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JAMB: MTH – Binary Operations
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Question 1 of 40
What is the locus of a point P which moves on one side of a straight line XY such that the angle XPY is always 90°?
Question 2 of 40
If M(4, q) is the midpoint of the line joining L(p, −2) and N(q, p), find the values of p and q.
Question 3 of 40
The equation of the line in the graph is
Question 4 of 40
The angle of depression of a boat from the top of a cliff 10 m high is 30°. How far is the boat from the foot of the cliff?
Question 5 of 40
What is the value of \(\scriptsize \sin(-690^\circ) \:?\)
Question 6 of 40
If
\(\scriptsize y=3t^3+2t^2-7t+3\)
find \(\frac{dy}{dt}\)
at t = –1
Question 7 of 40
Find the point (x, y) on the curve y = 2x² – 3x + 3, where the gradient is 2.
Question 8 of 40
Integrate \(\frac{1-x}{x^3}\)
with respect to x.
Question 9 of 40
Evaluate \(\scriptsize \int_{-1}^{1}(2x+1)^2dx\)
Question 10 of 40
The grades A1, A2, A3, C4 and F earned by students in a course are shown in a pie chart. What percentage of the students obtained a C4 grade?
Question 11 of 40
The table below shows the frequency distribution of a data. If the mean is \(\frac{43}{14}\), find y.
Question 12 of 40
The mean of twelve positive numbers is 3. When another number is added, the mean becomes 5. Find the thirteenth number.
Question 13 of 40
Find the mean deviation of the set of numbers 4, 5, 9.
Question 14 of 40
Estimate the median of the frequency distribution above.
Question 15 of 40
\( \scriptsize \begin{array}{c|c} x & 1 & 2 & 3 & 4 & 5 \\ \hline f & 2 & 1 & 2 & 1 & 2\end{array}\)
Find the variance of the frequency distribution above.
Question 16 of 40
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?
Question 17 of 40
In a survey, it was observed that 20 students read newspapers and 35 read novels. If 40 of the students read either newspapers or novels, what is the probability of the students who read both newspapers and novels?
Question 18 of 40
If ₦225.00 yields ₦27.00 in x years simple interest at the rate of 4% per annum, find x.
Question 19 of 40
The shaded portion in the Venn diagram is:
Question 20 of 40
If \(\scriptsize \sqrt{(x^2 \:+\: 9)} = x \: + \: 1 \)
Solve for x
Question 21 of 40
Make x the subject of the relation
\(\frac{1+ax}{1-ax}=\frac{p}{q}\)
Question 22 of 40
Which of the following is a factor of 15 + 7x – 2x²
Question 23 of 40
Evaluate \(\left(\scriptsize x+ \normalsize \frac{1}{x} \scriptsize+ 1\right)^2-\left(\scriptsize x-\normalsize\frac{1}{x}\scriptsize -1\right)^2\)
Question 24 of 40
Solve the following simultaneous equation for x.
x² + y – 5 =0
Question 25 of 40
Solve the following equation (3x -2)(5x – 4) = (3x -2)²
Question 26 of 40
The figure represents the graphs of y = x(2-x) and y =(x-1)(x-3). What are the x coordinates of P, Q and R respectively?
Question 27 of 40
If the function f is defined by f(x+2) = 2x² + 7x – 5, find f(-1)
Question 28 of 40
Divide the expression x³ + 7x² – x – 7 by -1 +x²
Question 29 of 40
Simplify \(\frac{1}{p}-\frac{1}{q}\div\frac{p}{q}-\frac{q}{p}\)
Question 30 of 40
Solve the inequality y² – 3y >18
Question 31 of 40
If x is negative, what is the range of value of x within which
\(\frac{x+1}{3} > \frac{1}{x+3}\)
Question 32 of 40
A man’s initial salary is ₦540.00 a month and increases after each period of six months by ₦36.00 a month. Find the salary in eighth month of the third year.
Question 33 of 40
If k + 1, 2k – 1, 3k + 1 are three consecutive terms of geometric progression, find the possible values of the common ratio
Question 34 of 40
A binary operation * is defined on a set of real numbers by x*y = xʸ for all real values of x and y. if x *2 = x, find the possible values of x
Question 35 of 40
PQRST is a regular pentagon, and PQVU is a rectangle with U and V lying on TS and SR, respectively, as shown in the diagram. Calculate TUP.
Question 36 of 40
A regular polygon has 150° as the size of each interior angle. How many sides has the polygon?
Question 37 of 40
Calculate the length in cm of the area of a circle of diameter 8 cm, which subtends an angle of 22 ½° at the centre of the circle.
Question 38 of 40
In the diagram. PQRS is a circle with O as centre and PQ/RT. If RTS = 32°. Find PSQ.
Question 39 of 40
Change 7110 to base 8
Question 40 of 40
Evaluate \(\frac{3524}{0.05}\) correct to 3 significant figures
