Find \(\frac{\mathrm d y}{\mathrm d x}\) if \(y = \cos x\).
- A. \(\sin x\)
- B. \(- \sin x\)
- C. \(\tan x\)
- D. \(- \tan x\)
A man stands on a tree 150 cm high and sees a boat at an angle of depression of 74°. Find the distance of the boat from the base of the tree.
- A. 52 cm
- B. 43 cm
- C. 40 cm
- D. 15 cm
A circular arc subtends angle 150° at the centre of a circle of radius 12cm. Calculate the area of the sector of the arc.
- A. 30\(\pi\) cm\(^2\)
- B. 60\(\pi\) cm\(^2\)
- C. 120\(\pi\) cm\(^2\)
- D. 150\(\pi\) cm\(^2\)
The bar chart above shows the distribution of marks in a class test. If the pass mark is 5, what percentage of students failed the test?
- A. 10%
- B. 20%
- C. 50%
- D. 60%
The grades of 36 students in a class test are as shown in the pie chart above. How many students have excellent?
- A. 12
- B. 9
- C. 8
- D. 7
Find the area of the trapezium above.
- A. 91 cm2
- B. 78 cm2
- C. 60 cm2
- D. 19 cm2
In the diagram above, PQR is a circle centre O. If < QPR is x°, find < QRP.
- A. x°
- B. (90 – x)°
- C. (90 + x)°
- D. (180 – x)°
In diagram above, QR//TU, < PQR = 80° and < PSU = 95°. Calculate < SUT.
- A. 15o
- B. 25o
- C. 30o
- D. 80o
The shaded region above is represented by
the equation
- A. y ≤ 4x + 2
- B. y ≥ 4x + 2
- C. y ≤ -4x + 4
- D. y ≤ 4x + 4
The probabilities that a man and his wife live for 80 years are \(\frac{2}{3}\) and \(\frac{3}{5}\) respectively. Find the probability that at least one of them will live up to 80 years
- A. \(\frac{2}{15}\)
- B. \(\frac{3}{15}\)
- C. \(\frac{7}{15}\)
- D. \(\frac{13}{15}\)
The probability that a student passes a physics test is \(\frac{2}{3}\). If he takes three physics tests, what is the probability that he passes two of the tests?
- A. \(\frac{2}{27}\)
- B. \(\frac{3}{27}\)
- C. \(\frac{4}{27}\)
- D. \(\frac{5}{3}\)
In how many ways can the letters of the word TOTALITY be arranged?
- A. 6720
- B. 6270
- C. 6207
- D. 6027
Find the standard deviation of 2,3,8,10 and 12
- A. 3.9
- B. 4.9
- C. 5.9
- D. 6.9
Find the median of 2,3,7,3,4,5,8,9,9,4,5,3,4,2,4 and 5
- A. 9
- B. 8
- C. 7
- D. 4
The mean of seven numbers is 96. If an eighth number is added, the mean becomes 112. Find the eighth number.
- A. 126
- B. 180
- C. 216
- D. 224
Evaluate \(\int^{\frac{\pi}{4}}_0sec^2 \theta d \theta\)
- A. 1
- B. 2
- C. 3
- D. 4
Evaluate \(\int^2_1(x^2 – 4x)dx\)
- A. \(\frac{11}{3}\)
- B. \(\frac{3}{11}\)
- C. \(-\frac{3}{11}\)
- D. \(-\frac{11}{3}\)
If y = x2 – \(\frac{1}{x}\), find \(\frac{\delta y}{\delta x}\)
- A. 2x - \(\frac{1}{x^2}\)
- B. 2x + x2
- C. 2x - x2
- D. 2x + \(\frac{1}{x^2}\)
If angle \(\theta\) is 135o, evaluate cos\(\theta\)
- A. \(\frac{1}{2}\)
- B. \(\frac{\sqrt{2}}{2}\)
- C. \(-\frac{\sqrt{2}}{2}\)
- D. \(-\frac{1}{2}\)