Find the length of the chord |AB| in the diagram shown above.
- A. 4.2 cm
- B. 4.3 cm
- C. 3.2 cm
- D. 3.4 cm
Rationalize \(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} – \sqrt{3}}\)
- A. \(-5 - 2\sqrt{6}\)
- B. \(-5 + 3\sqrt{2}\)
- C. \(5 - 2\sqrt{3}\)
- D. \(5 + 2\sqrt{6}\)
In a class of 50 students, 40 students offered Physics and 30 offered Biology. How many offered both Physics and Biology?
- A. 42
- B. 20
- C. 70
- D. 54
| Age in years | 7 | 8 | 9 | 10 | 11 |
| No of pupils | 4 | 13 | 30 | 44 | 9 |
The table above shows the number of pupils in a class with respect to their ages. If a pie chart is constructed to represent the age, the angle corresponding to 8 years old is
- A. 48.6°
- B. 56.3°
- C. 46.8°
- D. 13°
A binary operation \(\otimes\) is defined by \(m \otimes n = mn + m – n\) on the set of real numbers, for all m, n \(\in\) R. Find the value of 3 \(\otimes\) (2 \(\otimes\) 4).
- A. 6
- B. 25
- C. 15
- D. 18
The angle of elevation of the top of a tree from a point on the ground 60m away from the foot of the tree is 78°. Find the height of the tree correct to the nearest whole number.
- A. 148m
- B. 382m
- C. 282m
- D. 248m
Make q the subject of the formula in the equation \(\frac{mn}{a^2} – \frac{pq}{b^2} = 1\)
- A. \(q = \frac{b^2(mn - a^2)}{a^2 p}\)
- B. \(q = \frac{m^2 n - a^2}{p^2}\)
- C. \(q = \frac{mn - 2b^2}{a^2}\)
- D. \(q = \frac{b^2 (n^2 - ma^2)}{n}\)
The number line represents
- A. 0 > x \(\geq\) -7
- B. -7 \(\leq\) x < -1
- C. -7 < x \(\leq\) -1
- D. -7 < x < -1
In the diagram above, RST is a tangent to circle VSU center O ∠SVU = 50° and UV is a diameter. Calculate ∠RSV.
- A. 90°
- B. 50°
- C. 45°
- D. 40°
Using the cumulative frequency curve. What is the 80th percentile?
- A. 45.5
- B. 46.5
- C. 47.5
- D. 48.5
Using the cumulative frequency curve, estimate the median of the data represented on the graph.
- A. 35.5
- B. 36.5
- C. 37.5
- D. 38.5
If the angle of a sector of a circle with radius 10.5 cm is 120°, find the perimeter of the sector. [Take \(\pi = \frac{22}{7}\)]
- A. 48 cm
- B. 40 cm
- C. 43 cm
- D. 45 cm
P, Q and R are subsets of the universal set U. The Venn diagram showing the relationship \((P \cap Q) \cup R\) is
- A. 1
- B. 2
- C. 3
- D. 4
Evaluate \(\int_{0} ^{\frac{\pi}{2}} \sin x \mathrm d x\)
- A. -2
- B. 2
- C. 1
- D. -1
Integrate \(\frac{1 + x}{x^{3}} \mathrm d x\)
- A. \(2x^{2} - \frac{1}{x} + k\)
- B. \(-\frac{1}{2x^{2}} - \frac{1}{x} + k\)
- C. \(-\frac{x^{2}}{2} - \frac{1}{x} + k\)
- D. \(x^{2} - \frac{1}{x} + k\)
If \(\tan \theta = \frac{3}{4}\), find the value of \(\sin \theta + \cos \theta\).
- A. \(1\frac{1}{3}\)
- B. \(1\frac{2}{3}\)
- C. \(1\frac{3}{5}\)
- D. \(1\frac{2}{5}\)
In triangle PQR, q = 8 cm, r = 6 cm and cos P = \(\frac{1}{12}\). Calculate the value of p.
- A. \(\sqrt{108}\) cm
- B. 9 cm
- C. \(\sqrt{92}\) cm
- D. 10 cm
Find the equation of the perpendicular bisector of the line joining P(2, -3) to Q(-5, 1)
- A. 8y + 14x + 13 = 0
- B. 8y - 14x + 13 = 0
- C. 8y - 14x - 13 = 0
- D. 8y + 14x - 13 = 0
If the midpoint of the line PQ is (2,3) and the point P is (-2, 1), find the coordinate of the point Q.
- A. (8,6)
- B. (5,6)
- C. (0,4)
- D. (6,5)
The locus of the points which is equidistant from the line PQ forms a
- A. perpendicular line to PQ
- B. circle centre P
- C. circle centre Q
- D. pair of parallel lines to PQ