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. What Does Solving In Terms of Mean?
Find a common denominator - then add or subtract the numerators.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
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

2. 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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Adjacent angles are supplementary - Vertical angles are equal
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

3. Adding and Subtracting Fractions
The value that falls in the middle of the set.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
VofaC: (pie)r(2)h
Find a common denominator - then add or subtract the numerators.

4. What value of x is not in the domain of the function f(x)=x-2/x-3?
Use the units to keep things straight - Snowfall inches/hours
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
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.
(pie)r(squared)

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

6. Definition of an Irrational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

7. Formula to Find Average
(x1+x2)/2 -(y1+y2)/2
Factor out and cancel all factors the numerator and denominator have in common.
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.
Average: Sum of the Terms/Number of the Terms

8. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
Cancel factors common to the numerator and denominator.

9. 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?
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.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

10. 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.
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 value that appears the most often.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

11. 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
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.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

12. If 3(3x)=9(x+2) - what is the value of x?
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.
Slope=change in y/change in x
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.

13. Knowing if an Integer is a Multiple of 2 or 4
Adjacent angles are supplementary - Vertical angles are equal
-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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.

14. 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.
Use the formula distance=rate*time and its variations to help in this question.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

15. Solving a Linear Equation
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
Average the smallest and largest number
Do whatever is necessary to both sides to isolate the variable.

16. Knowing if an Integer is a Multiple of 5 or 10
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 falls in the middle of the set.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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.

17. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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
-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 simple numbers like 1 and 2 and see what happens.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

18. Converting from an Improper Fraction to a Mixed Number
Do whatever is necessary to both sides to isolate the variable.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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
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.

19. 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.
Get the absolute value equation by itself. Solve.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
(x1+x2)/2 -(y1+y2)/2

20. Simplifying an Algebraic Equation
Just add or subtract the coefficients in front of the radicals.
Find a common denominator - then add or subtract the numerators.
Express them with a common denominator.
Cancel factors common to the numerator and denominator.

21. Adding and Subtracting Monomials
Plug in the given values for the unknowns and calculate according to PEMDAS.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
VofaRS=lwh

22. Multiplying Binomials
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
FOIL: First - Outer - Inner - Last... Combine Like Terms

23. Simplifying Square Roots
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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 out the perfect squares under the radical - take their square roots - and put the result in front.

24. 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.
Get the absolute value equation by itself. Solve.
Adjacent angles are supplementary - Vertical angles are equal
(x1+x2)/2 -(y1+y2)/2

25. Dividing Fractions
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.
-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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Part=Percent x Whole

26. Finding the Length of an Arc in a Circle

27. Properties of a 45-45-90 Triangle
The value that appears the most often.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

28. 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
Four equal acute angles and four equal obtuse angles.
Get the absolute value equation by itself. Solve.
Find a common denominator - then add or subtract the numerators.

29. Finding the Area of a Circle
(pie)r(squared)
The whole number left over after division.
Two relatively prime numbers are integers that have no common factor other than 1.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

30. 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 the distributive property then combine the like terms.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

31. General Procedure for Multiplying Polynomials
The whole number left over after division.
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
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 distributive property then combine the like terms.

32. What are Two Special Pythagorean Triples?

33. Solving a Radical Equation
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Express them with a common denominator.
Isolate the radical expression and use the standard rules of algebra.

34. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Use the formula distance=rate*time and its variations to help in this question.
Get the absolute value equation by itself. Solve.
Put each number in the original ratio over the sum of the numbers.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

35. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

36. Multiplying Fractions
Multiply the numerators and multiply the denominators.
Average the smallest and largest number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.

37. Characteristics of a Rectangle
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
The value that falls in the middle of the set.

38. Definition of Remainder
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Multiply the numerators and multiply the denominators.
2(pie)r
The whole number left over after division.

39. If the average of a - b - and 48 is 48 - what is the value of a + b?
Factor out and cancel all factors the numerator and denominator have in common.
Use the formula distance=rate*time and its variations to help in this question.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

40. Solving a Problem Involving Rates
Cancel factors common to the numerator and denominator.
Use the units to keep things straight - Snowfall inches/hours
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Multiply the numerators and multiply the denominators.

41. Definition of a Rational Number
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
The value that falls in the middle of the set.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

42. Finding the Rate of Speed
Sum: Average x Number of 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
Use the formula distance=rate*time and its variations to help in this question.
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.

43. Finding the Volume of a Rectangular Solid
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Use the formula distance=rate*time and its variations to help in this question.
VofaRS=lwh
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

44. Adding and Subtracting Roots
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Just add or subtract the coefficients in front of the radicals.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

45. How do you know if an integer is a multiple of 3 or 9?
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 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.
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.
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.

46. What types of angles are formed when a transversal cross parallel lines?
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.
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.
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 equal acute angles and four equal obtuse angles.

47. Prime Factorization of a Number
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Sum: Average x Number of Terms
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

48. Scalene - Isosceles - and Equilateral Triangles
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.
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
(x1+x2)/2 -(y1+y2)/2
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.

49. Finding the Surface Area of a Rectangular Solid
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

50. Setting Up a Ratio
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use the distributive property then combine the like terms.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Find a common denominator - then add or subtract the numerators.