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 Area of a Sector

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

2. Multiplying Monomials
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

3. Multiply and Divide Positive and Negative Numbers
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.
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

4. Scalene - Isosceles - and Equilateral Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
-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.

5. Adding and Subtracting Fractions
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.
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
Find a common denominator - then add or subtract the numerators.

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

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

7. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Do whatever is necessary to both sides to isolate the variable.
The whole number left over after division.

8. If 3(3x)=9(x+2) - what is the value of x?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
(x1+x2)/2 -(y1+y2)/2

9. Comparing the values of two or more Fractions
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.
Express them with a common denominator.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Combine like terms.

10. Numbers that are Relatively Prime
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Average the smallest and largest number
Two relatively prime numbers are integers that have no common factor other than 1.
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.

11. Finding the Domain and Range of a Function
Express them with a common denominator.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
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.

12. 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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Part=Percent x Whole

13. PEMDAS
The value that falls in the middle of the set.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

14. If (Square Root: x-1)+5=12 - what is the value of x/2?
Use the distributive property then combine the like terms.
Combine like terms.
Use the formula distance=rate*time and its variations to help in this question.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

15. Properties of a 45-45-90 Triangle
Plug in the given values for the unknowns and calculate according to PEMDAS.
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
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

16. Finding the Median of a Set of Numbers
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Plug in the given values for the unknowns and calculate according to PEMDAS.
The value that falls in the middle of the set.
Express them with a common denominator.

17. Finding the Surface Area of a Rectangular Solid
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.

18. Evaluating an Algebraic Expression
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

19. Finding the Volume of a Rectangular Solid
VofaRS=lwh
The whole number left over after division.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

20. If x(2)=7x+18 - what is the positive value of x?
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
(x1+x2)/2 -(y1+y2)/2
Average: Sum of the Terms/Number of the Terms
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

21. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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.
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use simple numbers like 1 and 2 and see what happens.

22. Properties of Similar Triangles
The value that falls in the middle of the set.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use the distributive property then combine the like terms.
Multiply the numerators and multiply the denominators.

23. 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

24. An Important Property of a Line Tangent to a Circle
Four equal acute angles and four equal obtuse angles.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.

25. Characteristics of a Square
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime 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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Sum: Average x Number of Terms

26. Direct Variation and Inverse Variation
Part=Percent x Whole
The value that falls in the middle of the set.
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

27. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Express them with a common denominator.
Put each number in the original ratio over the sum of the numbers.
Multiply the exponents - (x^3)^4=x^3*4=x^12

28. Finding the GCF of Two or More Numbers
Use the units to keep things straight - Snowfall inches/hours
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Average the smallest and largest number

29. Solving a Linear Equation
FOIL: First - Outer - Inner - Last... Combine Like Terms
Do whatever is necessary to both sides to isolate the variable.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.

30. Knowing if an Integer is a Multiple of 2 or 4
-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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Put the equation into y=mx+b-- in which case b is the y-intercept.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

31. Converting from part-to-part ratios to part-to-whole ratios
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.
Put each number in the original ratio over the sum of the numbers.
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.
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.

32. Dividing Expressions with Exponents that Have a Common Base
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

33. Difference Between a Factor and a Multiple
Combine like terms.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
-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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

34. What types of angles are formed when a transversal cross parallel lines?
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.
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.
Four equal acute angles and four equal obtuse angles.
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.

35. Finding the y-intercept When Given an Equation of a Line
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.

36. Finding the Missing Number in a Series When You are Given the Average
Part=Percent x Whole
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
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.

37. Solving a Radical Equation
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.
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 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.

38. Finding a Term in a Geometric Sequence
A(2)+b(2)=c(2)
Combine like terms.
(x1+x2)/2 -(y1+y2)/2
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.

39. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
Cross multiply.
Express them with a common denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

40. Adding and Subtracting Roots
(pie)r(squared)
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.
Cancel factors common to the numerator and denominator.
Just add or subtract the coefficients in front of the radicals.

41. Counting the Total Number of Possibilities for Several Events to Occur
(x1+x2)/2 -(y1+y2)/2
VofaC: (pie)r(2)h
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.
-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.

42. Converting from an Improper Fraction to a Mixed Number
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

43. How do you know if an integer is a multiple of 3 or 9?
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.
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 falls in the middle of the set.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

44. Finding the Slope When Given an Equation of a Line
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Just add or subtract the coefficients in front of the radicals.

45. Finding the Rate of Speed
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use the formula distance=rate*time and its variations to help in this question.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

46. Finding the Volume of a Cylinder
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.
Switch the numerator and denominator.
VofaC: (pie)r(2)h
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

47. Multiplying and Dividing Roots
Put each number in the original ratio over the sum of the numbers.
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.
Find a common denominator - then add or subtract the numerators.
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.

48. Quickly Finding the Average of a Series of Evenly Spaced Numbers
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
VofaC: (pie)r(2)h
Average the smallest and largest number
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

49. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Just add or subtract the coefficients in front of the radicals.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

50. Factoring a Polynomial ('FOIL in Reverse')
The value that appears the most often.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.