BECE JHS Mathematics 2006 Past Questions

If Q = {1,3,5,7,9,11,13,15} and R = {1,2,3,5,6,7,10,11,12}, find Q ∩ R.

(a) A trader sold 250 articles for ¢525,000.00 at a profit of 25%.

(i)Calculate the cost price of each article
(ii) If the trader had wanted 45% profit on the cost price, how much should he have sold each of the articles?

(b)Find the simple interest on ¢880,000.00 for 2 ½ years at 3¼% per annum

If x is an integer, list the members of the set, {2 ≤ x < 10}

(a)The ratio of men to women in a village is 12:25. If there are 120 men,
(i)how many women are there?
(ii) what is the total number of men and women?

(b)A bag contains 70 pencils out of which 15 are green and 30 blue.
(i)How many pencils of other colours are in the bag?
(ii) A pencil is selected from the bag at random. What is the probability that it is blue?

(c)Solve⅓(x-1) - ½(x-3) ≤ 1¼ and illustrate your answer on the number line.

Simplify: 4/3x - 9/2x

(a) (i) Using a pair of compasses and ruler only, construct triangle XYZ with XZ = 12cm, XY = 10cm and angle XYZ = 90°.
(ii)Measure YZ.
(iii)Calculate the area of triangle XYZ
(iv)Measure angle ZXY.

(b)An isosceles triangle has a perimeter of (9y – 15) cm.
What is the length of each of the two equal sides, if its third side is (3y – 7) cm?

The number of boys in a school is 120. If the ratio of boys to girls is 5:7, find the total number of students in the school.

The mapping below has the rule, y = 2x + 3.
*insert image*
(a)(i) Copy the mapping and fill in the missing numbers
(ii) Using a scale of 2cm to 1 unit on both axes on a graph sheet, choose the origin O and draw the perpendicular axes OX and OY.
(iii) On the same graph sheet, mark the x-axis from 0 to 5 and the y-axis from 0 to 12.
(iv) Plot on the graph sheet the ordered pairs (x, y) from the mapping and join all the points using a straight edge.

(b)From your graph, find:
(i)y when x = 3.5;
(ii) x when y = 8;
(iii) the gradient of the liney = 2x + 3.

Find the circumference of a circle with radius 3.5 cm. (Take π = 22/7)

(a) A man spent ¼ of his monthly salary on rent, 2/5 on food and 1/6 on books. If he still had ¢55,000 left, what was his monthly salary?

(b)The average age of a family of eight is 30 years.

The average age of the six children in the family is 19 years.

If the mother is four years younger than the father, calculate the age of the father.

Which of the following are the prime factors of 12?

The following table shows the distribution of grades obtained by 120 students in an examination.
*insert image*
(a)Draw a pie chart for the distribution.

(b)(i) Evaluate: 5 7/15 - 2⅔ - 1 5/12.
(ii)Factorize: xy – xz + 5y – 5z

The base of an isosceles triangle is 7cm long. Each of the other two sides is x cm long. What will be the expression for its perimeter?

Correct 0.003858 to three significant figures

Find the value of a – 3abwhena = -2 and b = 3

A boy sold some oranges at three for ¢500.00. If his total sales was ¢100,000.00, how many oranges did he sell?

A train travels at a speed of 80km per hour. How long will it take to travel a distance of 320km?

Which of the following figures is a rhombus?

Three children share an amount of ¢910,800.00 in the ratio 2:3:4. What will be the highest share?

The next term in the sequence3, 6, 12, 24, …

Express 350 as a product of prime factors

Express 962 in standard form.

Which of the following inequalities is shown on the number line above, where p∈{real numbers}

Solve the equation

Arrange the fractions ¾ , 2/3, 4/5 in ascending order of magnitude.

Express 87_ten as a base five numeral.

A bag contains 6 blue and 5 black balls. What is the probability of picking a black ball at random?

Evaluate ${2^3×3^4×3^3}/{2^2×2×3^5}$

```The table below gives the ages of members of a juvenile club.
Use it to answer Questions 23 and 24
${\table Age(yrs),8,9,10,11;Frequency,5,10,6,9}$```
How many people are in the club?

```The table below gives the ages of members of a juvenile club.
Use it to answer Questions 23 and 24
${\table Age(yrs),8,9,10,11;Frequency,5,10,6,9}$```
What is the modal age of the members of the club?

In an examination, 154 out of 175 candidates passed. What percentage failed?

Expand (6 – x)(6 + y)

Find the highest common factor (HCF) of20, 12 and 28.

If F = 9/5c + 32 find F when C = 40.

Evaluate ⅔(27 – 12) – 6.

In the figure, PQR is a straight line. Angle TQP = x°, angle TQS = 102° and angle SQR = 2x°. Find the value of x.

Factorize22ab–11ac+6rb–3rc.

Find the sum of 124.3, 0.275 and 74.06. (Correct your answer to one decimal place)

Simplify 6p3 × p2 ÷ 3p4

Mr. Nkrumah saved ¢75,000.00 at a simple interest rate of 20% per annum for 3 years. Calculate the interest he earned on his savings

Find the rule for the mapping:
${\table 1,2,3,4,5,n;↓,↓,↓,↓,↓,↓;10,21,32,43,54,-}$

What is the value of the digit 9 in the number 624.93 ?

The marks obtained by 5 girls in a test are: 10, 15, 8, 18, 12. Find the median mark.

The point P(3, 4) is translated by the vector (<sup>3</sup><sub>-2</sub>) to a new position P′. Find the coordinates of the image P′.

In the diagram above, KGM is a right-angled triangle and angle GKM = 62°. Find the angle of elevation of K from M.

Given that vector a = (<sup>-2</sup><sub>3</sub>) and vector b = (<sup>2</sup><sub>-5</sub>), find a + 2b.