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 Binomials
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.

2. Adding and Subtracting Fractions
Two relatively prime numbers are integers that have no common factor other than 1.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Find a common denominator - then add or subtract the numerators.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

3. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
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.
2(pie)r
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.

4. Difference Between a Factor and a Multiple
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
-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.
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

5. Finding the Domain and Range of a Function
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.
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Do whatever is necessary to both sides to isolate the variable.

6. Finding the Mode of a Set of Numbers
The value that appears the most often.
Just add or subtract the coefficients in front of the radicals.
Sum: Average x Number of Terms
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

7. 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?
Part=Percent x Whole
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Cancel factors common to the numerator and denominator.
Use simple numbers like 1 and 2 and see what happens.

8. Counting Consecutive Integers
Part=Percent x Whole
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Subtract the smallest from the largest and add 1

9. Factoring a Polynomial ('FOIL in Reverse')
2(pie)r
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Put the equation into y=mx+b-- in which case b is the y-intercept.

10. Finding the Sum of the Interior Angles of a Polygon
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
Find a common denominator - then add or subtract the numerators.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

11. What types of angles are formed when two lines intersect?
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.
Adjacent angles are supplementary - Vertical angles are equal
Switch the numerator and denominator.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

12. Adding a Positive Number to a Negative Number
Plug in the given values for the unknowns and calculate according to PEMDAS.
-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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

13. Simplifying a Fraction to Lowest 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.
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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Factor out and cancel all factors the numerator and denominator have in common.

14. Knowing if an Integer is a Multiple of 2 or 4
Combine like terms.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
-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.

15. Convert From a Fraction to a Decimal - Vice Versa
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.

16. Finding the Surface Area of a Rectangular Solid
Get the absolute value equation by itself. Solve.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

17. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

18. Definition of Remainder
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The whole number left over after division.
Sum: Average x Number of Terms

19. Finding a Term in a Geometric Sequence
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-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

20. Finding the Slope of a Line When Given Two Points on the Line
The whole number left over after division.
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 the smallest and largest number
Slope=change in y/change in x

21. Counting the Total Number of Possibilities for Several Events to Occur
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.

22. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
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.

23. Determining Absolute Value of a Number
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.
Factor out and cancel all factors the numerator and denominator have in common.
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

24. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.

25. How do you know if an integer is a multiple of 3 or 9?
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.
Just add or subtract the coefficients in front of the radicals.
Do whatever is necessary to both sides to isolate the variable.
Subtract the smallest from the largest and add 1

26. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
The value that appears the most often.
Slope=change in y/change in x
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

27. Multiplying Expressions with Exponents that Have a Common Base
Use the distributive property then combine the like terms.
Subtract the smallest from the largest and add 1
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

28. 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
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
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Use the distributive property then combine the like terms.

29. PEMDAS
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.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

30. Multiplying Monomials
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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
Isolate the radical expression and use the standard rules of algebra.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

31. Finding the GCF of Two or More Numbers
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.
(pie)r(squared)
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

32. 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.
-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.
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.

33. Formula Used to Find Percent
Subtract the smallest from the largest and add 1
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 radical expression and use the standard rules of algebra.
Part=Percent x Whole

34. General Procedure for Multiplying Polynomials
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Use the distributive property then combine the like terms.
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

35. Definition of an Irrational Number
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.
Get the absolute value equation by itself. Solve.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

36. Adding and Subtracting Monomials
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.

37. If 4(x(2)-10x+25) - then what is the value of x?
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Multiply the whole number part by the denominator - then add the numerator. Keep the same 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.
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.

38. Adding and Subtracting Roots
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

39. Dividing Fractions
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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

40. Factoring the Difference of Two Squares
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Four equal acute angles and four equal obtuse angles.

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

42. Characteristics of a Square
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

43. Prime Factorization of a Number
Cross multiply.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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

44. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
(x1+x2)/2 -(y1+y2)/2
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

45. Finding the Rate of Speed
-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.
Combine like terms.
Use the formula distance=rate*time and its variations to help in this question.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

46. Finding the Area of a Circle
Switch the numerator and denominator.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
(pie)r(squared)
Do whatever is necessary to both sides to isolate the variable.

47. Finding the Circumference of a Circle
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
2(pie)r
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.

48. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Factor out and cancel all factors the numerator and denominator have in common.
Use the distributive property then combine the like terms.
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.
Isolate the radical expression and use the standard rules of algebra.

49. 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?
Use the units to keep things straight - Snowfall inches/hours
Part=Percent x Whole
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

50. Adding and Subtracting Polynomials
Combine like terms.
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
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.
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.