Quiz about X2 trial prep (NE20AP)

Question 1

Consider the following statement for $$n\in Z:$$

If $$n^2+4n+1$$ is even, then $$n$$ is odd.

Which of the following statements is the contrapositive of this statement for $$n\in Z\ ?$$

Accepted Answer

If n is even, then $$n^2+4n+1$$ is odd.

Answer

If $$n^2+4n+1$$ is odd, then n is even.

Answer

If n is odd, then $$n^2+4n+1$$ is even.

Answer

If $$n^2+4n+1$$ is even, then n is even.

Question 2

Which of the following expressions is equal to $$\int x^2e^{-x}\ dx$$ ?

Accepted Answer

$$-x^2e^{-x}+\int2xe^{-x}\ dx$$

Answer

$$-2xe^{-x}-\int2xe^{-x}\ dx$$

Answer

$$-x^2e^{-x}-\int2xe^{-x}\ dx$$

Answer

$$-2xe^{-x}+\int2xe^{-x}\ dx$$

Question 3

Which of the following expressions is the partial fraction form of the algebraic fraction $$\frac{x-4}{\left(x-3\right)^2\left(x^2+2\right)}\ ?$$

Accepted Answer

$$\frac{A}{x-3}+\frac{B}{\left(x-3\right)^2}+\frac{Cx+D}{x^2+2}$$

Answer

$$\frac{A}{\left(x-3\right)^2}+\frac{B}{x^2+2}$$

Answer

$$\frac{A}{\left(x-3\right)^2}+\frac{Bx+C}{x^2+2}$$

Answer

$$\frac{A}{x-3}+\frac{B}{\left(x-3\right)^2}+\frac{C}{x^2+2}$$

Question 4

The Argand diagram shows the rectangle OABC where OC = 2OA.

Vertex A corresponds to the complex number w.

Which of the following complex numbers corresponds to vertex C?

Accepted Answer

$$2iw$$

Answer

$$-2iw$$

Answer

$$-2w$$

Answer

$$2w$$

Question 5

If x, y and z are any real numbers and x > y, which of the following statements must be true?

Accepted Answer

$$x+z>y+z$$

Answer

$$x^2>y^2$$

Answer

$$\frac{1}{x}<\frac{1}{y}$$

Answer

$$xz>yz$$

Question 6

A particle moves in simple harmonic motion along the x-axis about the origin. Initially, the particle is at its extreme positive position. The amplitude of the motion is 12 metres and the particle returns to its initial position every 3 seconds.

What is the equation for the position of the particle at time t seconds?

Accepted Answer

$$x=12\cos\frac{2\pi t}{3}$$

Answer

$$x=24\cos\frac{2\pi t}{3}$$

Answer

$$x=12\cos3t$$

Answer

$$x=24\cos3t$$

Question 7

Question 7.

Accepted Answer

$$\left(x+3\right)^2+\left(y-1\right)^2+\left(z+2\right)^2=49$$

Answer

$$\left(x-3\right)^2+\left(y+1\right)^2+\left(z-2\right)^2=7$$

Answer

$$\left(x+3\right)^2+\left(y-1\right)^2+\left(z+2\right)^2=7$$

Answer

$$\left(x-3\right)^2+\left(y+1\right)^2+\left(z-2\right)^2=49$$

Question 8

Question 8.

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 9

Question 9.

Accepted Answer

$$\frac{1}{2}a^2$$

Answer

$$-\frac{\sqrt[]{3}}{2}a^2$$

Answer

$$-\frac{1}{2}a^2$$

Answer

$$\frac{\sqrt[]{3}}{2}a^2$$

X2 trial prep (NE20AP)

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