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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. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

2. How do you know if an integer is a multiple of 3 or 9?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
(pie)r(squared)
Part=Percent x Whole
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.

3. What types of angles are formed when a transversal cross parallel lines?
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Use simple numbers like 1 and 2 and see what happens.
Four equal acute angles and four equal obtuse angles.
The value that falls in the middle of the set.

4. If (Square Root: x-1)+5=12 - what is the value of x/2?
Plug in the given values for the unknowns and calculate according to PEMDAS.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

5. Finding the Area of a Sector

6. Adding and Subtracting Fractions
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
-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.
Find a common denominator - then add or subtract the numerators.
Use the distributive property then combine the like terms.

7. Finding the Length of an Arc in a Circle

8. Multiply and Divide Positive and Negative Numbers
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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 units to keep things straight - Snowfall inches/hours
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

9. Dividing Fractions
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.
Just add or subtract the coefficients in front of the radicals.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
(x1+x2)/2 -(y1+y2)/2

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

11. 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?
Sum: Average x Number of Terms
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Factor out and cancel all factors the numerator and denominator have in common.

12. Increasing and Decreasing a Number by a Certain Percentage
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Sum: Average x Number of Terms
-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.
Do whatever is necessary to both sides to isolate the variable.

13. Prime Factorization of a Number
VofaRS=lwh
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
-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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

14. If the average of a - b - and 48 is 48 - what is the value of a + b?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.

15. Multiplying Monomials
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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)

16. Properties of Similar Triangles
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Isolate the radical expression and use the standard rules of algebra.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

17. Finding a Term in a Geometric Sequence
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Express them with a common denominator.
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.
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.

18. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Sum: Average x Number of Terms
Combine like terms.

19. 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
A(2)+b(2)=c(2)
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 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.

20. 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.
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.
-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.
Factor out and cancel all factors the numerator and denominator have in common.

21. Finding the Circumference of a Circle
Isolate the radical expression and use the standard rules of algebra.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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
2(pie)r

22. An Important Property of a Line Tangent to a Circle
Two relatively prime numbers are integers that have no common factor other than 1.
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.
Just add or subtract the coefficients in front of the radicals.
-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.

23. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use the units to keep things straight - Snowfall inches/hours
Cross multiply.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

24. What types of angles are formed when two lines intersect?
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Adjacent angles are supplementary - Vertical angles are equal
Put the equation into y=mx+b-- in which case b is the y-intercept.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

25. Multiplying Fractions
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Multiply the numerators and multiply the denominators.
Use the formula distance=rate*time and its variations to help in this question.

26. Finding the Median of a Set of Numbers
Slope=change in y/change in x
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The value that falls in the middle of the set.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

27. Number of Groups - +1 Each Time
Use simple numbers like 1 and 2 and see what happens.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

28. Converting from part-to-part ratios to part-to-whole ratios
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Put each number in the original ratio over the sum of the numbers.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

29. What Does Solving In Terms of Mean?
Cross multiply.
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.
Four equal acute angles and four equal obtuse angles.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

30. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

31. Counting Consecutive Integers
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.

32. 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 value that falls in the middle of the set.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

33. Simplifying a Fraction to Lowest Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Factor out and cancel all factors the numerator and denominator have in common.
Use the distributive property then combine the like terms.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

34. Finding the Volume of a Rectangular Solid
VofaRS=lwh
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.
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 the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

35. Simplifying an Algebraic Equation
Plug in the given values for the unknowns and calculate according to PEMDAS.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Cancel factors common to the numerator and denominator.
Find a common denominator - then add or subtract the numerators.

36. What is the Pythagorean Theorem?
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
A(2)+b(2)=c(2)

37. Finding the GCF of Two or More Numbers
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Average: Sum of the Terms/Number of the Terms
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.

38. Converting from an Improper Fraction to a Mixed Number
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The whole number left over after division.
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.
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.

39. Finding the Distance Between Two Points on a Coordinate Graph
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Multiply the numerators and multiply the denominators.

40. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

41. Knowing if an Integer is a Multiple of 5 or 10
-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.
Adjacent angles are supplementary - Vertical angles are equal
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

42. 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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Put the equation into y=mx+b-- in which case b is the y-intercept.

43. Dividing Expressions with Exponents that Have a Common Base
Use the units to keep things straight - Snowfall inches/hours
Just add or subtract the coefficients in front of the radicals.
-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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

44. Difference Between a Factor and a Multiple
Find a common denominator - then add or subtract the numerators.
-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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

45. Comparing the values of two or more Fractions
Express them with a common denominator.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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.

46. Numbers that are Relatively Prime
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Two relatively prime numbers are integers that have no common factor other than 1.
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
The value that falls in the middle of the set.

47. Factoring a Polynomial ('FOIL in Reverse')
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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)
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

48. 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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
A(2)+b(2)=c(2)
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

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

50. What is a Function and how do you Evaluate one?