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

2. If 3(3x)=9(x+2) - what is the value of x?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Use the distance formula: d=(square root over) (x2-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
Average the smallest and largest number

3. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

4. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
2(pie)r
Plug in the given values for the unknowns and calculate according to PEMDAS.
(x1+x2)/2 -(y1+y2)/2

5. Properties of Similar Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Subtract the smallest from the largest and add 1
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

6. Finding the Surface Area of a Rectangular Solid
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
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
-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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

7. Definition of an Irrational 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.
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 distributive property then combine the like terms.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

8. 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
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
Cross multiply.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

9. Converting from an Improper Fraction to a Mixed Number
Multiply the numerators and multiply the denominators.
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.
Cancel factors common to the numerator and denominator.
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.

10. Finding the Area of a Sector

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

11. What value of x is not in the domain of the function f(x)=x-2/x-3?
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.
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
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.
A(2)+b(2)=c(2)

12. Definition of an Integer
Part=Percent x Whole
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

13. Finding the GCF of Two or More Numbers
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
(pie)r(squared)
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

14. Finding the Distance Between Two Points on a Coordinate Graph
Average: Sum of the Terms/Number of the Terms
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

15. 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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
VofaRS=lwh

16. Finding the Reciprocal of a Fraction
-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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use simple numbers like 1 and 2 and see what happens.
Switch the numerator and denominator.

17. Increasing and Decreasing a Number by a Certain Percentage
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
-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.

18. Difference Between a Factor and a Multiple
Cancel factors common to the numerator and denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
-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.

19. 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%
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.
Subtract the smallest from the largest and add 1
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

20. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
The value that falls in the middle of the set.
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.
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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

21. What types of angles are formed when a transversal cross parallel lines?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Four equal acute angles and four equal obtuse angles.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

22. Finding the Sum of the Interior Angles of a Polygon
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Use simple numbers like 1 and 2 and see what happens.

23. Converting from part-to-part ratios to part-to-whole ratios
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
Put each number in the original ratio over the sum of the numbers.
-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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

24. Finding the Volume of a Rectangular Solid
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
VofaRS=lwh
Use the formula distance=rate*time and its variations to help in this question.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

25. 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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Factor out and cancel all factors the numerator and denominator have in common.
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.

26. Finding the Circumference of a Circle
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
2(pie)r
(x1+x2)/2 -(y1+y2)/2

27. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
The value that falls in the middle of the set.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Put the equation into y=mx+b-- in which case b is the y-intercept.

28. If x(2)=7x+18 - what is the positive value of x?
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
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

29. Simplifying an Algebraic Equation
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.
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 simple numbers like 1 and 2 and see what happens.
Cancel factors common to the numerator and denominator.

30. Determining Absolute Value of a Number
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

31. 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.
2(pie)r
Isolate the radical expression and use the standard rules of algebra.
Multiply the numerators and multiply the denominators.

32. Knowing if an Integer is a Multiple of 2 or 4
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
-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.
Sum: Average x Number of Terms
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.

33. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
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.
Use the distributive property then combine the like terms.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

34. Formula to Find Average
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.
Average: Sum of the Terms/Number of the Terms
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.

35. Raising a Power to a Power
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Subtract the smallest from the largest and add 1
Just add or subtract the coefficients in front of the radicals.

36. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)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.
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

37. Simplifying Square Roots
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

38. 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

39. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Get the absolute value equation by itself. Solve.
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

40. Adding and Subtracting Monomials
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Slope=change in y/change in x
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Adjacent angles are supplementary - Vertical angles are equal

41. Converting From a Mixed Number to an Improper Fraction
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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
FOIL: First - Outer - Inner - Last... Combine Like Terms

42. PEMDAS
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

43. Factoring a Polynomial ('FOIL in Reverse')
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

44. Characteristics of a Rectangle
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Combine like terms.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

45. Adding and Subtracting Polynomials
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Combine like terms.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

46. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
-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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
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

47. Multiplying and Dividing Roots
The whole number left over after division.
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.
-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.
Get the absolute value equation by itself. Solve.

48. Finding the Midpoint Between Two Points
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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
(x1+x2)/2 -(y1+y2)/2
A(2)+b(2)=c(2)

49. Setting Up a Ratio
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.
-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.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

50. Definition of a Rational Number
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.