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. Solving a Radical Equation
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Isolate the radical expression and use the standard rules of algebra.
Four equal acute angles and four equal obtuse angles.

2. An Important Property of a Line Tangent to a Circle
Two relatively prime numbers are integers that have no common factor other than 1.
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.
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.
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.

3. If 4(x(2)-10x+25) - then what is the value of x?
Average the smallest and largest number
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

4. Definition of an Irrational Number
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Multiply the numerators and multiply the denominators.

5. Multiplying Monomials
Four equal acute angles and four equal obtuse angles.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

6. Solving a Proportion
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Cross multiply.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

7. Dividing Fractions
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

8. Finding the Circumference of a Circle
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Average: Sum of the Terms/Number of the Terms
-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.
2(pie)r

9. 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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
-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.
(pie)r(squared)

10. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

11. Simplifying an Algebraic Equation
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Adjacent angles are supplementary - Vertical angles are equal
Cancel factors common to the numerator and denominator.
Slope=change in y/change in x

12. If (Square Root: x-1)+5=12 - what is the value of x/2?
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.

13. Adding a Positive Number to a Negative Number
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

14. Properties of a 30-60-90 Triangle
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Cross multiply.

15. Raising a Power to a Power
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

16. Adding and Subtracting Roots
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.
Just add or subtract the coefficients in front of the radicals.
Adjacent angles are supplementary - Vertical angles are equal
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

17. Finding the Area of a Sector

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

19. Characteristics of a Parallelogram
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
(x1+x2)/2 -(y1+y2)/2
Plug in the given values for the unknowns and calculate according to PEMDAS.

20. Finding the Median of a Set of Numbers
Use the units to keep things straight - Snowfall inches/hours
The value that falls in the middle of the set.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.

21. Finding the Volume of a Cylinder
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
VofaC: (pie)r(2)h
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Average the smallest and largest number

22. Finding the Area of a Triangle

23. Characteristics of a Square
Two relatively prime numbers are integers that have no common factor other than 1.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Sum: Average x Number of Terms

24. Finding the Slope of a Line When Given Two Points on the Line
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Slope=change in y/change in x
Two relatively prime numbers are integers that have no common factor other than 1.

25. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Find a common denominator - then add or subtract the numerators.
-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 Area of a Circle
(pie)r(squared)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

27. How do you know if an integer is a multiple of 3 or 9?
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
The value that appears the most often.
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.

28. Determining Absolute Value of a Number
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
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.

29. Prime Factorization of a Number
Use simple numbers like 1 and 2 and see what happens.
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.

30. Increasing and Decreasing a Number by a Certain Percentage
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.

31. Factoring the Difference of Two Squares
Adjacent angles are supplementary - Vertical angles are equal
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
(x1+x2)/2 -(y1+y2)/2
The value that falls in the middle of the set.

32. Definition of Remainder
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
The whole number left over after division.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

33. Knowing if an Integer is a Multiple of 5 or 10
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
-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.

34. Solving an Inequality
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

35. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

36. Finding the y-intercept When Given an Equation of a Line
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 y=mx+b-- in which case b is the y-intercept.
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms

37. Comparing the values of two or more Fractions
Express them with a common denominator.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Average the smallest and largest number

38. Multiplying Binomials
Subtract the smallest from the largest and add 1
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.
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms

39. If 3(3x)=9(x+2) - what is the value of x?
Put each number in the original ratio over the sum of the numbers.
Multiply the exponents - (x^3)^4=x^3*4=x^12
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Isolate the radical expression and use the standard rules of algebra.

40. Converting from an Improper Fraction to a Mixed Number
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Just add or subtract the coefficients in front of the radicals.

41. 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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
FOIL: First - Outer - Inner - Last... Combine Like Terms

42. Finding the Midpoint Between Two Points
The value that falls in the middle of the set.
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
Two relatively prime numbers are integers that have no common factor other than 1.
(x1+x2)/2 -(y1+y2)/2

43. Definition of a Rational Number
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.

44. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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.
The whole number left over after division.
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.

45. 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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
-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.

46. What is the positive difference between the answers to the equation 35+x(2)=12x?

47. Finding the Missing Number in a Series When You are Given the Average
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
-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.
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.
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.

48. Calculating Negative Exponents and Radical Exponents
Multiply the numerators and multiply the denominators.
-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.
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

49. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.

50. Finding the Domain and Range of a Function
(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.
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.