Test your basic knowledge |

SAT Math

Subjects : 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. How do you know if an integer is a multiple of 3 or 9?
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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
Combine like terms.

2. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Probability: Number of Favorable Outcomes/Total Possible Outcomes
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Cancel factors common to the numerator and denominator.
(pie)r(squared)

3. Finding a Term in a Geometric Sequence
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
-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

4. 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?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

5. Finding the Circumference of a Circle
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Average: Sum of the Terms/Number of the Terms
2(pie)r
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

6. Definition of an Integer
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
VofaC: (pie)r(2)h

7. Finding the Reciprocal of a Fraction
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.
Switch the numerator and denominator.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

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

9. What types of angles are formed when two lines intersect?
Plug in the given values for the unknowns and calculate according to PEMDAS.
Adjacent angles are supplementary - Vertical angles are equal
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Use the formula distance=rate*time and its variations to help in this question.

10. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
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.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

11. Finding the Area of a Triangle

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

12. Finding the Area of a Sector

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

13. Raising a Power to a Power
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.
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
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.

14. Convert From a Fraction to a Decimal - Vice Versa
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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 units to keep things straight - Snowfall inches/hours
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.

15. Difference Between a Factor and a Multiple
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
-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.

16. Multiplying Fractions
Multiply the numerators and multiply the denominators.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

17. Properties of a 30-60-90 Triangle
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
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.

18. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 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.
Switch the numerator and denominator.

19. An Important Property of a Line Tangent to a Circle
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
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.

20. Finding the y-intercept When Given an Equation of a Line
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

21. Evaluating an Algebraic Expression
Subtract the smallest from the largest and add 1
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
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

22. Characteristics of a Square
Average the smallest and largest number
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

23. What value of x is not in the domain of the function f(x)=x-2/x-3?
Sum: Average x Number of Terms
The value that appears the most often.
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 the smallest and largest number

24. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Switch the numerator and denominator.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

25. 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
Put the equation into y=mx+b-- in which case b is the y-intercept.
Four equal acute angles and four equal obtuse angles.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

26. Simplifying an Algebraic Equation
-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.
Average: Sum of the Terms/Number of the Terms
Cancel factors common to the numerator and denominator.
Combine like terms.

27. Finding the Domain and Range of a Function
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
2(pie)r

28. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
The value that falls in the middle of the set.
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.

29. Number of Groups - +1 Each Time
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
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.

30. What is the Pythagorean Theorem?
Isolate the radical expression and use the standard rules of algebra.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
A(2)+b(2)=c(2)
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.

31. Solving an Inequality
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.
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Switch the numerator and denominator.

32. Adding and Subtracting Polynomials
Average the smallest and largest number
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.
Combine like terms.
2(pie)r

33. Numbers that are Relatively Prime
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Two relatively prime numbers are integers that have no common factor other than 1.
Use the formula distance=rate*time and its variations to help in this question.

34. If r#t=t(r)-r(t) - then what is 4#3?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.

35. Multiplying Monomials
-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 the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Get the absolute value equation by itself. Solve.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

36. Prime Factorization of a Number
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Subtract the smallest from the largest and add 1
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

37. 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.
VofaC: (pie)r(2)h
Find a common denominator - then add or subtract the numerators.
Just add or subtract the coefficients in front of the radicals.

38. Solving a Proportion
Subtract the smallest from the largest and add 1
Cross multiply.
Do whatever is necessary to both sides to isolate the variable.
-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.

39. Multiplying and Dividing Roots
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
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.
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. What is the Triangle Inequality Theorem?
Use the formula distance=rate*time and its variations to help in this question.
Just add or subtract the coefficients in front of the radicals.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.

41. Knowing if an Integer is a Multiple of 2 or 4
Cancel factors common to the numerator and denominator.
-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.
The value that falls in the middle of the set.

42. If the average of a - b - and 48 is 48 - what is the value of a + b?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Average: Sum of the Terms/Number of the Terms

43. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

44. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
The whole number left over after division.

45. Finding the Mode of a Set of Numbers
Find a common denominator - then add or subtract the numerators.
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 value that appears the most often.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

46. Formula Used to Find Percent
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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

47. Finding the GCF of Two or More Numbers
Subtract the smallest from the largest and add 1
Adjacent angles are supplementary - Vertical angles are equal
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

48. Adding and Subtracting Roots
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Use the units to keep things straight - Snowfall inches/hours
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.

49. Properties of the Interior and Exterior Angles of a Triangle
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.
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.
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.

50. Finding the LCM of Two or More Numbers

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183