of a + b?
Use simple numbers like 1 and 2 and see what happens.
Sum: Average x Number of Terms
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


38. If r#t=t(r)-r(t) - then what is 4#3?
Use the formula distance=rate*time and its variations to help in this question.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.


39. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Sum: Average x Number of Terms


40. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
VofaC: (pie)r(2)h
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


41. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
(pie)r(squared)
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


42. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Average: Sum of the Terms/Number of the Terms
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 simple numbers like 1 and 2 and see what happens.


43. Finding the Circumference of a Circle
2(pie)r
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


44. Solving a Proportion
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Cross multiply.
-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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


45. Converting From a Mixed Number to an Improper Fraction
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.
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
The value that appears the most often.


46. 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.
-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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Average the smallest and largest number


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

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48. Properties of a 30-60-90 Triangle
Use the distributive property then combine the like terms.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


49. If 3(3x)=9(x+2) - what is the value of x?
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


50. What are Two Special Pythagorean Triples?

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