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. Convert From a Fraction to a Decimal - Vice Versa
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Isolate the radical expression and use the standard rules of algebra.

2. If 2+l6-xl=10 and x>0 - what is the value of 2x?
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use the units to keep things straight - Snowfall inches/hours
-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.
Get the absolute value equation by itself. Solve.

3. Converting from an Improper Fraction to a Mixed Number
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.
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.
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.
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.

4. Finding the Volume of a Rectangular Solid
VofaRS=lwh
Use simple numbers like 1 and 2 and see what happens.
Average the smallest and largest number
Combine like terms.

5. Prime Factorization of a Number
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

6. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
-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.
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.
Part=Percent x Whole

7. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Combine like terms.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

8. 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 two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
VofaRS=lwh
Express them with a common denominator.

9. Finding the Area of a Circle
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
(pie)r(squared)

10. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
Sum: Average x Number of Terms
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

11. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

12. How do you know if an integer is a multiple of 3 or 9?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.

13. Knowing if an Integer is a Multiple of 5 or 10
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.
Part=Percent x Whole
-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.
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.

14. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

15. Dividing Fractions
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Cross multiply.

16. Scalene - Isosceles - and Equilateral Triangles
(pie)r(squared)
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.
Part=Percent x Whole
VofaC: (pie)r(2)h

17. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
Sum: Average x Number of 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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

18. Comparing the values of two or more Fractions
Express them with a common denominator.
Put the equation into y=mx+b-- in which case b is the y-intercept.
-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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

19. Finding the Missing Number in a Series When You are Given the Average
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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 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.

20. If (Square Root: x-1)+5=12 - what is the value of x/2?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
The whole number left over after division.
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

21. Determining Absolute Value of a Number
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
The value that falls in the middle of the set.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

22. Multiplying and Dividing Roots
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.
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.
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.

23. Finding the Length of an Arc in a Circle

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

24. Solving a System of Equations
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
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.
A(2)+b(2)=c(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.

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

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

26. Solving a Radical Equation
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.
Isolate the radical expression and use the standard rules of algebra.
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 whole number left over after division.

27. Finding the Reciprocal of a Fraction
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
Switch the numerator and denominator.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

28. Factoring a Polynomial ('FOIL in Reverse')
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use simple numbers like 1 and 2 and see what happens.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

29. Solving a Problem Involving Rates
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Use the units to keep things straight - Snowfall inches/hours

30. Multiply and Divide Positive and Negative Numbers
Plug in the given values for the unknowns and calculate according to PEMDAS.
Put each number in the original ratio over the sum of the numbers.
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
VofaC: (pie)r(2)h

31. Definition of Remainder
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 whole number left over after division.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

32. Finding the Sum of the Average of a Series of Numbers
FOIL: First - Outer - Inner - Last... Combine Like Terms
Sum: Average x Number of Terms
Average: Sum of the Terms/Number of the Terms
VofaRS=lwh

33. 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.
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

34. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
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
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

35. Counting the Total Number of Possibilities for Several Events to Occur
-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.
Subtract the smallest from the largest and add 1
Isolate the radical expression and use the standard rules of algebra.
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.

36. Finding the Domain and Range of a Function
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply the numerators and multiply the denominators.
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. Converting From a Mixed Number to an Improper Fraction
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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
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.

38. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Get the absolute value equation by itself. Solve.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.

39. 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
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.
Average the smallest and largest number
-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.

40. Finding the Circumference of a Circle
2(pie)r
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.
Adjacent angles are supplementary - Vertical angles are equal
Part=Percent x Whole

41. Properties of the Interior and Exterior Angles of a Triangle
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 distributive property then combine the like terms.
Factor out and cancel all factors the numerator and denominator have in common.
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.

42. Calculating the Probability that an Event will Take Place
Combine like terms.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

43. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Isolate the radical expression and use the standard rules of algebra.
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
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

44. Adding a Positive Number to a Negative 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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

45. Average Rate and How Do You Find It
FOIL: First - Outer - Inner - Last... Combine Like Terms
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Plug in the given values for the unknowns and calculate according to PEMDAS.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

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

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

47. Properties of Similar Triangles
Combine like terms.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
2(pie)r

48. An Important Property of a Line Tangent to a Circle
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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
VofaRS=lwh
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.

49. Multiplying Monomials
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Slope=change in y/change in x

50. If the average of a - b - and 48 is 48 - what is the value of a + b?
The whole number left over after division.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Adjacent angles are supplementary - Vertical angles are equal