SUBJECTS
|
BROWSE
|
CAREER CENTER
|
POPULAR
|
JOIN
|
LOGIN
Business Skills
|
Soft Skills
|
Basic Literacy
|
Certifications
About
|
Help
|
Privacy
|
Terms
Search
Test your basic knowledge |
SAT Math
Start Test
Study First
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. How do you know if an integer is a multiple of 3 or 9?
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%.
Part=Percent x Whole
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.
2. Formula Used to Find Percent
Part=Percent x Whole
Switch the numerator and denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
3. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
The whole number left over after division.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
4. Properties of a 45-45-90 Triangle
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
The whole number left over after division.
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.
5. What is the positive difference between the answers to the equation 35+x(2)=12x?
6. Number of Groups - +1 Each Time
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.
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
7. Finding the LCM of Two or More Numbers
8. Properties of the Interior and Exterior Angles of a Triangle
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
-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.
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
9. Adding and Subtracting Polynomials
Combine like terms.
Subtract the smallest from the largest and add 1
Put each number in the original ratio over the sum of the numbers.
Factor out and cancel all factors the numerator and denominator have in common.
10. 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
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Two relatively prime numbers are integers that have no common factor other than 1.
11. What are Two Special Pythagorean Triples?
12. Expressing the Union and Intersection of Sets
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Find a common denominator - then add or subtract the numerators.
13. Finding the Area of a Circle
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
(pie)r(squared)
(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.
14. Definition of an Irrational Number
Isolate the radical expression and use the standard rules of algebra.
-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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
15. Factoring a Polynomial ('FOIL in Reverse')
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 formula distance=rate*time and its variations to help in this question.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
16. Finding the Domain and Range of a Function
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Cancel factors common to the numerator and denominator.
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. Solving a Problem Involving Rates
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
Use the units to keep things straight - Snowfall inches/hours
(pie)r(squared)
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
18. Numbers that are Relatively Prime
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.
Two relatively prime numbers are integers that have no common factor other than 1.
The value that appears the most often.
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
19. What Does Solving In Terms of Mean?
Two relatively prime numbers are integers that have no common factor other than 1.
Isolate the radical expression and use the standard rules of algebra.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
20. Adding and Subtracting Roots
Just add or subtract the coefficients in front of the radicals.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use the units to keep things straight - Snowfall inches/hours
21. Multiplying Fractions
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Multiply the numerators and multiply the denominators.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
22. Knowing if an Integer is a Multiple of 5 or 10
-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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Get the absolute value equation by itself. Solve.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
23. Definition of Remainder
The whole number left over after division.
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
A(2)+b(2)=c(2)
24. Finding a Term in a Geometric Sequence
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
25. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
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.
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.
26. What is the Pythagorean Theorem?
The value that falls in the middle of the set.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
A(2)+b(2)=c(2)
27. Comparing the values of two or more Fractions
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.
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.
-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.
28. 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.
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
Factor out and cancel all factors the numerator and denominator 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
29. Multiply and Divide Positive and Negative 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.
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
Isolate the radical expression and use the standard rules of algebra.
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.
30. Characteristics of a Square
Cancel factors common to the numerator and denominator.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
VofaC: (pie)r(2)h
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
31. Prime Factorization of a Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Use the units to keep things straight - Snowfall inches/hours
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
The value that falls in the middle of the set.
32. Knowing if an Integer is a Multiple of 2 or 4
-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.
Find a common denominator - then add or subtract the numerators.
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.
The value that appears the most often.
33. What is a Function and how do you Evaluate one?
34. Dividing Expressions with Exponents that Have a Common Base
-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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
35. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Adjacent angles are supplementary - Vertical angles are equal
Use the distance formula: d=(square root over) (x2-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.
36. If the average of a - b - and 48 is 48 - what is the value of a + b?
Use the distributive property then combine the like terms.
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.
Do whatever is necessary to both sides to isolate the variable.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
37. Finding the Missing Number in a Series When You are Given the Average
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Switch the numerator and denominator.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
38. What types of angles are formed when a transversal cross parallel lines?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Four equal acute angles and four equal obtuse angles.
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
39. Finding the Length of an Arc in a Circle
40. 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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Express them with a common denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
41. 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?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Just add or subtract the coefficients in front of the radicals.
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.
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.
42. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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 formula distance=rate*time and its variations to help in this question.
43. Finding the Distance Between Two Points on a Coordinate Graph
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.
44. Properties of Similar Triangles
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
-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.
45. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
46. Solving an Inequality
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Switch the numerator and denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
47. What types of angles are formed when two lines intersect?
2(pie)r
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Adjacent angles are supplementary - Vertical angles are equal
48. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
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.
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.
(x1+x2)/2 -(y1+y2)/2
49. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
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.
50. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Use simple numbers like 1 and 2 and see what happens.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.