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. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Switch the numerator and denominator.
The value that falls in the middle of the set.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

2. An Important Property of a Line Tangent to a Circle
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
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 units to keep things straight - Snowfall inches/hours

3. Characteristics of a Square
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Part=Percent x Whole
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

4. Solving a System of Equations
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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 formula distance=rate*time and its variations to help in this question.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

5. Simplifying an Algebraic Equation
Multiply the exponents - (x^3)^4=x^3*4=x^12
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
2(pie)r
Cancel factors common to the numerator and denominator.

6. Finding the Mode of a Set of Numbers
Use the units to keep things straight - Snowfall inches/hours
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Cancel factors common to the numerator and denominator.
The value that appears the most often.

7. Finding a Term in a Geometric Sequence
Isolate the radical expression and use the standard rules of algebra.
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.
-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.
Two relatively prime numbers are integers that have no common factor other than 1.

8. Knowing if an Integer is a Multiple of 2 or 4
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Just add or subtract the coefficients in front of the radicals.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
-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.

9. 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
(x1+x2)/2 -(y1+y2)/2
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
The value that appears the most often.

10. 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

11. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
A(2)+b(2)=c(2)
FOIL: First - Outer - Inner - Last... 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.

12. If r#t=t(r)-r(t) - then what is 4#3?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

13. Finding the Slope When Given an Equation of a Line
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
VofaC: (pie)r(2)h
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.

14. Properties of the Interior and Exterior Angles of a Triangle
Average: Sum of the Terms/Number of the Terms
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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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. Finding the Volume of a Rectangular Solid
VofaRS=lwh
Subtract the smallest from the largest and add 1
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.

16. Finding the Domain and Range of a Function
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Multiply the numerators and multiply the denominators.
-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.
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.

17. Converting from part-to-part ratios to part-to-whole ratios
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.
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 the perfect squares under the radical - take their square roots - and put the result in front.
Put each number in the original ratio over the sum of the numbers.

18. Properties of a 45-45-90 Triangle
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
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

19. Finding the Median of a Set of Numbers
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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 value that falls in the middle of the set.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

20. Comparing the values of two or more Fractions
Put the equation into y=mx+b-- in which case b is the y-intercept.
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
Express them with a common denominator.
2(pie)r

21. 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
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.
Put each number in the original ratio over the sum of the numbers.

22. If 3(3x)=9(x+2) - what is the value of x?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.

23. 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

24. 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
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%
Combine like terms.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

25. Solving a Proportion
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
Cross multiply.
-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 the distributive property then combine the like terms.

26. Knowing if an Integer is a Multiple of 5 or 10
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Do whatever is necessary to both sides to isolate the variable.
Isolate the radical expression and use the standard rules of algebra.
-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.

27. 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
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.
Just add or subtract the coefficients in front of the radicals.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

28. Finding the Rate of Speed
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Get the absolute value equation by itself. Solve.
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.

29. 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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

30. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Use the formula distance=rate*time and its variations to help in this question.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

31. General Procedure for Multiplying Polynomials
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Use the distributive property then combine the like terms.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

32. Adding and Subtracting Roots
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Just add or subtract the coefficients in front of the radicals.
Get the absolute value equation by itself. Solve.

33. Finding the Missing Number in a Series When You are Given the Average
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
(x1+x2)/2 -(y1+y2)/2
2(pie)r

34. Definition of an Irrational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.

35. Adding and Subtracting Fractions
Cross multiply.
Find a common denominator - then add or subtract the numerators.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Just add or subtract the coefficients in front of the radicals.

36. Formula Used to Find Percent
Part=Percent x Whole
-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.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

37. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
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.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

38. Adding a Positive Number to a Negative Number
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

39. 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

40. PEMDAS
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
A(2)+b(2)=c(2)

41. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Switch the numerator and denominator.
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

42. Formula to Find Average
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: Sum of the Terms/Number of the Terms
Find a common denominator - then add or subtract the numerators.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

43. Multiplying and Dividing Roots
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

44. 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?
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.

45. Finding the Circumference of a Circle
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
2(pie)r
Isolate the radical expression and use the standard rules of algebra.

46. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

47. If the average of a - b - and 48 is 48 - what is the value of a + b?
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
Use the formula distance=rate*time and its variations to help in this question.
Express them with a common denominator.

48. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
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 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 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.

49. 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

50. Finding the Distance Between Two Points on a Coordinate Graph
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating 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.