(a) A bus travels with a velocity of \(6 ms ^{-1}\). It then accelerates uniformly and travels a distance of 70 m. If the final velocity is \(20 ms ^{-1}\), find, correct to one decimal place, the:
acceleration;
(b) A bus travels with a velocity of \(6 ms ^{-1}\). It then accelerates uniformly and travels a distance of 70 m. If the final velocity is \(20 ms ^{-1}\), find, correct to one decimal place, the:
time to travel this distance.
There are 6 boys and 8 girls in a class. If five students are selected from the class, find the probability that more girls than boys are selected
(a)The table shows the distribution of heights ( cm ) of 60 seedlings in a vegetable garden.
| Heights(cm) | 0.1 – 0.3 | 0.4 – 0.6 | 0.7 – 0.9 | 1.0 – 1.4 | 1.5 – 1.9 | 2.0 – 22 | 2.3 – 2.5 |
| Frequency | 6 | 9 | 12 | 15 | 3 | 6 | 9 |
Draw a histogram for the distribution.
(b) The table shows the distribution of heights ( cm ) of 60 seedlings in a vegetable garden.
| Heights(cm) | 0.1 – 0.3 | 0.4 – 0.6 | 0.7 – 0.9 | 1.0 – 1.4 | 1.5 – 1.9 | 2.0 – 2.2 | 2.3 – 2.5 |
| Frequency | 6 | 9 | 12 | 15 | 3 | 6 | 9 |
Use the histogram to estimate the modal height of the seedlings.
(a) The first term of an Arithmetic Progression is -8, the last term is 52 and the sum of terms is 286. Find the:
number of terms in the series;
(b) The first term of an Arithmetic Progression is -8, the last term is 52 and the sum of terms is 286. Find the:
common difference.
(a) The inverse of a function \(f\) is given by \(f^{-1}(x)=\frac{5x – 6}{4 – x},x ≠ 4\).Find the:
function, \(f (x)\)
(b) The inverse of a function \(f\) is given by \(f^{-1}(x)=\frac{5x – 6}{4 – x},x ≠ 4\).Find the:
value of x for which \(f (x) = 5\)
The volume of a cube is increasing at the rate of \(3\frac{1}{2} cm ^3 s^{ -1}\). Find the rate of change of the side of the base when its length is 6 cm .
If \((x – 5)\) is a factor of \(x^3 – 4x^2 – 11x + 30\), find the remaining factors.
- A. \((x + 3) and (x - 2)\)
- B. \((x - 3) and (x + 2)\)
- C. \((x - 3) and (x - 2)\)
- D. \((x + 3) and (x + 2)\)
In how many ways can four Mathematicians be selected from six ?
- A. 90
- B. 60
- C. 15
- D. 360
Find the coefficient of the \(6^{th}term\) in the binomial expansion of \((1 – \frac{2x}{3})10\) in ascending powers of \(x\).
- A. \(-\frac{896x^6}{9}\)
- B. \(-\frac{896x^5}{9}\)
- C. \(-\frac{896x^5}{27}\)
- D. \(-\frac{896x^6}{27}\)
If m and ( m + 4) are the roots of \(4x^2 – 4x – 15 = 0\), find the equation whose roots are 2 m and (2 m + 8).
- A. \(x^2+8x-15=0\)
- B. \(x^2-2x-15=0\)
- C. \(x^2-8x-15=0\)
- D. \(x^2+2x+15=0\)
Given that \(p = \begin{bmatrix} x&4\\3&7\end{bmatrix} Q =\begin{bmatrix} x&3\\1&2x\end{bmatrix}\) and the determinant of \(Q\) is three more than that of \(P\) , find the values of \(x\).
- A. \(-2,\frac{3}{2}\)
- B. \(2,\frac{3}{2}\)
- C. \(-2,-\frac{3}{2}\)
- D. \(2-,\frac{3}{2}\)
The probabilities that Atta and Tunde will hit a target in a shooting contest are \(\frac{1}{6}\) and \({1}{9}\) respectively. Find the probability that only one of them will hit the target.
- A. \(\frac{1}{54}\)
- B. \(\frac{41}{54}\)
- C. \(\frac{20}{27}\)
- D. \(\frac{13}{54}\)
A function \(f\) is defined by \(f :x→\frac{x + 2}{x – 3},x ≠ 3\).Find the inverse of \(f\) .
- A. \(\frac{x + 3}{x - 2},x ≠ 2\)
- B. \(\frac{x - 3}{x + 2},x ≠ -2\)
- C. \(\frac{3x - 2}{x+1},x ≠ -1\)
- D. \(\frac{3x + 2}{x - 1},x ≠ 1\)
If \(X\) and \(Y\) are two independent events such that \(P (X) = \frac{1}{8}\) and \(P (X ⋃ Y) = \frac{5}{8}\), find \(P (Y)\).
- A. \(\frac{1}{6}\)
- B. \(\frac{4}{7}\)
- C. \(\frac{4}{21}\)
- D. \(\frac{3}{7}\)
Given that \(y^2 + xy = 5,find \frac{dy}{dx}\).
- A. \(\frac{y}{2y + x}\)
- B. \(\frac{-y}{2y + x}\)
- C. \(\frac{-y}{2y - x}\)
- D. \(\frac{y}{2y + x}\)
A linear transformation on the oxy plane is defined by \(P : (x, y) → (2x + y, -2y)\). Find \(P^2\)
- A. \(\begin{bmatrix} 4&0\\1&4\end{bmatrix}\)
- B. \(\begin{bmatrix} 4&4\\0&0\end{bmatrix}\)
- C. \(\begin{bmatrix} 4&0\\0&4\end{bmatrix}\)
- D. \(\begin{bmatrix} 4&1\\0&4\end{bmatrix}\)
The velocity of a body of mass 4.56 kg increases from \((10 ms^{-1}, 060^o) to (50 ms ^{-1}, 060^o)\) in 16 seconds . Calculate the magnitude of force acting on it.
- A. 17.1 N
- B. 11.4 N
- C. 36.5 N
- D. 5.7 N
Given that \(\frac{3x + 4}{(x – 2)(x + 3)}≡\frac{P}{x + 3}+\frac{Q}{x – 2}\),find the value of Q.
- A. 2
- B. -2
- C. 1
- D. -1
If \(3x^2 + p x + 12 = 0\) has equal roots, find the values of p .
- A. ±12
- B. ±3
- C. ±4
- D. ±6
If α and β are the roots of \(7×2 +12x – 4 = 0\),find the value of \(\frac{αβ}{(α + β)^2}\)
- A. \( \frac{7}{36}\)
- B. -\( \frac{36}{7}\)
- C. \(\frac{36}{7}\)
- D. -\( \frac{7}{36}\)