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. Finding the Volume of a Cylinder
Multiply the exponents - (x^3)^4=x^3*4=x^12
2(pie)r
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
VofaC: (pie)r(2)h

2. Finding the LCM of Two or More Numbers

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

3. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
(pie)r(squared)
Part=Percent x Whole

4. 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?
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
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.
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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

5. 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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Part=Percent x Whole

6. Factoring a Polynomial ('FOIL in Reverse')
Isolate the radical expression and use the standard rules of algebra.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

7. Multiplying Expressions with Exponents that Have a Common Base
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.

8. Adding and Subtracting Roots
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Just add or subtract the coefficients in front of the radicals.
Put each number in the original ratio over the sum of the numbers.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

9. Simplifying a Fraction to Lowest Terms
Use the formula distance=rate*time and its variations to help in this question.
Slope=change in y/change in x
Factor out and cancel all factors the numerator and denominator have in common.
Isolate the radical expression and use the standard rules of algebra.

10. Properties of a 45-45-90 Triangle
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Factor out and cancel all factors the numerator and denominator have in common.

11. Properties of the Interior and Exterior Angles of a 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.
Switch the numerator and denominator.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

12. 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
Cross multiply.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

13. Finding the Area of a Circle
Just add or subtract the coefficients in front of the radicals.
(pie)r(squared)
Four equal acute angles and four equal obtuse angles.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

14. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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.
Get the absolute value equation by itself. Solve.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.

15. Adding a Positive Number to a Negative Number
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Express them with a common denominator.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

16. Simplifying Square Roots
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.
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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

17. Solving a Problem Involving Rates
Use the distributive property then combine the like terms.
Use the units to keep things straight - Snowfall inches/hours
Get the absolute value equation by itself. Solve.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

18. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
VofaC: (pie)r(2)h
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.

19. Factoring the Difference of Two Squares
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 whole number left over after division.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

20. Finding the Sum of the Interior Angles of a Polygon
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.
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.
Isolate the radical expression and use the standard rules of algebra.

21. Direct Variation and Inverse Variation
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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
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.

22. Definition of Remainder
The whole number left over after division.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Put each number in the original ratio over the sum of the numbers.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

23. If 4(x(2)-10x+25) - then what is the value of x?
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Slope=change in y/change in 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.

24. Scalene - Isosceles - and Equilateral Triangles
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
-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.

25. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

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

26. Raising a Power to a Power
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Do whatever is necessary to both sides to isolate the variable.
Multiply the exponents - (x^3)^4=x^3*4=x^12

27. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
Put each number in the original ratio over the sum of the numbers.
The whole number left over after division.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

28. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Plug in the given values for the unknowns and calculate according to PEMDAS.
Switch the numerator and denominator.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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

29. Difference Between a Factor and a Multiple
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
-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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

30. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
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.
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

31. Multiplying Fractions
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Multiply the numerators and multiply the denominators.
Combine like terms.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

32. Increasing and Decreasing a Number by a Certain Percentage
Four equal acute angles and four equal obtuse angles.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
-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.

33. Finding the Sum of the Average of a Series of Numbers
Multiply the numerators and multiply the denominators.
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
Sum: Average x Number of Terms
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.

34. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

35. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
-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.
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.

36. Finding the Surface Area of a Rectangular Solid
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

37. General Procedure for Multiplying Polynomials
Put the equation into y=mx+b-- in which case b is the y-intercept.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Use the distributive property then combine the like 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.

38. An Important Property of a Line Tangent to 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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
(x1+x2)/2 -(y1+y2)/2
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.

39. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.

40. Multiplying Monomials
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.
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

41. What types of angles are formed when two lines intersect?
Multiply the exponents - (x^3)^4=x^3*4=x^12
Use the distributive property then combine the like 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.
Adjacent angles are supplementary - Vertical angles are equal

42. What Does Solving In Terms of Mean?
Combine like terms.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
(pie)r(squared)

43. Adding and Subtracting Monomials
Four equal acute angles and four equal obtuse angles.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
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.

44. Finding the Domain and Range of a Function
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Express them with a common denominator.

45. Finding the Volume of a Rectangular Solid
VofaRS=lwh
Average the smallest and largest number
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
VofaC: (pie)r(2)h

46. Finding the Reciprocal of a Fraction
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
-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.
Switch the numerator and denominator.
Sum: Average x Number of Terms

47. Finding the Distance Between Two Points on a Coordinate Graph
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Put the equation into y=mx+b-- in which case b is the y-intercept.

48. Prime Factorization of a Number
-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.
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

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

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

50. Solving a System of Equations
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.