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. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
Get the absolute value equation by itself. Solve.
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


2. 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?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Part=Percent x Whole
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


3. Adding and Subtracting Monomials
Just add or subtract the coefficients in front of the radicals.
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4


4. What is the positive difference between the answers to the equation 35+x(2)=12x?

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5. Finding the Slope of a Line When Given Two Points on the Line
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Slope=change in y/change in x
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


6. 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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The whole number left over after division.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


7. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
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.
Average the smallest and largest number
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.


8. Properties of Similar Triangles
2(pie)r
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


9. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
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.
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
Get the absolute value equation by itself. Solve.


10. 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?
VofaRS=lwh
The whole number left over after division.
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 two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


11. Calculating the Probability that an Event will Take Place
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
-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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


12. Simplifying Square Roots
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


13. What value of x is not in the domain of the function f(x)=x-2/x-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.
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
Average: Sum of the Terms/Number of the Terms
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


14. Numbers that are Relatively Prime
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Two relatively prime numbers are integers that have no common factor other than 1.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


15. Quickly Finding the Average of a Series of Evenly Spaced Numbers
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Average the smallest and largest number


16. What is the Triangle Inequality Theorem?
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Use the distributive property then combine the like terms.


17. Number of Groups - +1 Each Time
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
The value that appears the most often.


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

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19. Finding the Median of a Set of Numbers
-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 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
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
The value that falls in the middle of the set.


20. Simplifying an Algebraic Equation
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Do whatever is necessary to both sides to isolate the variable.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Cancel factors common to the numerator and denominator.


21. Definition of Remainder
Use simple numbers like 1 and 2 and see what happens.
-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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The whole number left over after division.


22. How do you know if an integer is a multiple of 3 or 9?
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.
Cancel factors common to the numerator and denominator.
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


23. What types of angles are formed when two lines intersect?
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
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.
Adjacent angles are supplementary - Vertical angles are equal


24. Calculating Negative Exponents and Radical Exponents
Put each number in the original ratio over the sum of the 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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


25. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


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

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27. Properties of a 30-60-90 Triangle
-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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


28. Setting Up a Ratio
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
The value that falls in the middle of the set.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


29. Finding the Circumference of a Circle
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
2(pie)r
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.


30. Finding the Volume of a Rectangular Solid
Use the formula distance=rate*time and its variations to help in this question.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
VofaRS=lwh


31. Multiplying Monomials
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Four equal acute angles and four equal obtuse angles.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


32. Definition of an Irrational Number
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
The value that falls in the middle of the set.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


33. Converting from part-to-part ratios to part-to-whole ratios
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put each number in the original ratio over the sum of the numbers.
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


34. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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
Combine like terms.
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.


35. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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
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
Get the absolute value equation by itself. Solve.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


36. Finding the Domain and Range of a Function
2(pie)r
Part=Percent x Whole
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.


37. Comparing the values of two or more Fractions
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
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.
Express them with a common denominator.


38. Finding the Mode of a Set of Numbers
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
The value that appears the most often.
-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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


39. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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 - substitute for the variable. Then evaluate the expression using the correct order of operations.
Combine like terms.
Multiply the numerators and multiply the denominators.


40. Solving a Radical Equation
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Isolate the radical expression and use the standard rules of algebra.
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.
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.


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

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42. Scalene - Isosceles - and Equilateral Triangles
Use simple numbers like 1 and 2 and see what happens.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
VofaRS=lwh


43. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
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.
2(pie)r


44. Adding and Subtracting Roots
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Just add or subtract the coefficients in front of the radicals.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


45. Determining Absolute Value of a Number
Subtract the smallest from the largest and add 1
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
-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.


46. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
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
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Average: Sum of the Terms/Number of the Terms


47. Solving a Linear Equation
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
The whole number left over after division.
Do whatever is necessary to both sides to isolate the variable.


48. Finding the Area of a Sector

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49. Finding the Area of a Triangle

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50. Evaluating an Algebraic Expression
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Plug in the given values for the unknowns and calculate according to PEMDAS.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7