2011 Mathematics NECO Past Questions

 Express the sum of 0.0714 and 0.0163 in two significant figures.

Express the product of 0.0045 and 0.025 in standard form.

An item was sold for M650.00 with a profit of 30%. If the profit had been 20%, what was the selling price?

Find the compound interest on ₦225.00 invested for 20 years at 4% per annum.

Fin n the sum of the first 12 terms of The sequence 18, 11,4, — 3, …

The fifth term of a GP is 8 times the 2nd term. Find its common ratio.

Convert 59_ten to base two

If  ₦15,000.00 amounts to₦20,000.00 in two years at simple interest, what is the rate of interest?

A poultry farmer discovered that  ¹/₆  the eggs laid by the birds on the farm were bad. Find the percentage that was good

Evaluate (0.008)^1/₃

Find the value of x in the equation 4^x = 32

Solve the simultaneous equations

3x — y = 7 and 2x = 3-y

A father is 5 times as old as his son. If the sum of their ages is 60years, how old is the father?

Simplify  ⁵/_x-1  –  ⁶/_x-6

What is the common factor of the expressions y² + y and y² – 1

Solve the equation 2x² = 3x + 5

Factorise 5xy + 90qy -30y²  – 15xq.

Given that a² – b²  = 18 and a – b = 9. What is (a + b)?

An expression is given as ^a/_x +  ^b/_y = ^a/_y

Make a the subject of the formula

The number line below represents

-3        -2         -1         0          1          2          3          4          5

Construct a quadratic equation whose roots are   ¹/₂  and   ²/₃

If 3(4- y) > 6 – y, which of the following is true?

If a =1, b = 2 and d=3

Which of the following quadratic equations is represented by the graph below

Given that y = x² – 2, find the value of a + b in the table below.

Expand (a + b) (5a + b).

5a² + 6ab + b²

Which of these is NOT a property of a parallelogram?

Calculate, correct to 2 decimal places,

 the area of a triangle whose sides are 5cm, 6cm, and 7cm.

Calculate the length of the major arc ACB, correct to 2 decimal places.

Calculate the perimeter of a sector of a circle of radius 15cm, where the angle of the sector is 60° ( Take Π = 22/7)

An aircraft flew from city A (Lat 0°, Long 0° to another city B (Lat 0°, i ^ong 18°E) at an average speed of l000km/hr. Calculate the distance travelled to the nearest km. (Take ᴨ=22/7 and R=6370km)

A right circular cylinder of base radius 8cm has a height of 14cm.

Find the volume of the cylinder.

In the diagram below, O is the centre of the circle. Find the value of x + y.

Which of the following is correct about the figure shown below?

In the diagram below, O is the centre of the circle. If /AN/ is a tangent at M and ZAMQ 64°. Calculate the value of angle P

If XOY is a straight line, find the value of x

How many sides has a regular polygon if each of the interior angles is 120°?

In the diagram below, what is the value of ZABC ?

In the figure below, what is the value of P?

Calculate the area of an equilateral triangle of side t cm, leaving your answer in surd form.

O is the centre of the above circle and AXB is a chord. Find /OX/.

Given that sina 8/17, 0 ≤ a ≤ 90°, find the value  Of cosα

If sin 3x=cos 2x and0^o <x<90^o find x.

Solve the equation,   tan (ß-26°)= 1 .732

96° In the diagram above, determine the area of the parallelogram.

A town Q is 120km from a town B in the direction 050°. What is the bearing of B from Q?

PQR is a right-angled triangle in which PQR= 30°, /RQ/ =6cm. find the value of x in surd form

Weight of the boxers (kg)

The bar chart above shows the distribution of boxers’ weight in a row for boxing competition. Use the chart to answer the question below.

How many boxers have weight f 65kg and below?

Weight of the boxers (kg)

The bar chart above shows the distribution of boxers’ weight in a row for boxing competition. Use the chart to answer the question below.

How many boxers registered for the competition?

Weight of the boxers (kg)

The bar chart above shows the distribution of boxers’ weight in a row for boxing competition. Use the chart to answer the question below.

If a boxer is chosen at random, what is the probability that his weight is less than or equal to 60 kg?

A father was to share to his children {412,000,000.00} and demonstrated the sharing on a pie chart. If the sectorial angle of his only son is 60°, how much did the son take?

The average age of 10 boys was 12 years. A boy of 15years was replaced with that of 5 years. Find the new average age of the boys.

Given the following scores.2,3, 4, 5, 6. Use the information to answer the question below

Find the standard deviation.

Given the following scores.2,3, 4, 5, 6. Use the information to answer the question below

Find the variance.

The probabilities that Musa passes English, Mathematics and Geography are

¹/₃ , ²/₅ ,and ³/₄ respectively. What is the probability of passing all?

In a bag containing 12 oranges and 18 apples, what is the probability of not picking apple?

The table below shows the scores of a certain number of students in a class.

Find the mean score.

Calculate the median for the following set of numbers 3, 2, 6, 8, 9, 6,8, 12, 11, 12.

SECTION A

Answer All questions in this section

(a)      Given            that log (y – 2)³ = log 64, without using mathematical tables, find y.

(b)      If  μ ={x: The solution set of the inequalities 2x – 3 ≤27           and  2x – 1≤ 2 +     3x}.

                P is a subset of μ such that P = {Prime numbers}

                 List the elements in:

(i)               μ

(ii)             P     

8 marks

.           Among 40 applicants for a sales manager’s post, 26 have B.Sc. degree and 18 have NCE, 6 applicants have no certificate. Use a Venn diagram to illustrate the information. How many applicants have:

(i)       both B.Sc. and NCE;

(ii)      B.Sc. only;

(i)               NCE only?

8 marks

(a)      A fair die is rolled twice. Find the probability of getting:

(i)       the same number;

(ii)      at least a total of 7.

      (b)            Use the idea of difference of two squares to find the exact value of k in the equation:

                          24k = 106² – 94²

8 marks

.   (a)  Simplify 2 ÷  of 4

      (b)            The base diameter of a cone is 18cm and height is 24cm. Find the volume and the curved     surface area of the cone. (Correct to 2 decimal places).

8 marks

(a)      Find the sum of the first 9 terms of the A.P:  – 24, -18, -12, …

(b)      A dealer sells an article for N560.00 and makes a profit of 12%. Find the percentage of the profit he will realise, if he sells the article for N600.00.

8 marks

SECTION B

Answer any FIVE questions from this section

(6)         (a)   A ship moved from point A to point B 12km away on a bearing of 120°. It then moved westwards to another point C whose bearing from A is 250°.

(i)       Calculate the distance /AC/.

(ii)      Flow far west of A is C?

(b)      If 2 + x < 6 and 7 + x ≥ 4, what is the range of x satisfying both inequalities?

(a)      A civil servant obtained a loan of N350,000.00. He is expected to pay back the

loan over 4 years with a simple interest at a rate of 5% per annum.

(i)       Calculate the simple interest on the loan.

(ii)      How much did he pay back?

(iii)     If this amount is paid back in monthly instalments, how much did he pay back each month?

(b)      The interior angle of a regular polygon is four times the exterior angle. Calculate the:

(i)       exterior angle;

(ii)      number of sides of the polygon.

12 marks

(a) When the numerator and denominator of a fraction are increased by 1 and 3 respectively the fraction is 1/2 . The denominator of this fraction is 4 greater than its numerator. Find the fraction.

               (b)   Find the value of 5(x-y) if 4x² -9y² = 7 and 2x + 3y = 7.

The distribution below shows the number of cars attended to by a filling station in 40 days.

65       70       49       64       67       41       52       37       56       63

49       62       64       62       53       71       54       32       51       66

46       51       55       63       68       63       74       45       67       26

11       80       47       33       52       41       18       57       72       91

             Using a class interval of 11 – 20, 21 – 30, 31 – 40, …

(a)      Construct a group frequency table of the distribution.

(b)      i.  Using an assumed mean of 55.5, calculate correct to the nearest whole

number, the mean of the distribution,

                             ii. Find the mean deviation.

.       (a) The resistance R to the motion of a car is partly constant and partly varies as the square of the speed V. At 8Okmhr^-1, the resistance is 1060N and at 120kmhr^-1, its resistance is 1460N. What will be the resistance at 140kmhr^-1?

In the diagram above, O is the centre of the circle PQR, what are the values of a, b and c?

12 marks