(a) (i) Study the sequence -3, -2, -5, -7, -12 and -19, and then state a reason to verify that the sequence is Fibonacci. (ii) Use the divisibility rule to determine whether the number 9655 is divisible by 3. (b) Complete the blank spaces in the following pattern of numbers that obeys Pascal’s triangle.

1. Use the divisibility rule to determine whether the number 9655 is divisible by 3. (0 mk)
2. Complete the blank spaces in the following pattern of numbers that obeys Pascal’s triangle. (0 mk)

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(a) Simplify the expression 18r-(2r +10) – 14r + 25 to its lowest term (b) Expand completely the following expressions: (i) 3(2c + 3)2 – c2 (ii) 2x(x+4y) – x(8x + 14y) – 2(3 + 4y) (c) Write r in terms of x and y, given that

1. Simplify the expression 18r-(2r +10) – 14r + 25 to its lowest term (0 mk)
2. Expand completely the following expression: 2x(x+4y) – x(8x + 14y) – 2(3 + 4y) (0 mk)
3. Write r in terms of x and y, given that (0 mk)

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The size of an exterior angle of a certain polygon is p and the size of its interior angle is three times the size of the exterior angle. Find (a) The value of the expression (b) The size of the interior angle (c) The sum of the interior angles

1. The size of an exterior angle of a certain polygon is p and the size of its interior angle is three times the size of the exterior angle. Find the value of the expression. (0 mk)
2. The size of an exterior angle of a certain polygon is p and the size of its interior angle is three times the size of the exterior angle. Find the size of the interior angle. (0 mk)
3. The size of an exterior angle of a certain polygon is p and the size of its interior angle is three times the size of the exterior angle. Find the sum of the interior angles. (0 mk)

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(c) The locus of point P moves along the plane and intersects the lines whose equations are m(y – 3) = x + 1 and y = mx where, m is a variable. Find the equation of the locus of the point P.

1. An orange is falling vertically from a tree at a height of 2 metres from the ground (0 mk)
2. Describe the locus when the centre of a wheel as a cyclist ride along the road on a horizontal plane. (0 mk)
3. The centre of a wheel as a cyclist ride along the road on a horizontal plane. (0 mk)
4. Analyse the locus of the point P which is equidistant from the points L(-2,2) and (1, 1 ½ ). (0 mk)
5. The locus of point P moves along the plane and intersects the lines whose equations are m(y – 3) = x + 1 and y = mx where, m is a variable. Find the equation of the locus of the point P. (0 mk)

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(b) Determine the equation of a line passing through the point (-4, -4) and parallel to the line whose equation is 2x + 6y – 9 = 0

1. Calculate the height h given that the points A(2,5), B(h,-4) and C(1,2) are collinear. (0 mk)
2. Determine the equation of a line passing through the point (-4, -4) and parallel to the line whose equation is 2x + 6y – 9 = 0 (0 mk)

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(b) State the order of rotational symmetry for each of the objects given in the table. Name of the Object Order of Rotational Symmetry

1. State the number of lines of symmetry in each shape of the object when Chichi watched Drawing Art on Television, as she identified the following shapes of objects: (i) Circle (ii) tree (iii) flying kite (iv) cross shape (v) rectangular home mat. (0 mk)
2. Circle (0 mk)
3. A rectangle playing card (0 mk)
4. State the order of rotational symmetry for each of the objects given in the table. Name of the Object Order of Rotational Symmetry (i) A rectangle playing card (ii) A ten thousand Tanzania shillings (iii) A nonagon (iv) A pen (v) A soccer ball (0 mk)
5. tree (0 mk)
6. A ten thousand Tanzania shillings (0 mk)
7. A nonagon (0 mk)
8. flying kite (0 mk)
9. A pen (0 mk)
10. cross shape (0 mk)
11. A soccer ball (0 mk)
12. rectangular home mat (0 mk)

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The sales records of a certain fuel filling station were as follows; the total sales of six litres of diesel and five litres of petrol were Tsh. 6000, while the sales of seven litres of diesel and five litres of petrol were Tsh. 6800. Use elimination method to find the price of a litre of diesel and litre of petrol.

1. The sales records of a certain fuel filling station were as follows; the total sales of six litres of diesel and five litres of petrol were Tsh. 6000, while the sales of seven litres of diesel and five litres of petrol were Tsh. 6800. Use elimination method to find the price of a litre of diesel and litre of petrol. (0 mk)

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Given that μ is the universal set and D, P and S are subsets such that: μ = {x:x is an integer 3 ≤ x < 18} D = {x:x is an odd number} P = {x:x is prime number} S = {x:x is a perfect square} (a) List the elements of each set (b) Represent these sets in Venn diagram (c) Find (i) D ∩ P (ii) S - D

1. List the elements of each set (0 mk)
2. Represent these sets in Venn diagram (0 mk)
3. Find S - D (0 mk)

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(c) If P stands for “2 + 6 = 8” and Q stands for “6 x 5 = 11” write the symbolic form of the statement and draw an electric circuit; “either 2 + 6 = 8 or 6 x 5 = 11”.

1. Copy and complete the following truth table; (0 mk)
2. Represent the statement in symbolic form and test its validity by letting p represent “6 is even number,” q represent “6 is divisible by 2,” and r represent “6 is divisible by 4.” (0 mk)
3. If P stands for “2 + 6 = 8” and Q stands for “6 x 5 = 11” write the symbolic form of the statement and draw an electric circuit; “either 2 + 6 = 8 or 6 x 5 = 11”. (0 mk)

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Suppose p is directly proportional to q^2 and inversely proportional to r such that p = 10 when q = 6 and r = 16. Find the value of p when q = 2 and r = 64.

1. Determine the value of a when b = 12, given that a α (b^2 + 3) and a = 4 when b = 5. (0 mk)
2. The speed L of a certain particle moving on the surface of water is inversely proportional to the cube root of time n and L = 3 when n = 27. Determine the value of L when n = 64. (0 mk)
3. Suppose p is directly proportional to q^2 and inversely proportional to r such that p = 10 when q = 6 and r = 16. Find the value of p when q = 2 and r = 64. (0 mk)

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