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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Study First
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. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Solving an Inequality
Tangency
Multiples of 3 and 9
2. A square is a rectangle with four equal sides; Area of Square = side*side
The 5-12-13 Triangle
Finding the Distance Between Two Points
Circumference of a Circle
Characteristics of a Square
3. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them
Prime Factorization
Mixed Numbers and Improper Fractions
Even/Odd
Multiplying and Dividing Roots
4. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Volume of a Rectangular Solid
Parallel Lines and Transversals
Factor/Multiple
Multiples of 3 and 9
5. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Interior Angles of a Polygon
Adding and Subtracting monomials
Determining Absolute Value
Even/Odd
6. The whole # left over after division
Remainders
Probability
Relative Primes
Average Rate
7. Combine like terms
Comparing Fractions
Adding and Subtraction Polynomials
Using an Equation to Find an Intercept
Average Formula -
8. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height
Function - Notation - and Evaulation
Characteristics of a Parallelogram
Finding the midpoint
Characteristics of a Square
9. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of
Part-to-Part Ratios and Part-to-Whole Ratios
Exponential Growth
Adding and Subtracting monomials
Dividing Fractions
10. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees
Median and Mode
Interior and Exterior Angles of a Triangle
Direct and Inverse Variation
The 5-12-13 Triangle
11. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12
Multiplying/Dividing Signed Numbers
Part-to-Part Ratios and Part-to-Whole Ratios
Finding the Missing Number
PEMDAS
12. To find the reciprocal of a fraction switch the numerator and the denominator
Adding and Subtracting Roots
Reciprocal
Similar Triangles
Adding and Subtracting monomials
13. Multiply the exponents
Reciprocal
Number Categories
Raising Powers to Powers
Adding and Subtracting Roots
14. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Remainders
Adding/Subtracting Fractions
Volume of a Rectangular Solid
Reciprocal
15. To solve an inequality do whatever is necessary to both sides to isolate the variable. When you multiply or divide both sides by a negative number you must reverse the sign
Using an Equation to Find the Slope
Mixed Numbers and Improper Fractions
Evaluating an Expression
Solving an Inequality
16. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Adding and Subtracting monomials
Volume of a Rectangular Solid
Intersection of sets
Characteristics of a Parallelogram
17. To convert a mixed number to an improper fraction - multiply the whole number by the denominator - then add the numerator over the same denominator - to convert an improper fraction to a mixed number - divide the denominator into the numerator to get
Prime Factorization
Interior Angles of a Polygon
Reducing Fractions
Mixed Numbers and Improper Fractions
18. you can add/subtract when the part under the radical is the same
Identifying the Parts and the Whole
Adding and Subtracting Roots
Dividing Fractions
Remainders
19. The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides
Greatest Common Factor
Union of Sets
Relative Primes
Triangle Inequality Theorem
20. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Average Rate
Interior and Exterior Angles of a Triangle
Raising Powers to Powers
Rate
21. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Combined Percent Increase and Decrease
Prime Factorization
Length of an Arc
22. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa
Relative Primes
Domain and Range of a Function
Direct and Inverse Variation
Isosceles and Equilateral triangles
23. 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
Adding and Subtracting Roots
Counting the Possibilities
Combined Percent Increase and Decrease
Characteristics of a Parallelogram
24. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x
Even/Odd
Multiples of 2 and 4
Relative Primes
Using an Equation to Find an Intercept
25. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
Circumference of a Circle
Solving a System of Equations
Volume of a Cylinder
26. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Using an Equation to Find the Slope
Characteristics of a Rectangle
Evaluating an Expression
Volume of a Rectangular Solid
27. To divide fractions - invert the second one and multiply
Dividing Fractions
Intersection of sets
Average Formula -
Using an Equation to Find the Slope
28. To multiply or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign
Rate
Multiplying and Dividing Roots
Raising Powers to Powers
Multiplying/Dividing Signed Numbers
29. Example: If the ratio of males to females is 1 to 2 - then what is the ratio of males to people? - work: 1/(1+2) answer: 1/3
Area of a Sector
Circumference of a Circle
Direct and Inverse Variation
Part-to-Part Ratios and Part-to-Whole Ratios
30. To solve a proportion - cross multiply
Intersection of sets
Domain and Range of a Function
Solving a Proportion
Number Categories
31. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Solving a Quadratic Equation
Prime Factorization
Using Two Points to Find the Slope
Area of a Circle
32. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50
Number Categories
Percent Increase and Decrease
Multiplying and Dividing Roots
Determining Absolute Value
33. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation
Tangency
Percent Formula
Function - Notation - and Evaulation
Characteristics of a Rectangle
34. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Solving a System of Equations
Average Formula -
Area of a Circle
Finding the midpoint
35. pr^2
Area of a Circle
Repeating Decimal
Evaluating an Expression
Characteristics of a Rectangle
36. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds
Identifying the Parts and the Whole
Finding the Missing Number
Part-to-Part Ratios and Part-to-Whole Ratios
Average Formula -
37. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex
Multiplying and Dividing Roots
Area of a Triangle
Solving a Proportion
Multiplying Fractions
38. Add the exponents and keep the same base
The 5-12-13 Triangle
Multiplying and Dividing Powers
Greatest Common Factor
Using Two Points to Find the Slope
39. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Multiplying and Dividing Roots
Using Two Points to Find the Slope
Multiples of 3 and 9
Volume of a Cylinder
40. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle
Evaluating an Expression
(Least) Common Multiple
The 5-12-13 Triangle
Adding and Subtracting Roots
41. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Simplifying Square Roots
Solving an Inequality
Multiplying/Dividing Signed Numbers
Characteristics of a Rectangle
42. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Using an Equation to Find an Intercept
Using the Average to Find the Sum
Finding the Distance Between Two Points
Characteristics of a Square
43. Factor out the perfect squares
Even/Odd
Percent Formula
Simplifying Square Roots
Surface Area of a Rectangular Solid
44. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)
Identifying the Parts and the Whole
Area of a Sector
Adding/Subtracting Signed Numbers
Area of a Circle
45. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Number Categories
Multiplying/Dividing Signed Numbers
Using an Equation to Find the Slope
Similar Triangles
46. Surface Area = 2lw + 2wh + 2lh
Adding and Subtraction Polynomials
Surface Area of a Rectangular Solid
Using Two Points to Find the Slope
Adding/Subtracting Signed Numbers
47. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Intersection of sets
Characteristics of a Square
Union of Sets
Raising Powers to Powers
48. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Solving a Quadratic Equation
Combined Percent Increase and Decrease
Direct and Inverse Variation
49. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Pythagorean Theorem
Volume of a Rectangular Solid
Finding the Original Whole
Union of Sets
50. Sum=(Average) x (Number of Terms)
Interior and Exterior Angles of a Triangle
Using the Average to Find the Sum
Relative Primes
Part-to-Part Ratios and Part-to-Whole Ratios