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. Multiplying Binomials
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Cancel factors common to the numerator and denominator.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Just add or subtract the coefficients in front of the radicals.


2. Simplifying Square Roots
VofaRS=lwh
The value that appears the most often.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


3. Definition of a Rational Number
Do whatever is necessary to both sides to isolate the variable.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.


4. 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


5. 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%.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


6. Finding the Area of a Sector

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


7. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Use simple numbers like 1 and 2 and see what happens.
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.


8. Properties of Similar Triangles
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Isolate the radical expression and use the standard rules of algebra.


9. Finding the Area of a Circle
A(2)+b(2)=c(2)
(pie)r(squared)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Put the equation into y=mx+b-- in which case b is the y-intercept.


10. Knowing if an Integer is a Multiple of 2 or 4
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.
Two relatively prime numbers are integers that have no common factor other than 1.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


11. Solving a Radical Equation
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.
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.
Isolate the radical expression and use the standard rules of algebra.
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.


12. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Four equal acute angles and four equal obtuse angles.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


13. What types of angles are formed when a transversal cross parallel lines?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Four equal acute angles and four equal obtuse angles.
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.


14. 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


15. Finding the Sum of the Interior Angles of a Polygon
Average the smallest and largest number
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
The whole number left over after division.


16. What Does Solving In Terms of Mean?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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
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.


17. Scalene - Isosceles - and Equilateral Triangles
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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
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.
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.


18. Setting Up a Ratio
Multiply the exponents - (x^3)^4=x^3*4=x^12
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


19. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
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


20. 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


21. If the average of a - b - and 48 is 48 - what is the value of a + b?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Isolate the radical expression and use the standard rules of algebra.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


22. Definition of an Integer
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


23. Finding the Slope When Given an Equation of a Line
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.


24. Finding the Midpoint Between Two Points
-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.
Cancel factors common to the numerator and denominator.
(x1+x2)/2 -(y1+y2)/2
VofaC: (pie)r(2)h


25. 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 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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Express them with a common denominator.


26. 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


27. What value of x is not in the domain of the function f(x)=x-2/x-3?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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
Put the equation into y=mx+b-- in which case b is the y-intercept.
Switch the numerator and denominator.


28. Calculating Negative Exponents and Radical Exponents
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


29. Simplifying an Algebraic Equation
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
Cancel factors common to the numerator and 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.


30. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Part=Percent x Whole
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


31. 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.
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 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
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.


32. Calculating the Probability that an Event will Take Place
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Probability: Number of Favorable Outcomes/Total Possible Outcomes
-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.


33. Counting the Total Number of Possibilities for Several Events to Occur
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
(pie)r(squared)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


34. 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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


35. PEMDAS
Isolate the radical expression and use the standard rules of algebra.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Cancel factors common to the numerator and denominator.


36. Formula Used to Find Percent
FOIL: First - Outer - Inner - Last... Combine Like Terms
Part=Percent x Whole
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.
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.


37. Properties of the Interior and Exterior Angles of a Triangle
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
Two relatively prime numbers are integers that have no common factor other than 1.


38. Finding the Sum of the Average of a Series of Numbers
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.
Sum: Average x Number of Terms
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


39. Knowing if an Integer is a Multiple of 5 or 10
Do whatever is necessary to both sides to isolate the variable.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
-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.


40. Converting from an Improper Fraction to a Mixed Number
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.
Just add or subtract the coefficients in front of the radicals.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Combine like terms.


41. Definition of Remainder
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The whole number left over after division.


42. Finding the Rate of Speed
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.
Use the formula distance=rate*time and its variations to help in this question.
Part=Percent x Whole
The value that falls in the middle of the set.


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


44. What is the Triangle Inequality Theorem?
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Isolate the radical expression and use the standard rules of algebra.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


45. If (Square Root: x-1)+5=12 - what is the value of x/2?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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


46. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
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
Factor out and cancel all factors the numerator and denominator have in common.
Use the units to keep things straight - Snowfall inches/hours


47. Solving an Inequality
-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 whole number left over after division.
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


48. Evaluating an Algebraic Expression
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Plug in the given values for the unknowns and calculate according to PEMDAS.


49. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


50. Solving a Problem Involving Rates
Multiply the numerators and multiply the denominators.
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
A(2)+b(2)=c(2)