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SAT Math

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. Direct Variation and Inverse Variation
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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

2. Finding the Surface Area of a Rectangular Solid
The whole number left over after division.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Probability: Number of Favorable Outcomes/Total Possible Outcomes
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

3. Solving an Inequality
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

4. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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
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.
Isolate the radical expression and use the standard rules of algebra.

5. If 3(3x)=9(x+2) - what is the value of x?
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

6. An Important Property of a Line Tangent to a Circle
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
Four equal acute angles and four equal obtuse angles.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

7. Counting the Total Number of Possibilities for Several Events to Occur
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.
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
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.

8. Scalene - Isosceles - and Equilateral Triangles
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

9. Prime Factorization of a Number
Combine like terms.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Express them with a common denominator.
VofaRS=lwh

10. What value of x is not in the domain of the function f(x)=x-2/x-3?
FOIL: First - Outer - Inner - Last... Combine Like Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.
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 pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

11. Finding the Mode of a Set of Numbers
The value that appears the most often.
(pie)r(squared)
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.
-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.

12. Adding and Subtracting Roots
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
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.

13. What Does Solving In Terms of Mean?
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.
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the 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.

14. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
FOIL: First - Outer - Inner - Last... Combine Like Terms

15. Finding the Distance Between Two Points on a Coordinate Graph
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Sum: Average x Number of Terms
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
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

16. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Multiply the exponents - (x^3)^4=x^3*4=x^12
Factor out and cancel all factors the numerator and denominator have in common.
Cancel factors common to the numerator and denominator.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

17. Simplifying a Fraction to Lowest Terms
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.
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 and cancel all factors the numerator and denominator have in common.
Put each number in the original ratio over the sum of the numbers.

18. Adding and Subtracting Polynomials
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Combine like terms.
Express them with a common denominator.
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 Length of an Arc in a Circle

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20. Formula Used to Find Percent
Part=Percent x Whole
Use the units to keep things straight - Snowfall inches/hours
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.

21. Solving a Linear Equation
Use the distributive property then combine the like terms.
Use simple numbers like 1 and 2 and see what happens.
Do whatever is necessary to both sides to isolate the variable.
Multiply the exponents - (x^3)^4=x^3*4=x^12

22. Finding the GCF of Two or More Numbers
Just add or subtract the coefficients in front of the radicals.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.

23. Simplifying Square Roots
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Find a common denominator - then add or subtract the numerators.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

24. 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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

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

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26. Adding and Subtracting Monomials
Put each number in the original ratio over the sum of the numbers.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Four equal acute angles and four equal obtuse angles.

27. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Multiply the numerators and multiply the denominators.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
-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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

28. Determining Absolute Value of a Number
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Cross multiply.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

29. What types of angles are formed when a transversal cross parallel lines?
Part=Percent x Whole
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Four equal acute angles and four equal obtuse angles.
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.

30. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Use the units to keep things straight - Snowfall inches/hours
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Part=Percent x Whole

31. Multiply and Divide Positive and Negative Numbers
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
The value that falls in the middle of the set.
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
Use the formula distance=rate*time and its variations to help in this question.

32. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

33. Finding the Rate of Speed
Use the formula distance=rate*time and its variations to help in this question.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Plug in the given values for the unknowns and calculate according to PEMDAS.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

34. Increasing and Decreasing a Number by a Certain Percentage
The whole number left over after division.
-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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

35. Number of Groups - +1 Each Time
The value that falls in the middle of the set.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

36. Converting from part-to-part ratios to part-to-whole ratios
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
Put each number in the original ratio over the sum of the numbers.
Four equal acute angles and four equal obtuse angles.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

37. Finding the Sum of the Average of a Series of Numbers
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Sum: Average x Number of Terms
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.

38. 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.
Average: Sum of the Terms/Number of the Terms
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
VofaC: (pie)r(2)h

39. Finding the Missing Number in a Series When You are Given the Average
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.
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
(pie)r(squared)
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

40. If (Square Root: x-1)+5=12 - what is the value of x/2?
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.

41. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Average the smallest and largest number

42. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

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43. Definition of a Rational Number
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Subtract the smallest from the largest and add 1
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

44. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Put each number in the original ratio over the sum of the numbers.
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.

45. Counting Consecutive Integers
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Subtract the smallest from the largest and add 1
Adjacent angles are supplementary - Vertical angles are equal

46. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

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47. Knowing if an Integer is a Multiple of 5 or 10
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
-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
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

48. Solving a Radical Equation
Average: Sum of the Terms/Number of the Terms
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Multiply the numerators and multiply the denominators.
Isolate the radical expression and use the standard rules of algebra.

49. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
Average: Sum of the Terms/Number of the Terms
VofaC: (pie)r(2)h
Subtract the smallest from the largest and add 1

50. Properties of a 45-45-90 Triangle
Adjacent angles are supplementary - Vertical angles are equal
Part=Percent x Whole
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Do whatever is necessary to both sides to isolate the variable.