MCR3U - Mastery Sampler #4

Practice flashcards covering algebraic simplification, function transformations, quadratic factoring, trigonometric laws, and sinusoidal features based on Mastery Sampler #4.

Simplification of $4x^{2} + 4x^{2} + 4x^{2}$

$$12x^{2}$$

Simplification of $(4x^{2})(4x^{2})(4x^{2})$

$$64x^{6}$$

Expansion of $(4c + 2d)^{2}$

$$16c^{2} + 16cd + 4d^{2}$$

Equation for $y = f(x)$ with a shift right $2$ units and a horizontal compression by a factor of $\frac{1}{4}$

$$y = f(4x - 2)$$

Ordered transformations for $y = 9 - 4f(7 - \frac{1}{5}x)$

Vertical stretch by a factor of $4$, vertical reflection in $x$-axis, vertical shift up $9$, horizontal shift left $7$, horizontal reflection in the $y$-axis, and horizontal stretch by a factor of $5$

Mapping rule for $y = 9 - 4f(7 - \frac{1}{5}x)$

(x,y) ightarrow (5(x - 7), -4y + 9)

Transformed point of $(10, -2)$ for the function $y = 9 - 4f(7 - \frac{1}{5}x)$

$$(-15, 13)$$

Reflection of $y = |x|$ on the $y$-axis

$$y = -|x|$$

Expansion of $2(x + 3)^{2}$

$$2x^{2} + 12x + 18$$

Fully factored form of $6x^{2} - 13x + 6$

$$(3x - 2)(2x - 3)$$

Term needed to make $x^{2} - 8x$ a perfect square

$$16$$

Discriminant of the quadratic equation $4x^{2} - 3x + 2 = 0$

$$-23$$

Number of x-intercepts if the discriminant is $-16$

no x-intercept(s)

Necessary restrictions for $\frac{(x - 3)(x + 2)}{(x - 3)}$

$$x \neq 3$$

Necessary restrictions for $\frac{(x + 2)(7x - 1)}{(x - 4)(x + 2)^{2}} imes \frac{(x - 4)}{(7x - 1)}$

$$x \neq 4, x \neq 17, x \neq -2$$

Solution for x^{2} > 16

x > 4, x < -4

Primary trig ratios for $\angle heta$

$\sin( heta) = \frac{4}{5}$, $\cos( heta) = \frac{3}{5}$, $\tan( heta) = \frac{4}{3}$

Quadrants where the terminal arm of angle $\theta$ is located if the sine ratio is positive

$I$ and $II$

Values of $\theta$ for $0^{ ext{o}} \neq heta \neq 360^{ ext{o}}$ if $\tan( heta) = 1$

$45^{ ext{o}}, 225^{ ext{o}}$,

Cosine Law expression for side $a$

$$a = \frac{8^{2} + 12^{2} - 2(8)(12) ext{cos}(A)}{}$$

Sine Law expression for $\sin(B)$

$\sin(B) = \frac{12 ext{sin}(A)}{a}$ or $\sin(B) = \frac{12 ext{sin}(C)}{8}$

Amplitude of $f(x) = 2 ext{sin}(3x)$

$$2$$

Period of $f(x) = 2 ext{sin}(3x)$

$120^{ ext{o}}$,

Maximum value of $f(x) = 2 ext{sin}(3x)$

$$2$$

Period of the sinusoidal function shown in the graph

$360^{ ext{o}}$,

Sine equation for the function shown in the graph

$$f(x) = 2 ext{sin}(x)$$

Cosine equation for the function shown in the graph

$f(x) = 3 ext{cos}(x)$}],