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. Comparing the values of two or more Fractions
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Plug in the given values for the unknowns and calculate according to PEMDAS.
Express them with a common denominator.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

2. Finding the GCF of Two or More Numbers
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Break down the integers into their prime factorizations - and multiply all prime factors they 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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

3. Multiplying Expressions with Exponents that Have a Common Base
-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.
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

4. Solving a Linear Equation
-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.
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
Put the equation into y=mx+b-- in which case b is the y-intercept.
Do whatever is necessary to both sides to isolate the variable.

5. Dividing Expressions with Exponents that Have a Common Base
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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

6. Calculating the Probability that an Event will Take Place
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
-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.

7. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
-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.
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.

8. Formula to Find Average
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Average: Sum of the Terms/Number of the Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.

9. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
Use the distance formula: d=(square root over) (x2-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.
Find a common denominator - then add or subtract the numerators.

10. Solving a Proportion
Cross multiply.
-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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

11. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Four equal acute angles and four equal obtuse angles.
Average: Sum of the Terms/Number of the Terms
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

12. Multiplying Monomials
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.
Subtract the smallest from the largest and add 1
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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. Characteristics of a Square
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Average the smallest and largest number

14. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use simple numbers like 1 and 2 and see what happens.
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.

15. Evaluating an Algebraic Expression
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
Multiply the numerators and multiply the denominators.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

16. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Do whatever is necessary to both sides to isolate the variable.

17. Finding the Area of a Circle
(pie)r(squared)
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
(x1+x2)/2 -(y1+y2)/2
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.

18. 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?
(x1+x2)/2 -(y1+y2)/2
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.
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 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.

19. Determining Absolute Value of a Number
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply the numerators and multiply the denominators.

20. What is the Triangle Inequality Theorem?
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.
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
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.
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

21. Finding the Area of a Triangle

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

22. 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

23. Finding the Mode of a Set of Numbers
The value that appears the most often.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Put each number in the original ratio over the sum of the numbers.

24. 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.
2(pie)r
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.

25. Properties of the Interior and Exterior Angles of a Triangle
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 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 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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

26. Finding a Term in a Geometric Sequence
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.
Do whatever is necessary to both sides to isolate the variable.
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.
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

27. Multiplying Binomials
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.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
FOIL: First - Outer - Inner - Last... Combine Like Terms

28. Definition of Remainder
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.
The whole number left over after division.
Part=Percent x Whole
VofaRS=lwh

29. Numbers that are Relatively Prime
-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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Two relatively prime numbers are integers that have no common factor other than 1.

30. Knowing if an Integer is a Multiple of 5 or 10
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
-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.

31. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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
Average the smallest and largest number
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

32. Simplifying Square Roots
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
-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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

33. Scalene - Isosceles - and Equilateral Triangles
(pie)r(squared)
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.
Get the absolute value equation by itself. Solve.
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.

34. Direct Variation and Inverse Variation
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Multiply the numerators and multiply the denominators.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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

35. Counting Consecutive Integers
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Subtract the smallest from the largest and add 1
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 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.

36. Finding the Sum of the Average of a Series of Numbers
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Sum: Average x Number of Terms
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

37. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Adjacent angles are supplementary - Vertical angles are equal
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.

38. Converting from part-to-part ratios to part-to-whole ratios
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Put each number in the original ratio over the sum of the numbers.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

39. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Average the smallest and largest number
The value that appears the most often.
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

40. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Adjacent angles are supplementary - Vertical angles are equal
Express them with a common denominator.
Average the smallest and largest number

41. Multiply and Divide Positive and Negative Numbers
Use simple numbers like 1 and 2 and see what happens.
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
Use the formula distance=rate*time and its variations to help in this question.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

42. Adding and Subtracting Fractions
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Find a common denominator - then add or subtract the numerators.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.

43. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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 simple numbers like 1 and 2 and see what happens.

44. Average Rate and How Do You Find It
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
A(2)+b(2)=c(2)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

45. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
-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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

46. 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
-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.
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 whole number left over after division.

47. Multiplying Fractions
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Multiply the numerators and multiply the denominators.
VofaC: (pie)r(2)h

48. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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.
Get the absolute value equation by itself. Solve.
-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.
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.

49. If x varies directly with y - and the value of x is 12 when y is 11 - what is the value of y when x is 66?
Just add or subtract the coefficients in front of the radicals.
(pie)r(squared)
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

50. Solving an Inequality
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
A(2)+b(2)=c(2)
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.