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. Prime Factorization of a Number
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 units to keep things straight - Snowfall inches/hours
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use the distributive property then combine the like terms.

2. Finding the Midpoint Between Two Points
Plug in the given values for the unknowns and calculate according to PEMDAS.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
(x1+x2)/2 -(y1+y2)/2
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

3. Finding the Sum of the Average of a Series of Numbers
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.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Sum: Average x Number of Terms

4. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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

5. Adding and Subtracting Polynomials
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
A(2)+b(2)=c(2)
Find a common denominator - then add or subtract the numerators.
Combine like terms.

6. Dividing Expressions with Exponents that Have a Common Base
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
The value that appears the most often.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

7. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

8. Simplifying an Algebraic Equation
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-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.
The value that appears the most often.
Cancel factors common to the numerator and denominator.

9. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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.
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.
Cancel factors common to the numerator and denominator.

10. Characteristics of a Square
Slope=change in y/change in x
Factor out and cancel all factors the numerator and denominator have in common.
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

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

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

12. Finding the Surface Area of a Rectangular Solid
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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)

13. Adding and Subtracting Monomials
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Four equal acute angles and four equal obtuse angles.

14. Adding and Subtracting Roots
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Just add or subtract the coefficients in front of the radicals.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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. 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?
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.
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.
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

16. Knowing if an Integer is a Multiple of 2 or 4
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
-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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

17. Multiplying Fractions
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Average: Sum of the Terms/Number of the Terms
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Multiply the numerators and multiply the denominators.

18. Simplifying Square Roots
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.
A(2)+b(2)=c(2)
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

19. If 3(3x)=9(x+2) - what is the value of x?
Four equal acute angles and four equal obtuse angles.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
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.

20. Characteristics of a Rectangle
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Average the smallest and largest number
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

21. Solving a Proportion
VofaC: (pie)r(2)h
Do whatever is necessary to both sides to isolate the variable.
Cross multiply.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

22. Multiplying and Dividing Roots
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Adjacent angles are supplementary - Vertical angles are equal

23. Properties of the Interior and Exterior Angles of a Triangle
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Multiply the numerators and multiply the denominators.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

24. What are Two Special Pythagorean Triples?

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

25. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
VofaRS=lwh
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

26. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Isolate the radical expression and use the standard rules of algebra.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

27. 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
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Cancel factors common to the numerator and denominator.

28. Expressing the Union and Intersection of Sets
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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

29. Finding the Mode of a Set of Numbers
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.
Switch the numerator and denominator.
The value that appears the most often.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

30. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Find a common denominator - then add or subtract the numerators.
Four equal acute angles and four equal obtuse angles.

31. Finding the Distance Between Two Points on a Coordinate Graph
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use the distributive property then combine the like terms.

32. Properties of Similar Triangles
Average the smallest and largest number
Plug in the given values for the unknowns and calculate according to PEMDAS.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
(x1+x2)/2 -(y1+y2)/2

33. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
Two relatively prime numbers are integers that have no common factor other than 1.
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

34. Multiply and Divide Positive and Negative 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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

35. Finding the Circumference of a Circle
2(pie)r
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Find a common denominator - then add or subtract the numerators.
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

36. Convert From a Fraction to a Decimal - Vice Versa
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.
Switch the numerator and denominator.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
A(2)+b(2)=c(2)

37. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Sum: Average x Number of Terms
Combine like terms.
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.

38. Definition of a Rational 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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use the units to keep things straight - Snowfall inches/hours
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

39. 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
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.
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
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

40. Solving a Linear Equation
Get the absolute value equation by itself. Solve.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Do whatever is necessary to both sides to isolate the variable.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

41. Sale Price of a Jacket Marked Down 30% Each Week for 3 Weeks - What % of the Original Price is the Cost of the Jacket After the 3 Week Sale Period
Multiply the numerators and multiply the denominators.
Average the smallest and largest number
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.

42. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Cancel factors common to the numerator and denominator.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Subtract the smallest from the largest and add 1
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

43. Knowing if an Integer is a Multiple of 5 or 10
-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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Cancel factors common to the numerator and denominator.
Use the units to keep things straight - Snowfall inches/hours

44. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime 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.
-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.

45. Numbers that are Relatively Prime
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Adjacent angles are supplementary - Vertical angles are equal
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Two relatively prime numbers are integers that have no common factor other than 1.

46. Finding the Missing Number in a Series When You are Given the Average
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

47. Number of Groups - +1 Each Time
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

48. 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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

49. If 2+l6-xl=10 and x>0 - what is the value of 2x?
(pie)r(squared)
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Just add or subtract the coefficients in front of the radicals.
Get the absolute value equation by itself. Solve.

50. Finding the y-intercept When Given an Equation of a Line
Just add or subtract the coefficients in front of the radicals.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Switch the numerator and denominator.
Put the equation into y=mx+b-- in which case b is the y-intercept.