MAT01S1 Mathematics 1 Exam

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24 Questions

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)

y = 2x + 3

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

y = -5x + 31

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

𝒆𝒌𝒕 = (𝑩(𝒕) - 𝟑) / 𝟏𝟎

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

𝑩(5) = 𝟑 + 𝟏𝟎𝑒^(0.01*5)

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

𝒙 = 𝑒^(2)

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

𝑳𝒐𝒈 𝟐 ((𝒙 + 𝟑)^2 / 𝟑𝒙)

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?

𝑔(𝑥) = 3(−(𝑥+2))^2 - 3

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

ii. false

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

i. true

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

i. true

Which one is the correct mnemonic for trigonometric ratios?

iv. PASS THE EXAM

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

-43046720

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

$(2x-3)(3x+4)$

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

$y = -5x + 31$

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

$x = \frac{3}{2}$ or $x = -\frac{3}{2}$

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

7

Rearrange the model to solve for 𝑒𝑘𝑡?

$𝑒𝑘𝑡 = rac{𝑩(𝒕) - 3}{10}$

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

The total number of bees after 5 days will be 13.5

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

$x = 2$

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

$rac{log((x+2)^2)}{log(3x)}$

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?

$𝑔(𝑥) = 3(-x-2)^2 - 3$

This is an exam for Mathematics 1, where sufficient working out must be shown to avoid deduction of marks. The permissible materials include pens, pencils, rubbers, rulers, and white-out, but no calculators or unauthorized materials are allowed. The exam includes a reading time of 10 minutes and a writing time of 120 minutes.

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