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 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.
Just add or subtract the coefficients in front of the radicals.
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
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.

2. What is the Triangle Inequality Theorem?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

3. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Do whatever is necessary to both sides to isolate the variable.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

4. Scalene - Isosceles - and Equilateral Triangles
Combine like terms.
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.
The value that falls in the middle of the set.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

5. Finding the Rate of Speed
Use the formula distance=rate*time and its variations to help in this question.
Express them with a common denominator.
Adjacent angles are supplementary - Vertical angles are equal
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.

6. 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?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
VofaRS=lwh
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

7. 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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Find a common denominator - then add or subtract the numerators.

8. What is the Pythagorean Theorem?
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
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.
A(2)+b(2)=c(2)
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

9. How do you know if an integer is a multiple of 3 or 9?
Express them with a common denominator.
Plug in the given values for the unknowns and calculate according to PEMDAS.
(x1+x2)/2 -(y1+y2)/2
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.

10. Finding the Slope When Given an Equation of a Line
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Subtract the smallest from the largest and add 1
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

11. 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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Use the formula distance=rate*time and its variations to help in this question.

12. Adding and Subtracting Roots
-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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Just add or subtract the coefficients in front of the radicals.
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.

13. Finding the y-intercept When Given an Equation of a Line
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.
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

14. Finding the Slope of a Line When Given Two Points on the Line
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
Slope=change in y/change in x
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Switch the numerator and denominator.

15. What types of angles are formed when a transversal cross parallel lines?
Cross multiply.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Four equal acute angles and four equal obtuse angles.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

16. Raising a Power to a Power
The value that falls in the middle of the set.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

17. If (Square Root: x-1)+5=12 - what is the value of x/2?
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.
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
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.

18. Numbers that are Relatively Prime
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Two relatively prime numbers are integers that have no common factor other than 1.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

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.
Get the absolute value equation by itself. Solve.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The whole number left over after division.

20. Multiply and Divide Positive and Negative Numbers
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Use the formula distance=rate*time and its variations to help in this question.
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

21. Finding the Missing Number in a Series When You are Given the Average
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
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

22. Solving a System of Equations
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
Combine like terms.
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.

23. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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
Switch the numerator and denominator.

24. Finding the Median of a Set of Numbers
Put the equation into y=mx+b-- in which case b is the y-intercept.
The value that falls in the middle of the set.
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.

25. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Slope=change in y/change in x

26. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Multiply the numerators and multiply the denominators.
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.
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.

27. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Slope=change in y/change in x
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Get the absolute value equation by itself. Solve.

28. Finding the Circumference of a Circle
-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.
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
2(pie)r
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.

29. 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

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

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

31. 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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.

32. Direct Variation and Inverse Variation
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.
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.
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.
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

33. 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

34. Converting From a Mixed Number to an Improper Fraction
Find a common denominator - then add or subtract the numerators.
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.
The value that falls in the middle of the set.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

35. Adding a Positive Number to a Negative Number
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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
Part=Percent x Whole

36. General Procedure for Multiplying Polynomials
VofaRS=lwh
Use the distributive property then combine the like terms.
Average: Sum of the Terms/Number of the Terms
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.

37. Convert From a Fraction to a Decimal - Vice Versa
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.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

38. Adding and Subtracting Polynomials
Get the absolute value equation by itself. Solve.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Combine like terms.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

39. Dividing Fractions
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
-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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

40. 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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^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.

41. Definition of Remainder
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Cross multiply.
The whole number left over after division.

42. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
The whole number left over after division.
-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.

43. Finding the Sum of the Interior Angles of a Polygon
2(pie)r
Use simple numbers like 1 and 2 and see what happens.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Find a common denominator - then add or subtract the numerators.

44. Factoring the Difference of Two Squares
Just add or subtract the coefficients in front of the radicals.
Use the formula distance=rate*time and its variations to help in this question.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

45. Evaluating an Algebraic Expression
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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 one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

46. Finding the Surface Area of a Rectangular Solid
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Subtract the smallest from the largest and add 1
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

47. Multiplying Binomials
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
FOIL: First - Outer - Inner - Last... Combine Like Terms

48. Knowing if an Integer is a Multiple of 2 or 4
-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.
The value that falls in the middle of the set.
Get the absolute value equation by itself. Solve.
Use the units to keep things straight - Snowfall inches/hours

49. What are Two Special Pythagorean Triples?

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

50. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Average the smallest and largest number
Use simple numbers like 1 and 2 and see what happens.
The whole number left over after division.