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. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
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
Switch the numerator and denominator.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

2. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Slope=change in y/change in x
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

3. Converting from an Improper Fraction to a Mixed 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.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
FOIL: First - Outer - Inner - Last... Combine Like Terms

4. Direct Variation and Inverse Variation
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.
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
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
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

5. Finding the Volume of a Cylinder
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
(x1+x2)/2 -(y1+y2)/2

6. If 4(x(2)-10x+25) - then what is the value of x?
Factor out and cancel all factors the numerator and denominator have in common.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
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.

7. 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
-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.
Isolate the radical expression and use the standard rules of algebra.
Use the distributive property then combine the like terms.

8. Numbers that are Relatively Prime
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Part=Percent x Whole
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.
Two relatively prime numbers are integers that have no common factor other than 1.

9. Characteristics of a Square
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Cancel factors common to the numerator and denominator.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

10. Finding the Area of a Triangle

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

11. Increasing and Decreasing a Number by a Certain Percentage
-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: Sum of the Terms/Number of the Terms
Adjacent angles are supplementary - Vertical angles are equal
Put each number in the original ratio over the sum of the numbers.

12. An Important Property of a Line Tangent to a Circle
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 whole number left over after division.
Use the distance formula: d=(square root over) (x2-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.

13. Finding the Circumference of a Circle
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.
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(pie)r

14. Properties of the Interior and Exterior Angles of a Triangle
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

16. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

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

17. Finding the Area of a Circle
(pie)r(squared)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
FOIL: First - Outer - Inner - Last... Combine Like Terms
Do whatever is necessary to both sides to isolate the variable.

18. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Get the absolute value equation by itself. Solve.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

19. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Two relatively prime numbers are integers that have no common factor other than 1.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

20. Prime Factorization of a Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
(x1+x2)/2 -(y1+y2)/2
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.
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.

21. 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?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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. 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?
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)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.

23. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Put the equation into y=mx+b-- in which case b is the y-intercept.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

24. Finding the Slope When Given an Equation of a Line
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

25. Raising a Power to a Power
Put each number in the original ratio over the sum of the numbers.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

26. Definition of an Irrational Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
(x1+x2)/2 -(y1+y2)/2
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

27. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

28. Finding the Mode of a Set of Numbers
The value that appears the most often.
Subtract the smallest from the largest and add 1
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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

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

30. Factoring the Difference of Two Squares
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
Use the formula distance=rate*time and its variations to help in this question.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

31. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Isolate the radical expression and use the standard rules of algebra.
Two relatively prime numbers are integers that have no common factor other than 1.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

32. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
A(2)+b(2)=c(2)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Put the equation into y=mx+b-- in which case b is the y-intercept.

33. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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

34. Finding the Length of an Arc in a Circle

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

35. Adding and Subtracting Polynomials
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Combine like terms.

36. 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
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

37. Factoring a Polynomial ('FOIL in Reverse')
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

38. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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

39. What Does Solving In Terms of Mean?
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
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

40. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
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.
Isolate the radical expression and use the standard rules of algebra.
Subtract the smallest from the largest and add 1

41. Dividing Fractions
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
-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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

42. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

43. Knowing if an Integer is a Multiple of 5 or 10
-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.
Adjacent angles are supplementary - Vertical angles are equal
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.

44. 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

45. Adding and Subtracting Roots
Use the formula distance=rate*time and its variations to help in this question.
Just add or subtract the coefficients in front of the radicals.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

46. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

47. Multiplying Binomials
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

48. 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 base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Plug in the given values for the unknowns and calculate according to PEMDAS.

49. Finding the Surface Area of a Rectangular Solid
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Probability: Number of Favorable Outcomes/Total Possible Outcomes

50. Simplifying Square Roots
Get the absolute value equation by itself. Solve.
Combine like terms.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.