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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. Solving a System of Equations
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.

2. Properties of the Interior and Exterior Angles of a Triangle
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.
Average the smallest and largest number
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.
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.

3. Counting the Total Number of Possibilities for Several Events to Occur
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

4. If (Square Root: x-1)+5=12 - what is the value of x/2?
Cancel factors common to the numerator and denominator.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

5. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
The whole number left over after division.
Get the absolute value equation by itself. Solve.
-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.

6. Multiplying Fractions
Use the units to keep things straight - Snowfall inches/hours
Subtract the smallest from the largest and add 1
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Multiply the numerators and multiply the denominators.

7. Converting From a Mixed Number to an Improper Fraction
Just add or subtract the coefficients in front of the radicals.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

8. 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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
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.

9. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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
Combine like terms.
VofaC: (pie)r(2)h
Use simple numbers like 1 and 2 and see what happens.

10. Knowing if an Integer is a Multiple of 5 or 10
Subtract the smallest from the largest and add 1
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.
-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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

11. General Procedure for Multiplying Polynomials
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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 whole number left over after division.
Use the distributive property then combine the like terms.

12. Simplifying Square Roots
-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.
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

13. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Use the units to keep things straight - Snowfall inches/hours
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

14. Characteristics of a Square
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Factor out and cancel all factors the numerator and denominator have in common.

15. Convert From a Fraction to a Decimal - Vice Versa
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

16. What types of angles are formed when a transversal cross parallel lines?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Four equal acute angles and four equal obtuse angles.
Do whatever is necessary to both sides to isolate the variable.

17. Solving a Linear Equation
Average the smallest and largest number
-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.
Two relatively prime numbers are integers that have no common factor other than 1.
Do whatever is necessary to both sides to isolate the variable.

18. Counting Consecutive Integers
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
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.
Subtract the smallest from the largest and add 1
Four equal acute angles and four equal obtuse angles.

19. 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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Slope=change in y/change in x

20. Increasing and Decreasing a Number by a Certain Percentage
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
-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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.

21. PEMDAS
Cross multiply.
Cancel factors common to the numerator and denominator.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

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?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Average: Sum of the Terms/Number of the Terms
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

23. 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
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

24. Number of Groups - +1 Each Time
Put each number in the original ratio over the sum of the numbers.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Switch the numerator and denominator.

25. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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%.
Cross multiply.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

26. If x(2)=7x+18 - what is the positive value of x?
Slope=change in y/change in x
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

27. Finding the Area of a Sector

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28. Finding the Sum of the Average of a Series of Numbers
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Sum: Average x Number of Terms
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Put the equation into y=mx+b-- in which case b is the y-intercept.

29. Prime Factorization of a Number
Put each number in the original ratio over the sum of the numbers.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

30. Definition of a Rational Number
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.

31. Difference Between a Factor and a Multiple
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.
Factor out and cancel all factors the numerator and denominator have in common.
Switch the numerator and 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.

32. 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
Multiply the exponents - (x^3)^4=x^3*4=x^12
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

33. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
Multiply the numerators and multiply the denominators.
-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

34. 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.
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.
Combine like terms.

35. Finding the Volume of a Cylinder
Switch the numerator and denominator.
Just add or subtract the coefficients in front of the radicals.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
VofaC: (pie)r(2)h

36. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

37. Evaluating an Algebraic Expression
VofaC: (pie)r(2)h
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
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.

38. Solving an Inequality
The value that falls in the middle of the set.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Get the absolute value equation by itself. Solve.
Use the distributive property then combine the like terms.

39. Adding and Subtracting Polynomials
Sum: Average x Number of Terms
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 like terms.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

40. Finding the Length of an Arc in a Circle

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41. Solving a Problem Involving Rates
x(2)-5x+6 - What factors of +6 also have a sum of -5? (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.
-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.
Use the units to keep things straight - Snowfall inches/hours

42. Properties of a 45-45-90 Triangle
(x1+x2)/2 -(y1+y2)/2
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.

43. 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?
(x1+x2)/2 -(y1+y2)/2
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Switch the numerator and denominator.
Get the absolute value equation by itself. Solve.

44. Expressing the Union and Intersection of Sets
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

45. Calculating Negative Exponents and Radical Exponents
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Isolate the radical expression and use the standard rules of algebra.

46. Factoring the Difference of Two Squares
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 coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

47. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Combine like terms.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

48. Multiplying Binomials
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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

49. Dividing Expressions with Exponents that Have a Common Base
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Slope=change in y/change in x
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

50. Finding the Area of a Circle
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
(pie)r(squared)
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.