National Examinations Council

NECO General Mathematics · Paper II — Essay

Written answers, marked against a rubric.

8 exam-style questions, written to the National Examinations Council format and free to read. The answers are here too — what they do not tell you is how many you would get right with a clock running.

Sit this paper timed All NECO General Mathematics papers

1. (a) Convert 1101₂ to base ten. [6 marks] (b) Convert 45₁₀ to base two. [8 marks] (c) Add 1011₂ and 110₂, giving your answer in base two. [6 marks]
2. (a) A trader allows a 15% discount on a marked price of ₦8,000. Calculate the selling price. [6 marks] (b) If the trader still makes a 20% profit, calculate the cost price. [10 marks] (c) Calculate the profit in naira. [4 marks]
3. (a) A ladder 10 m long leans against a wall making an angle of 65° with the ground. Calculate how far up the wall it reaches, correct to one decimal place. [8 marks] (b) Calculate the distance of its foot from the wall. [6 marks] (c) State one assumption made in this calculation. [6 marks]
4. (a) The angles of a quadrilateral are (x + 20)°, (2x − 10)°, (x + 30)° and 3x°. Find x. [8 marks] (b) Hence state the size of each angle. [6 marks] (c) State whether the quadrilateral can be a parallelogram, giving a reason. [6 marks]
5. (a) A cone has base radius 7 cm and slant height 25 cm. Calculate its curved surface area, taking π = 22/7. [8 marks] (b) Calculate its vertical height. [6 marks] (c) Calculate its volume, correct to the nearest whole number. [6 marks]
6. The ages of 30 pupils are grouped: 10–12 (6), 13–15 (11), 16–18 (9), 19–21 (4). (a) Construct a frequency table with midpoints. [5 marks] (b) Calculate the mean age, correct to one decimal place. [8 marks] (c) State the modal class and the median class. [7 marks]

Reading these is not the same as sitting them.

Every question above is answerable given time. The exam does not give you time. Sit the whole paper on the real clock and the number you get back is the one that means something.

Sit it against the clock — free

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NECO General Mathematics · Paper II — Essay

1. (a) Convert 1101₂ to base ten. [6 marks] (b) Convert 45₁₀ to base two. [8 marks] (c) Add 1011₂ and 110₂, giving your answer in base two. [6 marks]

2. (a) A trader allows a 15% discount on a marked price of ₦8,000. Calculate the selling price. [6 marks] (b) If the trader still makes a 20% profit, calculate the cost price. [10 marks] (c) Calculate the profit in naira. [4 marks]

3. (a) A ladder 10 m long leans against a wall making an angle of 65° with the ground. Calculate how far up the wall it reaches, correct to one decimal place. [8 marks] (b) Calculate the distance of its foot from the wall. [6 marks] (c) State one assumption made in this calculation. [6 marks]

4. (a) The angles of a quadrilateral are (x + 20)°, (2x − 10)°, (x + 30)° and 3x°. Find x. [8 marks] (b) Hence state the size of each angle. [6 marks] (c) State whether the quadrilateral can be a parallelogram, giving a reason. [6 marks]

5. (a) A cone has base radius 7 cm and slant height 25 cm. Calculate its curved surface area, taking π = 22/7. [8 marks] (b) Calculate its vertical height. [6 marks] (c) Calculate its volume, correct to the nearest whole number. [6 marks]

6. The ages of 30 pupils are grouped: 10–12 (6), 13–15 (11), 16–18 (9), 19–21 (4). (a) Construct a frequency table with midpoints. [5 marks] (b) Calculate the mean age, correct to one decimal place. [8 marks] (c) State the modal class and the median class. [7 marks]

Reading these is not the same as sitting them.

7. (a) Solve the equation 2x² − 7x + 3 = 0 by factorisation. [8 marks] (b) Make y the subject of the formula 3x + 2y = 5xy. [8 marks] (c) If x = 2 and y = 3, evaluate (x² + y²) ÷ (x + y). [4 marks]

8. A box contains 4 red, 6 white and 5 blue balls. One ball is drawn at random. (a) Find the probability that it is white. [5 marks] (b) Find the probability that it is not blue. [7 marks] (c) If two balls are drawn with replacement, find the probability that both are red. [8 marks]