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. Multiplying and Dividing Roots
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
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.
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.
Switch the numerator and denominator.

2. Characteristics of a Rectangle
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The whole number left over after division.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

3. What is the Pythagorean Theorem?
Part=Percent x Whole
A(2)+b(2)=c(2)
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.
Isolate the radical expression and use the standard rules of algebra.

4. What Does Solving In Terms of Mean?
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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 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.

5. Characteristics of a Parallelogram
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply the exponents - (x^3)^4=x^3*4=x^12
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

6. If 4(x(2)-10x+25) - then what is the value of x?
Part=Percent x Whole
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.
A(2)+b(2)=c(2)
Four equal acute angles and four equal obtuse angles.

7. Counting the Total Number of Possibilities for Several Events to Occur
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.
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.
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.
Switch the numerator and denominator.

8. Properties of the Interior and Exterior Angles of a Triangle
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.
Adjacent angles are supplementary - Vertical angles are equal
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.
-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.

9. 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.
Get the absolute value equation by itself. Solve.
A(2)+b(2)=c(2)
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.

10. Converting From a Mixed Number to an Improper Fraction
Adjacent angles are supplementary - Vertical angles are equal
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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
Just add or subtract the coefficients in front of the radicals.

11. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
The whole number left over after division.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Cancel factors common to the numerator and denominator.

12. Number of Groups - +1 Each Time
Average the smallest and largest number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Find a common denominator - then add or subtract the numerators.

13. Simplifying Square Roots
Put each number in the original ratio over the sum of the numbers.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.

14. 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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

15. Finding the Area of a Circle
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
(pie)r(squared)
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.
Factor out and cancel all factors the numerator and denominator have in common.

16. 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

17. Dividing Expressions with Exponents that Have a Common Base
FOIL: First - Outer - Inner - Last... Combine Like Terms
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

18. 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

19. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Put each number in the original ratio over the sum of the numbers.
Sum: Average x Number of 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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

20. If (Square Root: x-1)+5=12 - what is the value of x/2?
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.

21. Finding the Missing Number in a Series When You are Given the Average
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 the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
2(pie)r
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.

22. Converting from an Improper Fraction to a Mixed Number
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

23. Properties of Similar Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Average: Sum of the Terms/Number of the Terms
Use the formula distance=rate*time and its variations to help in this question.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

24. Finding the Area of a Sector

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

25. Expressing the Union and Intersection of Sets
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.
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

26. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
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 each number in the original ratio over the sum of the numbers.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

27. Adding and Subtracting Fractions
Average: Sum of the Terms/Number of the Terms
Find a common denominator - then add or subtract the numerators.
(x1+x2)/2 -(y1+y2)/2
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.

28. Multiply and Divide Positive and Negative Numbers
The whole number left over after division.
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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

29. 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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

30. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Put the equation into y=mx+b-- in which case b is the y-intercept.

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

32. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

33. Multiplying Fractions
Part=Percent x Whole
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.
Multiply the numerators and multiply the denominators.
The value that appears the most often.

34. Increasing and Decreasing a Number by a Certain Percentage
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
-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.

35. Raising a Power to a Power
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.
Cross multiply.
A(2)+b(2)=c(2)

36. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Factor out and cancel all factors the numerator and denominator have in common.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Average the smallest and largest number

37. Converting from part-to-part ratios to part-to-whole ratios
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Subtract the smallest from the largest and add 1
Put each number in the original ratio over the sum of the numbers.

38. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
Multiply the numerators and multiply the denominators.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Put each number in the original ratio over the sum of the numbers.

39. How do you know if an integer is a multiple of 3 or 9?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
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.
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

40. Finding the GCF of Two or More 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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

41. Characteristics of a Square
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Sum: Average x Number of Terms
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

42. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
A(2)+b(2)=c(2)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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
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.

43. Difference Between a Factor and a Multiple
Get the absolute value equation by itself. Solve.
Average: Sum of the Terms/Number of the Terms
Use the formula distance=rate*time and its variations to help in this question.
-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.

44. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
(pie)r(squared)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Put the equation into y=mx+b-- in which case b is the y-intercept.

45. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Use the formula distance=rate*time and its variations to help in this question.
-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 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

46. Finding the Slope When Given an Equation of a Line
A(2)+b(2)=c(2)
Get the absolute value equation by itself. Solve.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Average: Sum of the Terms/Number of the Terms

47. 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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Switch the numerator and denominator.
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.

48. 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
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
Find a common denominator - then add or subtract the numerators.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

49. Prime Factorization of a Number
(x1+x2)/2 -(y1+y2)/2
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

50. Finding the Median of a Set of Numbers
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
The value that falls in the middle of the set.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4