\(\begin{array}{c|c} \text{Age in years} & 10 & 11 & 12 \\ \hline \text{Number of pupils} & 6 & 27 & 7\end{array}\)

The table above shows the number of pupils in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years old?

• A. \(\frac{27}{40}\)
• B. \(\frac{17}{20}\)
• C. \(\frac{33}{40}\)
• D. \(\frac{3}{20}\)

Find the standard deviation of 5, 4, 3, 2, 1

• A. √2
• B. √3
• C. √6
• D. √10

A pyramid has a rectangular base with dimensions 12m by 8m. If its height is 14m, calculate the volume

• A. 322m³
• B. 448m³
• C. 632m³
• D. 840m³

Find the positive number n, such that thrice its square is equal to twelve times the number

• A. 1
• B. 2
• C. 3
• D. 4

Calculate the total surface area of a cupboard which measures 12cm by 10cm by 8cm

• A. 1920cm²
• B. 592cm²
• C. 296cm²
• D. 148cm²

In the diagram, a ladder TF, 10 metres long is placed against a wall at an angle of 70° to the horizontal.

(a) How high up the wall, correct to the nearest metre, does the ladder reach?

(b) If the foot (F) of the ladder is pulled from the wall to F\(^{1}\) by 1 metre, (i) how far, correct to 2 significant figures, does the top T slide down the wall to T\(^{1}\).

(ii) Calculate, correct to the nearest degree, \(QF^{1}T^{1}\).

Evaluate: \(\int^{z}_{0}(sin x - cos x) dx \hspace{1mm}

Where\hspace{1mm}letter\hspace{1mm}z = \frac{\pi}{4}. (\pi = pi)\)

• A. \(\sqrt{2 +1}\)
• B. \(\sqrt{2 }-1\)
• C. \(-\sqrt{2 }-1\)
• D. \(1-\sqrt{2}\)

lf \(log_q p= r\), express p in terms of q and r

• A. p =qr
• B. p =r^q
• C. \(p = \frac{r}{q}\)
• D. p=q^r

Find the constant term in the binomial expansion of \((2x - \frac{3}{x})^{8}\).

• A. 90720
• B. 1296
• C. 1120
• D. 672

Three exterior angles of a polygon are 30°, 40° and 60°. If the remaining exterior angles are 46° each, name the polygon.

• A. decagon
• B. nonagon
• C. octagon
• D. hexagon