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
(pie)r(squared)
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.

2. Knowing if an Integer is a Multiple of 2 or 4
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.
-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.
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.
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

3. Finding the Area of a Sector

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

4. Properties of a 45-45-90 Triangle
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.

5. Let N represent the smallest positive integer that is a multiple of 6 and 8 - but leaves a remainder of 2 when divided by 7. What is the value of N?
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

6. Solving a Proportion
Cross 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.
Two relatively prime numbers are integers that have no common factor other than 1.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

7. Definition of a Rational Number
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

8. Calculating Negative Exponents and Radical Exponents
Use simple numbers like 1 and 2 and see what happens.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Factor out and cancel all factors the numerator and denominator have in common.

9. What is the Triangle Inequality Theorem?
Do whatever is necessary to both sides to isolate the variable.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.

10. 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.
(pie)r(squared)
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

11. Finding the Surface Area of a Rectangular Solid
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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 the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

12. 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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

13. Increasing and Decreasing a Number by a Certain Percentage
Do whatever is necessary to both sides to isolate the variable.
A(2)+b(2)=c(2)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
-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.

14. Solving a Problem Involving Rates
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
Use the units to keep things straight - Snowfall inches/hours
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

15. 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

16. Characteristics of a Rectangle
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

17. Formula Used to Find Percent
Part=Percent x Whole
(pie)r(squared)
Do whatever is necessary to both sides to isolate the variable.
Use the formula distance=rate*time and its variations to help in this question.

18. Direct Variation and Inverse Variation
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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Use the formula distance=rate*time and its variations to help in this question.
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.

19. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

20. Counting the Total Number of Possibilities for Several Events to Occur
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.

21. Solving a Linear Equation
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Average the smallest and largest number
-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.
Do whatever is necessary to both sides to isolate the variable.

22. Finding the Sum of the Interior Angles of a Polygon
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

23. Setting Up a Ratio
FOIL: First - Outer - Inner - Last... Combine Like Terms
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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
Plug in the given values for the unknowns and calculate according to PEMDAS.

24. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Express them with a common denominator.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Use the units to keep things straight - Snowfall inches/hours

25. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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
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.

26. Multiply and Divide Positive and Negative Numbers
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
(x1+x2)/2 -(y1+y2)/2
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

27. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

28. Adding and Subtracting Polynomials
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Subtract the smallest from the largest and add 1
Combine like terms.

29. If r#t=t(r)-r(t) - then what is 4#3?
Cancel factors common to the numerator and denominator.
A(2)+b(2)=c(2)
Find a common denominator - then add or subtract the numerators.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

30. Multiplying and Dividing Roots
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
VofaRS=lwh
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.
2(pie)r

31. Scalene - Isosceles - and Equilateral Triangles
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.

32. Multiplying Binomials
(pie)r(squared)
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
FOIL: First - Outer - Inner - Last... Combine Like Terms

33. Simplifying a Fraction to Lowest Terms
Express them with a common denominator.
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.
Factor out and cancel all factors the numerator and denominator have in common.
(x1+x2)/2 -(y1+y2)/2

34. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
Average: Sum of the Terms/Number of the Terms
Combine like terms.

35. What is the Pythagorean Theorem?
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
(pie)r(squared)
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
A(2)+b(2)=c(2)

36. How do you know if an integer is a multiple of 3 or 9?
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
FOIL: First - Outer - Inner - Last... Combine Like Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.

37. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the 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.
(x1+x2)/2 -(y1+y2)/2
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

38. Finding the Median of a Set of Numbers
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.
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.
The value that falls in the middle of the set.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

39. Definition of an Irrational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Use the distributive property then combine the like terms.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Sum: Average x Number of Terms

40. Determining Absolute Value of a Number
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

41. Finding the Slope of a Line When Given Two Points on the Line
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Slope=change in y/change in x
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

42. Converting from an Improper Fraction to a Mixed Number
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Average the smallest and largest number

43. Factoring the Difference of Two Squares
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
Use the formula distance=rate*time and its variations to help in this question.

44. Adding and Subtracting Fractions
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Use the formula distance=rate*time and its variations to help in this question.
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.
Find a common denominator - then add or subtract the numerators.

45. Prime Factorization of a Number
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Four equal acute angles and four equal obtuse angles.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

46. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Just add or subtract the coefficients in front of the radicals.
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 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.
Get the absolute value equation by itself. Solve.

47. If x(2)=7x+18 - what is the positive value of x?
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
VofaRS=lwh
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

48. Definition of Remainder
The whole number left over after division.
Cross multiply.
Use the distributive property then combine the like terms.
Just add or subtract the coefficients in front of the radicals.

49. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
Plug in the given values for the unknowns and calculate according to PEMDAS.
2(pie)r
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

50. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Find a common denominator - then add or subtract the numerators.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.