MAT01S1 Mathematics 1 Exam
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Questions and Answers

Simplify the expression: $5^2 - 3^4 - 5^{16}$

-244227

Solve for $x$ in the equation: $4x - \frac{3}{3x} = 10$

x = 3

Factorise the expression: $x^2 - 3x + 2$

$(x-1)(x-2)$

Find a linear equation with a gradient of 2 that passes through the point (4, 11)

<p>y = 2x + 3</p> Signup and view all the answers

Find the equation of the line passing through (3,16) and (7,-4)

<p>y = -5x + 31</p> Signup and view all the answers

Rearrange the model 𝑩(𝒕) = 𝟑 + 𝟏𝟎𝒆𝒌𝒕 to solve for 𝒆𝒌𝒕.

<p>𝒆𝒌𝒕 = (𝑩(𝒕) - 𝟑) / 𝟏𝟎</p> Signup and view all the answers

If 𝒌 = 𝟎. 𝟎𝟏, after 5 days, what will be the total number of bees?

<p>𝑩(5) = 𝟑 + 𝟏𝟎𝑒^(0.01*5)</p> Signup and view all the answers

Solve the following equation: 𝟏𝟎𝑳𝒐𝒈 𝟏𝟎 (𝒙) = 𝟐𝟎

<p>𝒙 = 𝑒^(2)</p> Signup and view all the answers

Rewrite 𝟐 𝑳𝒐𝒈 𝟐 (𝒙 + 𝟑) − 𝑳𝒐𝒈 𝟐 𝟑𝒙 as one logarithm.

<p>𝑳𝒐𝒈 𝟐 ((𝒙 + 𝟑)^2 / 𝟑𝒙)</p> Signup and view all the answers

If 𝑓(𝑥) = 3𝑥^2 – 3 is reflected along the y-axis then shifted 2 units to the left, obtain 𝑔(𝑥). What is 𝑔(𝑥) in terms of 𝑥?

<p>𝑔(𝑥) = 3(−(𝑥+2))^2 - 3</p> Signup and view all the answers

Is the statement y = sin(x) the same as y = -1 sin(x)?

<p>ii. false</p> Signup and view all the answers

Is sin(45 degrees) equal to sin(pi / 4 radians)?

<p>i. true</p> Signup and view all the answers

Is the trigonometric identity sin^2𝑥 + cos^2𝑥 = 1 true?

<p>i. true</p> Signup and view all the answers

Which one is the correct mnemonic for trigonometric ratios?

<p>iv. PASS THE EXAM</p> Signup and view all the answers

Simplify the expression: $(5^2 - 3^4) - 5^{16}$

<p>-43046720</p> Signup and view all the answers

Factorise the expression: $6x^2 - x - 12$

<p>$(2x-3)(3x+4)$</p> Signup and view all the answers

Find the equation of the line that passes through the points (3,16) and (7,-4)

<p>$y = -5x + 31$</p> Signup and view all the answers

Solve for $x$ in the equation: $4x - \frac{3}{3x} = 10$

<p>$x = \frac{3}{2}$ or $x = -\frac{3}{2}$</p> Signup and view all the answers

Find the initial value of the exponential equation $A(t) = \frac{21-7e^{-6t}}{1-4e^{-3t}}$

<p>7</p> Signup and view all the answers

Rearrange the model to solve for 𝑒𝑘𝑡?

<p>$𝑒𝑘𝑡 = rac{𝑩(𝒕) - 3}{10}$</p> Signup and view all the answers

If 𝒌 = 𝟎. 𝟎𝟏, after 5 days, what will be the total number of bees?

<p>The total number of bees after 5 days will be 13.5</p> Signup and view all the answers

Solve the following equation: $𝟏𝟎𝑳𝒐𝒈 𝟏𝟎 (𝒙) = 𝟐𝟎$

<p>$x = 2$</p> Signup and view all the answers

Rewrite $𝟐 𝑳𝒐𝒈 𝟐 (𝒙 + 𝟑) − 𝑳𝒐𝒈 𝟐 𝟑𝒙$ as one logarithm.

<p>$rac{log((x+2)^2)}{log(3x)}$</p> Signup and view all the answers

If 𝑓(𝑥) = 3𝑥^2 – 3 is reflected along the y-axis then shifted 2 units to the left, obtain 𝑔(𝑥). What is 𝑔(𝑥) in terms of 𝑥?

<p>$𝑔(𝑥) = 3(-x-2)^2 - 3$</p> Signup and view all the answers

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