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. If the average of a - b - and 48 is 48 - what is the value of a + b?
Average: Sum of the Terms/Number of the Terms
The value that falls in the middle of the set.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Put the equation into y=mx+b-- in which case b is the y-intercept.

2. 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%.
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.
The whole number left over after division.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

3. Definition of a Rational Number
(x1+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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

4. PEMDAS
Sum: Average x Number of Terms
Express them with a common denominator.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.

5. Number of Groups - +1 Each Time
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The value that appears the most often.
Use the formula distance=rate*time and its variations to help in this question.

6. Solving a Proportion
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Cancel factors common to the numerator and denominator.
Cross multiply.
A(2)+b(2)=c(2)

7. Raising a Power to a Power
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Multiply the exponents - (x^3)^4=x^3*4=x^12
A(2)+b(2)=c(2)

8. Dividing Fractions
(x1+x2)/2 -(y1+y2)/2
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

9. Expressing the Union and Intersection of Sets
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Four equal acute angles and four equal obtuse angles.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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

10. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
(x1+x2)/2 -(y1+y2)/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.

11. Finding the Area of a Circle
(pie)r(squared)
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
A(2)+b(2)=c(2)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

12. Characteristics of a Square
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.

13. Adding a Positive Number to a Negative Number
VofaRS=lwh
Average: Sum of the Terms/Number of the Terms
Combine like terms.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

14. Counting the Total Number of Possibilities for Several Events to Occur
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Combine like terms.
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.
Get the absolute value equation by itself. Solve.

15. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
VofaC: (pie)r(2)h
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Express them with a common denominator.

16. Finding the Domain and Range of a Function
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.
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.
Express them with a common denominator.
Isolate the radical expression and use the standard rules of algebra.

17. Finding the Circumference of a Circle
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.
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
2(pie)r

18. 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.
Use simple numbers like 1 and 2 and see what happens.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

19. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
Get the absolute value equation by itself. Solve.
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 numerators and multiply the denominators.

20. 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.
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
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Slope=change in y/change in x

21. Finding the Area of a Triangle

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

22. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Slope=change in y/change in x

23. Finding the Volume of a Cylinder
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
VofaC: (pie)r(2)h
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.

24. Knowing if an Integer is a Multiple of 2 or 4
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.
-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: Sum of the Terms/Number of 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.

25. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
The value that falls in the middle of the set.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Use simple numbers like 1 and 2 and see what happens.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

26. 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.
Use the distributive property then combine the like terms.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Use the formula distance=rate*time and its variations to help in this question.

27. Multiplying Fractions
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Just add or subtract the coefficients in front of the radicals.
Multiply the numerators and multiply the denominators.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

28. If 3(3x)=9(x+2) - what is the value of x?
Part=Percent x Whole
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

29. Dividing Expressions with Exponents that Have a Common Base
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Four equal acute angles and four equal obtuse angles.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

30. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

31. Finding the y-intercept When Given an Equation of a Line
VofaC: (pie)r(2)h
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Switch the numerator and denominator.
Put the equation into y=mx+b-- in which case b is the y-intercept.

32. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Multiply the exponents - (x^3)^4=x^3*4=x^12

33. Adding and Subtracting Roots
Multiply the exponents - (x^3)^4=x^3*4=x^12
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
Just add or subtract the coefficients in front of the radicals.

34. How do you know if an integer is a multiple of 3 or 9?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
-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 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.

35. Setting Up a Ratio
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
-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.
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

36. Finding the Slope When Given an Equation of a Line
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Switch the numerator and denominator.
Plug in the given values for the unknowns and calculate according to PEMDAS.

37. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
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.
The whole number left over after division.

38. Finding the Median of a Set of Numbers
Do whatever is necessary to both sides to isolate the variable.
The whole number left over after division.
The value that falls in the middle of the set.
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.

39. Characteristics of a Rectangle
Multiply the numerators and multiply the denominators.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

40. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
Switch the numerator and denominator.

41. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

42. Converting from part-to-part ratios to part-to-whole ratios
Subtract the smallest from the largest and add 1
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Put each number in the original ratio over the sum of the numbers.
Multiply the exponents - (x^3)^4=x^3*4=x^12

43. 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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Subtract the smallest from the largest and add 1
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.

44. Finding the Volume of a Rectangular Solid
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Put each number in the original ratio over the sum of the numbers.
VofaRS=lwh

45. Definition of Remainder
The whole number left over after division.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Cross multiply.

46. Adding and Subtracting Monomials
-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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12

47. Knowing if an Integer is a Multiple of 5 or 10
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
-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.
(x1+x2)/2 -(y1+y2)/2
Find a common denominator - then add or subtract the numerators.

48. Multiplying Expressions with Exponents that Have a Common Base
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

49. Formula Used to Find Percent
Part=Percent x Whole
Cancel factors common to the numerator and denominator.
Use the distributive property then combine the like terms.
A(2)+b(2)=c(2)

50. Determining Absolute Value of a Number
VofaRS=lwh
2(pie)r
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Put the equation into y=mx+b-- in which case b is the y-intercept.