cameroon gce intermediate level 2025 mathematics 2

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Question 2:

Evaluate the integral ∫13f(x)dx.

Question 3:

A civil engineer wishes to design a foot path on a lawn in front of a building. The engineer comes out with a table of values below to assist him in his design.

$x$	$- \infty$		3		$+ \infty$
$f^{'} (x)$		$+$		$+$
$f (x)$					$- 1$
		$+ \infty$

(a) Complete the table above and state the domain of definition of the portion to be used.

(b) Determine in the form of equation the places where the foot path are not supposed to pass or touch.

(c) Given that the portion in front of the building is represented as f(x)=3−xx+5, determine an equation of a line that will touch one of the paths at the point (−1,1).

(d) Using appropriate point of intersection, make a sketch of the paths on the (x,f(x)) plane, showing the paths.

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Question 5b:

Solve for x in the following equations:

(i) 2x−1=641

(ii) log2(x+1)−log2x=log27

(iii) 25x−6(5x)+5=0

Question 6a:

A certain girl is saving money to buy a car. She has 125000FCFA and she plans to save 37500FCFA per week from her job as a waitress.

(i) How much will she have saved after 8 weeks?

(ii) If the car cost 1,000,000FCFA, how long will it take her to save enough money at this rate?

Question 6b:

High Tech Electronics advertises a weekly installment plan for the purchase of a popular brand of high definition television. The buyer pays 2500FCFA at the end of the first week, 2750 FCFA at the end of the second week, 3025FCFA at the end of the third week, and so on for one year. (Assume 1 year = 52 weeks).

(i) What will the payments be at the end of the 10th, 20th, and 40th weeks?

(ii) Find the total cost of the TV.

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Sonita sells one litre of fuel for 600FCFA. How many litres of fuel will she sell if her take home package is 208,800FCFA?
What is 36 written as a product of its prime factors?
Evaluating $0.1 \times 0.2$ gives
The place value of 6 in the number 7364318 is
The relationship between $m$ and $n$ in the equation $2^{m} = 8^{n}$ is
The LCM of 8, 9 and 12 is
The class average of students at the end of the year is 7.097. Approximate this average to 3 significant figures.
The conjugate of the surd $3 + 4$ is
Electricity bills in an institution are paid to the nearest thousands. In the month of May, the bill was 689354FCFA. The amount paid by the institution is
The coefficient of $x$ in the expression $2 - x + 3 x^{2}$ is
The exact value of $(425)^{2}$ is
The simple interest on 7500 FCFA for 3 years at 2% is
Evaluating $3 - 5 + 2 2 1$ gives

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Question 1:

(a) Given that (x+1) and (x−2) are both factors of the expression bx3−x2+cx−b, find the values of the constants b and c.

(b) Write out the expression completely with the values of b and c.

(d) Determine the remaining factor and hence, solve for the values of x when the expression is equated to zero.

Question 2:

Express f(x)=x2−4x in partial fractions.

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The degree of the function $x - 2 x^{2}$ is
Writing the number 7369 in standard form is
The geometric mean of 4 and 16 is
The expression $a - b a ^{2} - b ^{2}$ is simplified as
The figure below is a right-angled triangle. The value of the unknown side labelled $x$ is 19. Given $2.2360 < 5 < 2.2361$ , the value of $- 5$ is
Write down the quadratic equation whose roots are $x = - 1$ and $x = 7$ .
Students are arranged such that the first group is made up of 10 students, the second group is 13 students and the third group is 16 students, then the fifth group is
If $f (x) = - 2 x + 5$ , then $f (- 2)$ is
The value of $(27)^{3 1}$ is
The number of nodes in the network below are

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Question 4:

Q is a circle whose equation is given by Q:x2+y2+4x−12=0.

(a) Find the coordinates of the Centre (Ω) and radius (r) of Q.

(b) A line (T) passes through the Centre$(\Omega)$ and meets the point P(2,2). Calculate the distance of the point P from the centre$(\Omega)$.

(d) Draw the circle indicating the centre, the point P and the line (T).

(e) Determine the point, B on the circle where the line y=4 touches the circle(Q).

Question 5a:

Solve in R3 the system of equations:

5x+4y−3z=32

2x+y−z=0

−5x+z=0

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cameroon gce intermediate level 2025 mathematics 2