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DAT > QRT > Flashcards

QRT Flashcards

1
Q

Multiplying Fractions

a/b x x/y

A

Multiply numerators together and denominator together

= ax/by

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2
Q

Dividing Fractions

a/b ÷ x/y

A

Flip the fraction you’re dividing by then multiply

= a/b x y/x = ay/bx

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3
Q

Solving a Proportion

x/5 = 3/4

A

Cross-multiply

4x = 15

4 = 15/4

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4
Q

(xm)(xn)

A

=xm+n

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5
Q

xm / xn

A

=xm-n

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6
Q

(xm)n

A

xmn

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7
Q

(xn)(yn)

A

xyn

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8
Q

xn / yn

A

(x/y)n

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9
Q

Multiplying Polynomials

(x2 + 3x + 4)(x + 5)

A

Multiply each term in the first polynomial with each term in the second

=x2(x + 5) + 3x(x + 5) + 4(x + 5)

=x3 + 5x2 + 3x2 + 15x + 4x + 20

x3 + 8x2 + 19x + 20

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10
Q

Dividing Polynomials

(2x3 + 13x2 + 11x -16) ÷ (x + 5)

A

Use long division:

= 2x2 + 3x - 4

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11
Q

Factoring

ax + ay

A

a(x + y)

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12
Q

Factoring

a2 - b2

A

Difference of squares:

(a + b)(a - b)

eg 4x2 - 9 = (2x + 3)(2x - 3)

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13
Q

Factoring

a2 + 2ab + b2

A

Squares of binomials:

(a + b)2

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14
Q

Factoring

a2 -2ab + b2

A

Squares of binomials

(a - b)2

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15
Q

For all x ≠ ±3,

(3x2 - 11x + 6) / (9 - x2)

A
  1. Factorising: denominator - difference of squares -

(9 - x2) = (3 - x)(3 + x)

  1. Factorising: numerator -

(3x2 - 11x + 6) = (x -3)(3x - 2)

  1. Factorising numerator for -1:

(x -3)(3x - 2) = (-1)(3 - x)(3x - 2)

  1. Cancelling (3 - x):

(-3x + 2)/(3 + x)

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16
Q

Unknown in a Denominator

1 + 1/x = 2 - 1/x

A

Cross multiply:

(x + 1)/x = (2x-1)/x

x2 + x = 2x2 - x

2x2 - x2 = x + x

x2 = 2x

Dividing both sides by x:

x = 2

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17
Q

Unknown In an Exponent

If 8x = 16x-1, x = ?

A

Since both bases are factors of two, can be reexpressed as powers of two:

(23)x = (24)x-1

3x = 4x - 4

x = 4

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18
Q

Quadratic Formula

A
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19
Q

‘In terms of’

If a = (b + x)(c + x), what is the value of x in terms of a, b and c

A

b + x = ac + ax

ax - x = b - ac

x(a - 1) = b - ac

x = (b - ac)/(a - 1)

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20
Q

Simulataneous Equations

2x - 9y = 11 and x + 12y = -8

What is the value of x + y?

A

Add the equations:

3x + 3y = 3

x + y = 1

21
Q

Absolute Value

|x - 12| = 3

A

x - 12 = 3

x - 12 = -3

x = 15 or 9

22
Q

Inequalities

|whatever| < p

A

-p < |whatever| < +p

23
Q

Inequalities

|2x - 3| < 7

A

= -7 < 2x - 3 < 7

2x - 3 > -7, 2x > -4, x > -2

2x - 3 < 7, 2x < 10, x < 5

24
Q

Sum of Exterior Angles of a Triangle

25
Q

Triangle Inequality Theorum

A

The length of any one side of a triangle must be greater than the positive difference between the two other sides and less that their sum

For example, if one side is 3 and another is 7, then the length of the third must be between 4 < x < 10

26
Q

Similar Triangles

Area od A in tems of B if length of sides of A are twice that of B

A

A:B = 2:1

Areas = 22:12 = 4:1

27
Q

Area of an Equilateral Triangle

A

= (s2√3) / 4

where s is the side length

28
Q

Special Right Triangles

A
  1. 3-4-5
  2. 5-12-13
  3. 45º-45º-90º - sides in ratio 1:1:√2 (if sides are 3, 3, x, x = 3√2)
  4. 30º-60º-90º - sides in ratio 1:√3:2 (if sides 3, 6, x, x = 3√3)
29
Q

Area of a Trapezoid

A

= ((base1 + base2) / 2) x height

30
Q

Area of a Parallelogram

A

= base x height

31
Q

Area of a Hexagon

A

=(3s2√3)/2

32
Q

Length of an Arc

A

= (n/360) x 2πr

33
Q

Area of a Sector

A

= (n/360) x π r2

34
Q

Area of a Cone

A

= π r2 + π rl

r = base radius

l = slant length

35
Q

Volume of a Cone

A

= 1/3 π r2 h

36
Q

Surface Area of a Sphere

37
Q

Volume of a Sphere

A

= 4/3 π r3

38
Q

Volume of a Pyramid

A

= 1/3 Bh

B = area of base

h = height

39
Q

Coordinate Geometry

Distance Between Two Points

A

√(x1-x2)2 + (y1-y2)2

40
Q

Slope Intercept

Which of the following has no intercept with the line

y = 4x + 5

(A) y = 0.25x - 5

(B) y = -0.25x -5

(C) y = 4x + 0.2

(D) y = -4x + 0.2

(E) y = -4x -0.5

A

Must be parallel - gradient 4x

(C)

41
Q

Cotangent

A

= 1/tangent

=Adjacent/Opposite

42
Q

Secant

A

=1/cos

=Hypotenuse/Adjacent

43
Q

Cosecant

A

=1/sine

=Hypotenuse/Opposite

44
Q

Trigonometry

Important Identities

A
  1. sin2 x + cos2 x = 1
  2. tan2 x + 1 = sec2 x
  3. 1 + cot2 x = csc2 x
45
Q

Radian in Degrees

46
Q

Degrees in Radians

A

One degree = π/180 radians

DAT (53 decks)

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