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. 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.
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.
-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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


2. Scalene - Isosceles - and Equilateral Triangles
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 - substitute for the variable. Then evaluate the expression using the correct order of operations.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


3. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
VofaRS=lwh
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
Two relatively prime numbers are integers that have no common factor other than 1.


4. Formula Used to Find Percent
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.
(pie)r(squared)
Part=Percent x Whole
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.


5. Finding the Area of a Sector

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


6. Definition of a Rational Number
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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 rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Slope=change in y/change in x


7. Adding and Subtracting Polynomials
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Get the absolute value equation by itself. Solve.
Combine like terms.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


8. Converting From a Mixed Number to an Improper Fraction
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Subtract the smallest from the largest and add 1
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


9. Dividing Fractions
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
Sum: Average x Number of Terms


10. Expressing the Union and Intersection of Sets
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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 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


11. Converting from an Improper Fraction to a Mixed Number
Cancel factors common to the numerator and 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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


12. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Get the absolute value equation by itself. Solve.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-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.


13. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
Put each number in the original ratio over the sum of the numbers.
Four equal acute angles and four equal obtuse angles.
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


14. Definition of an Integer
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
-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.


15. Properties of a 45-45-90 Triangle
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
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
A(2)+b(2)=c(2)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


16. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Put each number in the original ratio over the sum of the numbers.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-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.


17. What Does Solving In Terms of Mean?
Switch the numerator and denominator.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Average: Sum of the Terms/Number of the Terms


18. How do you know if an integer is a multiple of 3 or 9?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Cross multiply.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.


19. Finding the Reciprocal of a Fraction
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
Switch the numerator and denominator.
Use the formula distance=rate*time and its variations to help in this question.


20. If r#t=t(r)-r(t) - then what is 4#3?
Use the units to keep things straight - Snowfall inches/hours
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
VofaRS=lwh
Combine like terms.


21. Characteristics of a Parallelogram
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.
Average: Sum of the Terms/Number of the Terms
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


22. 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%
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
Isolate the radical expression and use the standard rules of algebra.


23. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Put the equation into y=mx+b-- in which case b is the y-intercept.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Do whatever is necessary to both sides to isolate the variable.


24. Finding the Domain and Range of a Function
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.
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


25. Number of Groups - +1 Each Time
Two relatively prime numbers are integers that have no common factor other than 1.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Part=Percent x Whole
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


26. Finding the Area of a Circle
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
(pie)r(squared)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle


27. Factoring the Difference of Two Squares
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)
The value that appears the most often.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


28. Adding and Subtracting Fractions
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
Get the absolute value equation by itself. Solve.
Find a common denominator - then add or subtract the numerators.


29. If 4(x(2)-10x+25) - then what is the value of x?
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.
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Switch the numerator and denominator.


30. Prime Factorization of a Number
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Put the equation into y=mx+b-- in which case b is the y-intercept.


31. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
-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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
2(pie)r


32. Finding the Median of a Set of Numbers
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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 falls in the middle of the set.


33. What is the Triangle Inequality Theorem?
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.
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.
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.
VofaRS=lwh


34. If x(2)=7x+18 - what is the positive value of x?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


35. Multiplying Monomials
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.


36. 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


37. What value of x is not in the domain of the function f(x)=x-2/x-3?
-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.
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
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.
Express them with a common denominator.


38. Finding the Volume of a Cylinder
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
VofaC: (pie)r(2)h
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


39. Finding the Sum of the Average of a Series of Numbers
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Sum: Average x Number of Terms
Cancel factors common to the numerator and denominator.
FOIL: First - Outer - Inner - Last... Combine Like Terms


40. 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


41. Finding the GCF of Two or More 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
Break down the integers into their prime factorizations - and multiply all prime factors they 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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


42. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


43. Solving a Problem Involving Rates
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.
Use the units to keep things straight - Snowfall inches/hours
Put each number in the original ratio over the sum of the numbers.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


44. An Important Property of a Line Tangent to a Circle
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.
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.
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
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.


45. What is the positive difference between the answers to the equation 35+x(2)=12x?

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


46. 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?
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.


47. Solving a Linear Equation
Plug in the given values for the unknowns and calculate according to PEMDAS.
Factor out and cancel all factors the numerator and denominator have in common.
Do whatever is necessary to both sides to isolate the variable.
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.


48. Finding the Length of an Arc in a Circle

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


49. What types of angles are formed when a transversal cross parallel lines?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Four equal acute angles and four equal obtuse angles.
Get the absolute value equation by itself. Solve.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


50. Finding the Volume of a Rectangular Solid
Sum: Average x Number of Terms
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
VofaRS=lwh
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.