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(Free mathematics and statistics online books section)
GCE OL MATHEMATICS – MODEL QUESTIONS
MATHEMATICS I
(1) Solve the following simultaneous equations
2 x + y = 7
3 x + 2 y = 12
(2) Simplify the following expression
(2x + 3) (3x – 5)
(3) There is a circle having a diameter of 18 cm. What is the area of the one half of the circle?
(4) The gradient m of a straight line is 6. The straight line passes through 1, 4. What is the equation of the straight line?
(5) If a+ b = 7 and ab = 6 what is the value of a3 + b3
(6) ABC is a triangle. AB = AC. The angle BAC is 76 degrees. What is the value of angle ABC?
(7) A building has a height of 10 metres. A person creates an elevation of 32 degrees on the top of the building from a point situated few metres horizontally away from the foot of the building. What is the distance between the person and the foot of the building?
(8) 16 men need 5 days to complete a certain task. How many days would 8 men take to complete a task which is 3 times the above task?
(9) The length of a chord which is 4 cm away from the center of the circle is 9 cm. What is the diameter of the circle?
(10) ABCD is a parallelogram where DC = 15 cm. The AX is a perpendicular drawn from A to DC. AX = 6 cm. What is the area of ABCD?
MATHEMATICS II
(1) (a) Factorize 6x2 -2x -6
(b) Solve 3x + 2y =10
3x – 4y = 1
4x + y + z = 17.
( c ) The Length of a building exceeds its breath by 2 m. The area of the building is 960 square metres.
(i) Assuming that the breath of the building is x, write down the quadratic equation to solve for x.
(ii) Find the value of length and breath of the building
(2) (a) The annual value of a business of an organization is Rs. 500,000.00. Tax payable to the Government is 5% of the annual value. How much has to be paid as tax for the period
(b) A product was sold at Rs. 6000.00 during the first month and the amount collected was Rs. 120,000.00.
During the second month the price was reduced by 10%. The total amount collected during the second month was Rs. 135,000.00
(i) How many items were sold during the first month?
(ii) What was the selling price of the item during the second month?
(iii) What was the percentage increase of the sales during the second month?
(3) (a) The 5th term of an arithmetical progression is 17. The 16th term is 50.
(i) Find the First Term and the Common Difference of the progression.
(ii) Find the sum of the first 25 terms of the progression.
(iii) Starting from the first term how many terms to be added to bring the total sum to 1575
. (b) The 3rd term of a geometric progression is 40. The 5th term is 160.
(iv) Find the First Term and the Common Ratio of the progression.
(v) Find the sum of the first 12 terms of the progression.
(vi) What are the two values expected for the 2nd term of the progression
(4) (a) There is a category of electronic equipment for which custom duty is charged at 45% of its original cost.
A person imports 10 items of that category. The original price of that item is Rs. 8500/-
(i) Determine the amount paid as custom duty for entire stock.
(ii) If the selling price is 16,500/- how much is the amount of profit gained from this transaction.