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. Converting From a Mixed Number to an Improper Fraction
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Isolate the radical expression and use the standard rules of algebra.

2. What is the Triangle Inequality Theorem?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
Sum: Average x Number of Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

3. Characteristics of a Parallelogram
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.
-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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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

4. Adding and Subtracting Fractions
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
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.

5. Converting from part-to-part ratios to part-to-whole ratios
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.
Put each number in the original ratio over the sum of the numbers.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Express them with a common denominator.

6. How do you know if an integer is a multiple of 3 or 9?
2(pie)r
A(2)+b(2)=c(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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

7. Dividing Expressions with Exponents that Have a Common Base
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Part=Percent x Whole
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

8. Properties of a 30-60-90 Triangle
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

9. Definition of Remainder
The whole number left over after division.
Do whatever is necessary to both sides to isolate the variable.
'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.

10. 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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

11. 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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Factor out and cancel all factors the numerator and denominator have in common.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

12. 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.
Average: Sum of the Terms/Number of the Terms
Adjacent angles are supplementary - Vertical angles are equal
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

13. Prime Factorization of a 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.
The value that falls in the middle of the set.
Find a common denominator - then add or subtract the numerators.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

14. Simplifying Square Roots
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Get the absolute value equation by itself. Solve.

15. Multiplying Expressions with Exponents that Have a Common Base
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Just add or subtract the coefficients in front of the radicals.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

16. Definition of an Integer
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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

17. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

18. Solving a Problem Involving Rates
Factor out and cancel all factors the numerator and denominator have in common.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use the units to keep things straight - Snowfall inches/hours
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

19. If 2+l6-xl=10 and x>0 - what is the value of 2x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Cancel factors common to the numerator and denominator.
Get the absolute value equation by itself. Solve.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

20. Finding the GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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
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
Use the formula distance=rate*time and its variations to help in this question.

21. Definition of an Irrational Number
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

22. Multiplying Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Multiply the numerators and multiply the denominators.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

23. 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

24. Expressing the Union and Intersection of Sets
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
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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
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.

25. Characteristics of a Square
Get the absolute value equation by itself. Solve.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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

26. What is the Pythagorean Theorem?
A(2)+b(2)=c(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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

27. Adding and Subtracting Polynomials
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
Combine like terms.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

28. Number of Groups - +1 Each Time
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
VofaRS=lwh
Adjacent angles are supplementary - Vertical angles are equal
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

29. Finding the Midpoint Between Two Points
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.
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.
Get the absolute value equation by itself. Solve.
(x1+x2)/2 -(y1+y2)/2

30. Adding a Positive Number to a Negative Number
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Average: Sum of the Terms/Number of the Terms
2(pie)r
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

31. Finding the Volume of a Cylinder
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
VofaC: (pie)r(2)h

32. Knowing if an Integer is a Multiple of 2 or 4
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Factor out and cancel all factors the numerator and denominator have in common.
-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.
Multiply the numerators and multiply the denominators.

33. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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
Average the smallest and largest number
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

34. Finding the Slope of a Line When Given Two Points on the Line
-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.
Slope=change in y/change in x
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.

35. 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%.
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.
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 the whole number part by the denominator - then add the numerator. Keep the same denominator.

36. Formula to Find Average
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Average: Sum of the Terms/Number of the Terms

37. 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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Put each number in the original ratio over the sum of the numbers.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

38. Finding the Area of a Circle
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.
(pie)r(squared)
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.
Slope=change in y/change in x

39. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

40. Formula Used to Find Percent
Part=Percent x Whole
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

41. Properties of Similar Triangles
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)
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
-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.

42. Average Rate and How Do You Find It
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

43. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
-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.
Average the smallest and largest number
Put the equation into y=mx+b-- in which case b is the y-intercept.

44. Evaluating an Algebraic Expression
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.
Subtract the smallest from the largest and add 1
Use the units to keep things straight - Snowfall inches/hours
Plug in the given values for the unknowns and calculate according to PEMDAS.

45. An Important Property of a Line Tangent to a Circle
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
2(pie)r
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

46. Finding the Volume of a Rectangular Solid
VofaRS=lwh
(x1+x2)/2 -(y1+y2)/2
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
Average: Sum of the Terms/Number of the Terms

47. 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

48. What types of angles are formed when two lines intersect?
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Cancel factors common to the numerator and denominator.
Adjacent angles are supplementary - Vertical angles are equal

49. Solving a Proportion
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Cross multiply.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Combine like terms.

50. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
FOIL: First - Outer - Inner - Last... Combine Like Terms
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.