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. 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


2. Adding and Subtracting Polynomials
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
(x1+x2)/2 -(y1+y2)/2
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Combine like terms.


3. 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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Cancel factors common to the numerator and denominator.


4. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Plug in the given values for the unknowns and calculate according to PEMDAS.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Switch the numerator and denominator.
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


5. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
VofaRS=lwh
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Combine like terms.


6. General Procedure for Multiplying Polynomials
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use the distributive property then combine the like terms.
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.


7. Finding the Area of a Sector

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


8. Finding the Mode of a Set of Numbers
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The value that appears the most often.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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


9. Solving a Proportion
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Cross multiply.
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.


10. What types of angles are formed when two lines intersect?
Factor out and cancel all factors the numerator and denominator have in common.
Adjacent angles are supplementary - Vertical angles are equal
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.
Express them with a common denominator.


11. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
Just add or subtract the coefficients in front of the radicals.
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.
VofaC: (pie)r(2)h


12. 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
Use simple numbers like 1 and 2 and see what happens.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
The value that falls in the middle of the set.


13. Finding the Area of a Circle
Four equal acute angles and four equal obtuse angles.
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.
(pie)r(squared)
Get the absolute value equation by itself. Solve.


14. Solving a Linear Equation
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.
Combine like terms.
Use the formula distance=rate*time and its variations to help in this question.
Do whatever is necessary to both sides to isolate the variable.


15. 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?
VofaC: (pie)r(2)h
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
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


16. Direct Variation and Inverse Variation
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.
Adjacent angles are supplementary - Vertical angles are equal
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
Average the smallest and largest number


17. Adding and Subtracting Roots
Use simple numbers like 1 and 2 and see what happens.
Get the absolute value equation by itself. Solve.
Just add or subtract the coefficients in front of the radicals.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


18. Multiply and Divide Positive and Negative Numbers
Adjacent angles are supplementary - Vertical angles are equal
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 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Use the distributive property then combine the like terms.


19. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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
Slope=change in y/change in x
A(2)+b(2)=c(2)


20. Multiplying Binomials
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
-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.


21. Finding a Term in a Geometric Sequence
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.
Just add or subtract the coefficients in front of the radicals.
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


22. If 4(x(2)-10x+25) - then what is the value of x?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
The value that appears the most often.
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
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.


23. 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.
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


24. Number of Groups - +1 Each Time
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.


25. 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


26. Finding the Volume of a Cylinder
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
VofaC: (pie)r(2)h


27. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


28. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Average: Sum of the Terms/Number of the Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.


29. Simplifying an Algebraic Equation
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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Cancel factors common to the numerator and denominator.


30. Converting from an Improper Fraction to a Mixed Number
Express them with a common 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 value that falls in the middle of the set.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


31. Dividing Expressions with Exponents that Have a Common Base
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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


32. Knowing if an Integer is a Multiple of 5 or 10
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.
Switch the numerator and denominator.
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 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.


33. 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


34. Finding the y-intercept When Given an Equation of a Line
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.
Cross multiply.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Put the equation into y=mx+b-- in which case b is the y-intercept.


35. Finding the Volume of a Rectangular Solid
VofaRS=lwh
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Average the smallest and largest 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.


36. Increasing and Decreasing a Number by a Certain Percentage
-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.
(x1+x2)/2 -(y1+y2)/2
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Four equal acute angles and four equal obtuse angles.


37. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
(pie)r(squared)
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.


38. Solving a System of Equations
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.
Four equal acute angles and four equal obtuse angles.
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.
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.


39. Counting the Total Number of Possibilities for Several Events to Occur
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.
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.
Two relatively prime numbers are integers that have no common factor other than 1.
2(pie)r


40. What types of angles are formed when a transversal cross parallel lines?
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The value that appears the most often.
Four equal acute angles and four equal obtuse angles.
Switch the numerator and denominator.


41. 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


42. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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
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.
Average the smallest and largest number


43. Characteristics of a Rectangle
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


44. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


45. Properties of a 45-45-90 Triangle
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Adjacent angles are supplementary - Vertical angles are equal
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Average the smallest and largest number


46. Finding the Midpoint Between Two Points
Cancel factors common to the numerator and denominator.
(x1+x2)/2 -(y1+y2)/2
Put the equation into y=mx+b-- in which case b is the y-intercept.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


47. Finding the Surface Area of a Rectangular Solid
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Put each number in the original ratio over the sum of the numbers.


48. Solving a Problem Involving Rates
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 units to keep things straight - Snowfall inches/hours
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


49. Properties of the Interior and Exterior Angles of a Triangle
Do whatever is necessary to both sides to isolate the variable.
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.
2(pie)r
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


50. Simplifying Square Roots
Part=Percent x Whole
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Slope=change in y/change in x
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2