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. Finding the Volume of a Rectangular Solid
VofaRS=lwh
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.
Average the smallest and largest number
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

2. Simplifying a Fraction to Lowest Terms
Cross multiply.
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.
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.
Factor out and cancel all factors the numerator and denominator have in common.

3. If 4(x(2)-10x+25) - then what is the value of x?
-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.
-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.
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.
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.

4. Raising a Power to a Power
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

5. 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
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Use the units to keep things straight - Snowfall inches/hours

6. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Switch the numerator and denominator.
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.

7. 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.
-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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.

8. Increasing and Decreasing a Number by a Certain Percentage
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Two relatively prime numbers are integers that have no common factor other than 1.
-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. Adding and Subtracting Polynomials
Combine like terms.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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
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

10. Adding and Subtracting Roots
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
Adjacent angles are supplementary - Vertical angles are equal
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Just add or subtract the coefficients in front of the radicals.

11. Expressing the Union and Intersection of Sets
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
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
2(pie)r
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.

12. Finding the Rate of Speed
Use the formula distance=rate*time and its variations to help in this question.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Cancel factors common to the numerator and denominator.

13. Definition of Remainder
Two relatively prime numbers are integers that have no common factor other than 1.
Slope=change in y/change in x
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
The whole number left over after division.

14. Finding the Circumference of a Circle
Sum: Average x Number of Terms
Use simple numbers like 1 and 2 and see what happens.
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.
2(pie)r

15. If x(2)=7x+18 - what is the positive value of x?
The whole number left over after division.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

16. Definition of an Irrational Number
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

17. Calculating the Probability that an Event will Take Place
Do whatever is necessary to both sides to isolate the variable.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Use the distributive property then combine the like terms.
Slope=change in y/change in x

18. If (Square Root: x-1)+5=12 - what is the value of x/2?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Express them with a common denominator.
FOIL: First - Outer - Inner - Last... Combine Like Terms

19. Finding a Term in a Geometric Sequence
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 - 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.
Slope=change in y/change in x
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

20. Adding and Subtracting Monomials
-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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

21. Finding the Slope When Given an Equation of a Line
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
(pie)r(squared)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

22. Knowing if an Integer is a Multiple of 5 or 10
Sum: Average x Number of Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.
-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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

23. Difference Between a Factor and a Multiple
Switch the numerator and denominator.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
-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

24. Finding the Area of a Circle
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
(pie)r(squared)

25. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Switch 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.

26. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

27. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Just add or subtract the coefficients in front of the radicals.

28. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Sum: Average x Number of Terms
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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

29. Finding the Mode of a Set of Numbers
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
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
The value that appears the most often.

30. Formula Used to Find Percent
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.
Part=Percent x Whole
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Slope=change in y/change in x

31. Knowing if an Integer is a Multiple of 2 or 4
The whole number left over after division.
VofaC: (pie)r(2)h
-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.
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.

32. Solving a Linear Equation
Use the distributive property then combine the like terms.
Do whatever is necessary to both sides to isolate the variable.
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)

33. Converting From a Mixed Number to an Improper Fraction
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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

34. 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.
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Cancel factors common to the numerator and denominator.

35. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.

36. What is the greatest of three consecutive odd integers where the sum of the third and twice the first is equal to nine more than twice the second?
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.
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.
Part=Percent x Whole

37. Finding the Area of a Triangle

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

38. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Average the smallest and largest number
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

39. What are Two Special Pythagorean Triples?

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

40. Finding the Volume of a Cylinder
-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.
VofaC: (pie)r(2)h
VofaRS=lwh
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.

41. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.

42. Direct Variation and Inverse Variation
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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

43. Solving a System of Equations
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.
Switch the numerator and denominator.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

44. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Get the absolute value equation by itself. Solve.
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.

45. Scalene - Isosceles - and Equilateral Triangles
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.
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.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

46. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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
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 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.

47. Convert From a Fraction to a Decimal - Vice Versa
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
Use the units to keep things straight - Snowfall inches/hours
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.

48. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Use the distributive property then combine the like terms.

49. What Does Solving In Terms of Mean?
Put each number in the original ratio over the sum of the numbers.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

50. Number of Groups - +1 Each Time
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use simple numbers like 1 and 2 and see what happens.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides