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 y-intercept When Given an Equation of a Line
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Put the equation into y=mx+b-- in which case b is the y-intercept.
The whole number left over after division.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

2. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Just add or subtract the coefficients in front of the radicals.
-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 up an equation. Think of the result of a 15 percent increase over x as 1.15x.

3. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 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.
Use the formula distance=rate*time and its variations to help in this question.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.

4. Finding the Slope When Given an Equation of a Line
Get the absolute value equation by itself. Solve.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Find a common denominator - then add or subtract the numerators.
Use simple numbers like 1 and 2 and see what happens.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Slope=change in y/change in x

6. What is the greatest of three consecutive odd integers where the sum of the third and twice the first is equal to nine more than twice the second?
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.
Two relatively prime numbers are integers that have no common factor other than 1.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.

7. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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 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.
(x1+x2)/2 -(y1+y2)/2
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

8. If x(2)=7x+18 - what is the positive value of x?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

9. Convert From a Fraction to a Decimal - Vice Versa
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
-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.
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 number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

10. Scalene - Isosceles - and Equilateral Triangles
Use the formula distance=rate*time and its variations to help in this question.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
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.

11. Properties of a 45-45-90 Triangle
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Adjacent angles are supplementary - Vertical angles are equal

12. Converting From a Mixed Number to an Improper Fraction
Isolate the radical expression and use the standard rules of algebra.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.

13. Solving a Linear Equation
The whole number left over after division.
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.
Just add or subtract the coefficients in front of the radicals.
Do whatever is necessary to both sides to isolate the variable.

14. Properties of a 30-60-90 Triangle
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

15. 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

16. 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.
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.
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 numerators and multiply the denominators.

17. Definition of a Rational Number
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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
A(2)+b(2)=c(2)
Find a common denominator - then add or subtract the numerators.

18. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Combine like terms.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

19. 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

20. Multiply and Divide Positive and Negative Numbers
Use the units to keep things straight - Snowfall inches/hours
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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

21. Finding the Sum of the Interior Angles of a Polygon
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Factor out and cancel all factors the numerator and denominator have in common.
Sum: Average x Number of Terms
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

22. 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?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
VofaC: (pie)r(2)h
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

23. Direct Variation and Inverse Variation
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.
The whole number left over after division.
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
Get the absolute value equation by itself. Solve.

24. Simplifying an Algebraic Equation
The value that appears the most often.
Adjacent angles are supplementary - Vertical angles are equal
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Cancel factors common to the numerator and denominator.

25. Numbers that are Relatively Prime
A(2)+b(2)=c(2)
Two relatively prime numbers are integers that have no common factor other than 1.
Use the distributive property then combine the like terms.
Plug in the given values for the unknowns and calculate according to PEMDAS.

26. Characteristics of a Square
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
VofaRS=lwh
Just add or subtract the coefficients in front of the radicals.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

27. Finding the Mode of a Set of Numbers
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
The value that appears the most often.
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

28. Finding the GCF of Two or More Numbers
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Express them with a common denominator.

29. 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.
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
Multiply the numerators and multiply the denominators.
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.

30. Multiplying and Dividing Roots
-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.
-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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.

31. How do you know if an integer is a multiple of 3 or 9?
Just add or subtract the coefficients in front of the radicals.
The whole number left over after division.
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.
Four equal acute angles and four equal obtuse angles.

32. Finding the Circumference of a Circle
2(pie)r
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
(pie)r(squared)
Get the absolute value equation by itself. Solve.

33. Dividing Expressions with Exponents that Have a Common Base
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
(x1+x2)/2 -(y1+y2)/2
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

34. Factoring the Difference of Two Squares
Four equal acute angles and four equal obtuse angles.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Switch the numerator and denominator.

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%.
Use the units to keep things straight - Snowfall inches/hours
-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.
Multiply the numerators and multiply the denominators.

36. Calculating the Probability that an Event will Take Place
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

37. If 4(x(2)-10x+25) - then what is the value of x?
Average: Sum of the Terms/Number of the Terms
(x1+x2)/2 -(y1+y2)/2
Put each number in the original ratio over the sum of the numbers.
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.

38. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Part=Percent x Whole
Average the smallest and largest number
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

39. Expressing the Union and Intersection of Sets
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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The value that falls in the middle of the set.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

40. Finding the Reciprocal of a Fraction
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Switch the numerator and denominator.
Adjacent angles are supplementary - Vertical angles are equal

41. 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

42. Solving an Inequality
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
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

43. Adding and Subtracting Polynomials
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
-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.
Combine like terms.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

44. Formula Used to Find Percent
Subtract the smallest from the largest and add 1
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.
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.
Part=Percent x Whole

45. Properties of the Interior and Exterior Angles of a Triangle
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.

46. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Get the absolute value equation by itself. Solve.

47. 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
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.
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

48. Simplifying Square Roots
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
Put each number in the original ratio over the sum of the numbers.

49. Definition of Remainder
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 whole number left over after division.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
-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.

50. What is the Pythagorean Theorem?
Put each number in the original ratio over the sum of the numbers.
A(2)+b(2)=c(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.
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