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. Definition of a Rational Number
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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

2. Finding the GCF of Two or More Numbers
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
The value that falls in the middle of the set.

3. Determining Absolute Value of a Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.

4. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The value that falls in the middle of the set.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Probability: Number of Favorable Outcomes/Total Possible Outcomes

5. Multiplying Fractions
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Multiply the numerators and multiply the denominators.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.

6. Adding and Subtracting Fractions
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.
Find a common denominator - then add or subtract the numerators.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

7. 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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.

8. Converting from part-to-part ratios to part-to-whole ratios
A(2)+b(2)=c(2)
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Put each number in the original ratio over the sum of the numbers.

9. If 3(3x)=9(x+2) - what is the value of x?
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 base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

10. Simplifying Square Roots
-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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Combine like terms.

11. Converting From a Mixed Number to an Improper Fraction
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Put the equation into y=mx+b-- in which case b is the y-intercept.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

12. 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?
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

13. 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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
The whole number left over after division.

14. Finding the Sum of the Interior Angles of a Polygon
Multiply the exponents - (x^3)^4=x^3*4=x^12
Put each number in the original ratio over the sum of the numbers.
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

15. Properties of the Interior and Exterior Angles of a Triangle
Use simple numbers like 1 and 2 and see what happens.
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.

16. Characteristics of a Parallelogram
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
Just add or subtract the coefficients in front of the radicals.
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.

17. Adding a Positive Number to a Negative Number
-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.
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

18. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
VofaC: (pie)r(2)h
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)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

19. If 4(x(2)-10x+25) - then what is the value of x?
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

20. What Does Solving In Terms of Mean?
Isolate the radical expression and use the standard rules of algebra.
-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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

21. Multiplying and Dividing Roots
2(pie)r
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.

22. Formula Used to Find Percent
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Part=Percent x Whole
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

23. Raising a Power to a Power
The value that falls in the middle of the set.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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
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.

24. Converting from an Improper Fraction to a Mixed 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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

25. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Multiply the exponents - (x^3)^4=x^3*4=x^12
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
-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.

26. Finding the Distance Between Two Points on a Coordinate Graph
-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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.

27. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Use the distributive property then combine the like terms.
Get the absolute value equation by itself. Solve.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.

28. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Switch the numerator and denominator.
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

29. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Express them with a common 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.
Average the smallest and largest number
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

30. Characteristics of a Rectangle
Get the absolute value equation by itself. Solve.
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Average: Sum of the Terms/Number of the Terms

31. Solving an Inequality
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

32. Counting Consecutive Integers
Sum: Average x Number of Terms
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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

33. Definition of Remainder
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The whole number left over after division.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Isolate the radical expression and use the standard rules of algebra.

34. Multiply and Divide Positive and Negative Numbers
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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

35. If (Square Root: x-1)+5=12 - what is the value of x/2?
Adjacent angles are supplementary - Vertical angles are equal
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
VofaC: (pie)r(2)h

36. Knowing if an Integer is a Multiple of 2 or 4
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Cancel factors common to the numerator and denominator.

37. Scalene - Isosceles - and Equilateral Triangles
Part=Percent x Whole
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the distributive property then combine the like terms.

38. Finding a Term in a Geometric Sequence
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Subtract the smallest from the largest and add 1

39. Number of Groups - +1 Each Time
Multiply the whole number part by the denominator - then add the numerator. Keep the same 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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

40. Simplifying a Fraction to Lowest Terms
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Average: Sum of the Terms/Number of the Terms
Factor out and cancel all factors the numerator and denominator have in common.

41. Evaluating an Algebraic Expression
-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.
A(2)+b(2)=c(2)
Plug in the given values for the unknowns and calculate according to PEMDAS.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

42. Finding the Circumference of a Circle
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
2(pie)r
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

43. Multiplying Monomials
-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.
Use simple numbers like 1 and 2 and see what happens.
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 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.

44. Factoring a Polynomial ('FOIL in Reverse')
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

45. Properties of a 45-45-90 Triangle
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
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 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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

46. Definition of an Irrational 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.
-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.
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

47. Adding and Subtracting Polynomials
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Combine like terms.
Use simple numbers like 1 and 2 and see what happens.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

48. Finding the Mode of a Set of Numbers
The value that appears the most often.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

49. Solving a Radical Equation
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.

50. 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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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