Advanced level 2026 North west regional mock mathematics with statistics 1

The value of $\int \frac{1}{\sqrt{1-x^2}} dx$ is

A. $\tan^{-1} x + C$

B. $\cos^{-1} x + C$

C. $\sin^{-1} x + C$

D. $\sec^{-1} x + C$

The integral $\int \frac{1}{1+x^2} dx$ equals:

A. $\cos^{-1} x + C$

B. $\tan^{-1} x + C$

C. $\sin^{-1} x + C$

D. $\log(1+x^2) + C$

The $4^{th}$ term of a geometric progression is 81 and the $2^{nd}$ term is 9. The first term and common ratio are respectively:

A. 1 and 3

B. 8 and 3

C. 3 and 3

D. 27 and 3

If $1, \omega, \omega^2$ are the cube roots of unity, then the value of $(1 + \omega)^2$ is:

A. 1

B. $\omega^2$

C. $\omega$

D. 0

Which one of the following is not true for the cube roots of unity?

A. $\omega^3 = 1$

B. $\omega^2 = \frac{1}{\omega}$

C. $\omega + \omega^2 = -1$

D. $\omega – \omega^2 = \sqrt{3}i$

The parametric equations $x = a \cos 2t$ and $y = a \sin 2t$ represent:

A. Ellipse

B. Parabola

C. Circle

D. Hyperbola

Given $x = t^2, y = 2t$, eliminating the parameter, $t$, the cartesian equation is:

A. $y = 2x$

B. $x = \frac{y^2}{4}$

C. $y = x^2$

D. $x = y^2$

From 5 men and 4 women, the number of ways a committee of 3 people can be formed with at least one woman is:

A. 56

B. 64

C. 84

D. 74

The number of distinct arrangements of the letters of the word SUCCESS is:

A. 720

B. 630

C. 420

D. 360

The primary assumption of the trapezoidal rule is:

A. The function $f(x)$ is periodic.

B. The area under $f(x)$ can be approximated by trapezoids.

C. The derivative $f'(x)$ is zero.

D. The integral has no singularities.

For $\int_{0}^{2} 2x^2 dx$ with $n = 4$ subintervals, the trapezoidal rule approximation is:

A. 2.5

B. 2.75

C. 3.0

D. 3.5

The horizontal asymptote of $f(x) = \frac{3x^2 + 2x – 1}{2x^2 – 5x + 3}$ is:

A. $y = 0$

B. $y = \frac{3}{2}$

C. $y = \frac{-1}{3}$

D. $y = \frac{2}{-5}$

Which of the following is a valid conclusion using modus ponens?

i. If there is noise, the children are in the field

ii. there is noise

A. The children might be seen

B. The children are not out

C. The children are in the field

D. The children are not around

By using binomial expansion, approximating $(1.01)^5$ to 3 decimal places, gives;

A. 1.051

B. 1.050

C. 1.049

D. 1.048

If a relation $\mathcal{R}$ on $\mathbb{Z}$ is defined by $a\mathcal{R}b$, iff $a \equiv b \pmod 4$, the number of equivalence classes is:

A. 2

B. 3

C. 4

D. Infinite