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Quantitative Reasoning Flashcards

1
Q

distance = ?

A

distance = speed x time

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2
Q

speed = ?

A

speed = distance/time

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3
Q

time = ?

A

time = distance/speed

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4
Q

upstream speed = ?

A

upstream speed = distance/time upstream

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5
Q

downstream speed = ?

A

downstream speed = distance/time downstream

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6
Q

speed of stream = ?

A

speed of stream = downstream speed - upstream speed / 2

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7
Q

speed of boat in stillwater = ?

A

speed of boat in stillwater = (downstream speed + upstream speed) / 2

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8
Q

average speed of boat = ?

A

average speed of boat = downstream speed x upstream speed / (downstream speed + upstream speed / 2)

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9
Q

relative speed (moving towards each other) = ?

A

relative speed (moving towards each other) = speed of object 1 + speed of object 2

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10
Q

relative speed (moving in the same direction) = ?

A

relative speed (moving in the same direction) = speed of faster object - speed of slower object

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11
Q

time taken = ?

A

time taken = work done/rate of work

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12
Q

work done = ?

A

work done = time taken x rate of work

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13
Q

rate of work = ?

A

rate of work = work done/time taken

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14
Q

% = ?

A

% = (part/whole) x 100

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15
Q

part = ?

A

part = (%/100) x whole

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16
Q

whole = ?

A

whole = part / (%/100)

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17
Q

% increase = ?

A

% increase = (new value - old value / old value) x 100

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18
Q

% decrease = ?

A

% decrease = (old value - new value / old value) x 100

“decrease %: old minus new over old times 100”

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19
Q

Price = ?

A

Price = (no. of items)(cost per item)

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20
Q

Sale price = ?

(price at which an item is sold)

A

Sale price = Cost price (1 + Profit %/100)

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21
Q

Sale price = ?

A

Sale price = Cost price (1 - Loss %/100)

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22
Q

Profit = ?

A

Profit = Sale price - Cost price

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23
Q

Loss = ?

A

Loss = Cost price - Sale price

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24
Q

Profit % = ?

A

Profit % = (Profit/CP) x 100

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25
Q

Loss % = ?

A

Loss % = (Loss/CP) x 100

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26
Q

Principal = ?

A

Principal = (SI × 100) / RT

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27
Q

Rate of interest = ?

A

Rate of interest = (SI × 100) / PT

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28
Q

Time = ?

A

Time = (SI × 100) / PR

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29
Q

Simple interest = ?

A

Simple interest = PRT/100 or Total Amount (A) - Principal (P)

30
Q

Amount after interest (A) = ?

A

Amount after interest (A) = Principal (P) + Simple Interest (SI)

31
Q

Compound interest = ?

A

Compound interest = A - P

32
Q

Amount after compound interest (A) = ?

A

Amount after compound interest (A) = P (1 + R/100) ^T

33
Q

Compound interest (n no. of times)= ?

A

Compound interest = P (1 + R/n) ^n^T - P

34
Q

Compound interest (half-yearly)= ?

A

Compound interest (half-yearly)= P [1 + (R/2)/100]^2T - P

35
Q

Principal (of CI) = ?

A

Principal = A/(1 + R/100)^T

36
Q

Area of square = ?
Area of square (diagonals) = ?
Perimeter of square = ?

A

Area of square = a^2
Area of square (diagonals) = 1/2 diagonal^2
Perimeter of square = 4a

37
Q

Area of rectangle = ?
Perimeter of rectangle = ?
d² = ?
L = ?

A

Area of rectangle = LW
Perimeter of rectangle = 2(L+W)
d² = L² + W²
L = Area/W

38
Q

Area of triangle = ?
Perimeter of triangle = ?

A

Area of triangle = 1/2 bh
Perimeter of triangle = sum of all sides

39
Q

Area of parallelogram = ?
Perimeter of parallelogram = ?

A

Area of parallelogram = bh
Perimeter of parallelogram = 2 (base + side) | 2 (b + a)

40
Q

Area of rhombus = ?
Perimeter of rhombus = ?
a = ?

A

Area of rhombus = 1/2 (diagonal1)(diagonal2)
Perimeter of rhombus = 4a
a = √(diagonal1/2)² + (diagonal2/2)²

41
Q

Area of trapezoid = ?
Perimeter of trapezoid = ?

A

Area of trapezoid = 1/2 (a + b; sum of parallel sides)(h; perpendicular distance between the sides) | 1/2 (a + b)(h)

Perimeter of trapezoid = (a + b + c + d; sum of all sides)

42
Q

Area of circle = ?
Circumference = ?
Diameter = ?
r = ?
distance = ?
midpoint = ?

A

Area of circle = πr²
Circumference = 2πr
Diameter = 2r
r = Diameter/2
distance = √(x2 - x1)² + (y2 - y1)²
midpoint = (x1+x2/2 , y1+y2/2) = (h, k)

43
Q

equation of the circle = ?

A

equation of the circle = (x-h)² + (y-k)² = r²

44
Q

Cube surface area = ?
Cube volume = ?
Diagonal = ?

A

Cube surface area = 6a²
Cube volume = a³
Diagonal = a√3

45
Q

Rectangle/cuboid surface area = ?
Rectangle/cuboid volume = ?
Diagonal = ?

A

Rectangle/cuboid surface area = 2(LW+WH+HL)

Rectangle/cuboid volume = LWH

Diagonal = √L²+W²+H²

46
Q

Cylinder surface area = ?

Cylinder volume = ?

A

Cylinder surface area = 2πr² + 2πrh

Cylinder volume = πr²h

47
Q

Sphere surface area = ?

Sphere volume = ?

A

Sphere surface area = 4πr²

Sphere volume = 4/3πr³

48
Q

Cone total surface area = ?
Cone curved surface area = ?
Slant height = ?

Cone volume = ?

A

Cone total surface area = πr² + πrl

• r = radius of the base of the cone
• l = slant height of the cone

Cone curved surface area = πrl

Slant height (l): l² = r² + h²

Cone volume = 1/3πr²h

49
Q

Pyramid surface area = ?
Pyramid volume = ?

A

Pyramid surface area =
Pyramid volume = 1/3 (base area)(h)

50
Q

Coordinate
Distance = ?
Midpoint = ?
Slope (m) = ?
Slope intercept form: ?
Point-slope form: ?

A

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope intercept form: y = mx + b
Point-slope form: y - y₁ = m(x - x₁)

51
Q

sin x = ?
cos x = ?
tan x = ?

sec x = ?
csc x = ?
cot x = ?

A

SOH sin x = opp/hyp
CAH cos x = adj/hyp
TOA tan x = opp/adj

SHA sec x = hyp/adj
CHO csc x = hyp/opp
CAH cot x = adj/hyp

52
Q

Pythagorean identities

(fundamental trigonometric identities derived from the Pythagorean theorem; they relate the squares of sine, cosine, and tangent)

• ? + ? = 1

• 1 + ? = sec² x

• 1 + ? = csc² x

A

• sin² x + cos² x = 1

• 1 + tan² x = sec² x

• 1 + cot² x = csc² x

53
Q

Reciprocal identities

A

sin x = 1/csc x
cos x = 1/sec x
tan x = 1/cot x

csc x = 1/sin x
sec x = 1/cos x
cot x = 1/tan x

54
Q

Quotient identities

(relate the tangent and cotangent functions to sine and cosine)

• tan x = ____/cos x

• cot x = ____/sin x

A

• tan x = sin x/cos x

• cot x = cos x/sin x

55
Q

Cofunction identities

[show the relationship between trigonometric functions of complementary angles (angles that add up to 90° or π/2)]

A

• sin (90° - x) = cos x, cos (90° - x) = sin x

• tan (90° - x) = cot x, cot (90° - x) = tan x

• sec (90° - x) = csc x, csc (90° - x) = sec x

56
Q

Sum and difference formulas

(allow you to calculate the sine, cosine, and tangent of the sum or difference of two angles)

• sin (A+B) = ?
• sin (A-B) = ?

• cos (A+B) = ?
• cos (A-B) = ?

• tan (A+B) = ?
• tan (A-B) = ?

A

• sin (A+B) = sinAcosB + cosAsinB
• sin (A-B) = sinAcosB - cosAsinB

• cos (A+B) = cosAcosB - sinAsinB
• cos (A-B) = cosAcosB + sinAsinB

• tan (A+B) = (tanA + tanB)/(1 - tanAtanB)
• tan (A-B) = (tanA - tanB)/(1 + tanAtanB)

57
Q

Double angle formulas

• sin (2x) = 2sinx____

• cos (2x) = cos²x - _____
• cos (2x) = ______ - 1
• cos (2x) = 1 - ______

• tan (2x) = 2tanx/(1 - _____)

A

• sin (2x) = 2sinxcosx

• cos (2x) = cos²x - sin²x
• cos (2x) = 2cos²x - 1
• cos (2x) = 1 - 2sin²x

• tan (2x) = 2tanx/(1 - tan²x)

58
Q

Half angle formulas

• sin (x/2) = ±√[(1 - ____) / 2]

• cos (x/2) = ±√[(1 + ____) / 2]

• tan (x/2) = ±√[(1 - ____) / (1 + ____)]
• tan (x/2) = ____ / (1 + cosx)
• tan (x/2) = (1 - ____) / ____

A

• sin (x/2) = ±√[(1 - cosx) / 2]

• cos (x/2) = ±√[(1 + cosx) / 2]

• tan (x/2) = ±√[(1 - cosx) / (1 + cosx)]
• tan (x/2) = sinx / (1 + cosx)
• tan (x/2) = (1 - cosx) / sinx

*The ± sign depends on the quadrant in which x/2 lies: ASTC rule (All Students Take Calculus) to determine the sign of each function based on the quadrant.

A (All): In QI, all trigonometric functions (sin, cos, tan, and their reciprocals) are positive.

S (Sine): In QII, only sin and its reciprocal csc are positive. All others are negative.

T (Tangent): In QIII, only tan and its reciprocal cot are positive. All others are negative.

C (Cosine): In QIV, only cos and its reciprocal sec are positive. All others are negative.

Diagram Representation

1st Quadrant (0° to 90°): All positive
2nd Quadrant (90° to 180°): Sine positive
3rd Quadrant (180° to 270°): Tangent positive
4th Quadrant (270° to 360°): Cosine positive

59
Q

Product to sum formulas

(used to rewrite the product of sine and cosine functions as a sum or difference of trigonometric functions)

Product of sines and cosines
sinAcosB = ?

Product of cosines and sines
cosAsinB = ?

Product of cosines
cosAcosB = ?

Product of sines
sinAsinB = ?

A

Product of sines and cosines
sinAcosB = (1/2) [ sin(A + B) + sin(A - B) ]

Product of cosines and sines
cosAsinB = (1/2) [ sin(A + B) - sin(A - B) ]

Product of cosines
cosAcosB = (1/2) [ cos(A + B) + cos(A - B) ]

Product of sines
sinAsinB = (1/2) [ cos(A - B) - cos(A + B) ]

60
Q

Sum to product formulas

(used to rewrite the sum or difference of trigonometric functions as a product)

• sin(A) + sin(B) = ?
• sin(A) - sin(B) = ?

• cos(A) + cos(B) = ?
• cos(A) - cos(B) = ?

A

• sin(A) + sin(B) = 2sin[(A + B)/2] cos[(A - B)/2]
• sin(A) - sin(B) = 2cos[(A + B)/2] sin[(A - B)/2]

*pos: sin-cos, neg: cos-sin

• cos(A) + cos(B) = 2cos[(A + B)/2] cos[(A - B)/2]
• cos(A) - cos(B) = -2sin[(A + B)/2] sin[(A - B)/2]

*pos: cos-cos, neg: sin-sin

61
Q

maximum value
sin (x) = ?
cos (x) = ?

minimum value
sin (x) = ?
cos (x) = ?

A

maximum value
sin (x) = 1
cos (x) = 1

minimum value
sin (x) = -1
cos (x) = -1

62
Q

Maximum and mnimum values

R = ?

A

R = √A² + B²

63
Q

1 kg = ? g

64
Q

1 mi = ? km

A

1.609344 km

1️⃣▪️6️⃣0️⃣9️⃣3️⃣4️⃣4️⃣

65
Q

1 L = ? gallons

A

0.2641720524 gallons

0-264-172-0524

66
Q

1 in = ? cm

67
Q

1 ft = ? in

68
Q

1 m = ? cm

69
Q

1 km/h = ? m/s

70
Q

m/s to km/h?

71
Q

Radians = ?

A

Radians = Degrees × π/180

Quantitative Reasoning (1 decks)

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