The equation 8(9x + 7) 7(6x 5) = 1 has the solution x = k, where k is a positive integer. Pass on the value of k.

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1 A1 The equation 8(9x + 7) 7(6x 5) = 1 has the solution x = k, where k is a positive integer. Pass on the value of k. A3 Y is proportional to the reciprocal of the square of X. Y = 20 when X = 6. Pass on the value of Y when X = T 1.

2 A2 The expression 64 1 T can be simplified to p, where p and q are positive integers with q no common factor greater than 1. Pass on the value of p + q. A4 In the diagram V XY and W X Z are straight lines. The lines VW and ZY are parallel. W X = 36 cm, XY = 30 cm, Z X = d cm and XV = T cm. V W T cm 36 cm d cm X 30 cm Z Y Write down the value of d.

3 B1 (10!) (6!) = n! Pass on the value of n. [The notation n! means the factorial of n, which is n (n 1) 2 1. For example, 6! means ] B3 An equilateral triangle has its vertices on a circle of area 1 5 πt cm2, as shown. The perimeter of the triangle has length x cm. Pass on the value of x. [sin 30 = cos 60 = 1 2 and sin 60 = cos 30 = 3 2.]

4 B2 Evaluate T 3 3 T and write your answer in the form a b, where a and b are positive integers with no common factor greater than 1. Pass on the value of a + b 1. B4 The graph of y = x 2 6x T meets the y-axis at P, and the x-axis at Q and R, as shown. y Write down the area of the triangle PQR as a simplified surd a b, where a and b are integers and b is not divisible by any square greater than 1. Q P R x

5 C1 U, K, M and T are positive integers with 1 < U < K < M < T < 10 such that U M = K T. Pass on the value of U + K + M + T. C3 The line y = 4x +T intersects the curve y = x 2 (T 14)x 9T at the points (x 1, y 1 ) and (x 2, y 2 ). Pass on the value of x 1 + x 2.

6 C2 The diagram shows parts of two regular polygons with a common edge. A B 3(T + 1) Polygon A has five more sides than polygon B and the sum of their exterior angles is 3(T + 1). Pass on the sum of the numbers of sides of the two polygons. C4 x satisfies the equation Write down the value of x x 2 (T+1)x = 16 3x+T

7 D1 B x D 20 C A The lines C A and CB are tangents to the circle. D is a point on the circle on the minor arc between A and B. The angle BC A = 20. Pass on the value of x. D3 The integer k is such that the expression k ( ) ( ) T 2T 3T is an integer. Pass on the value of 6k.

8 D2 A rectangle is drawn with its vertices on a circle, as shown. The width of the rectangle is 4 cm. The height of the rectangle is T cm. The area of the circle can be written in the form Aπ cm 2. Pass on the value of 2A 4. D4 A bag contains (T 3) balls, each of which is red, blue or green. There is at least one red ball. There are more blue balls than red balls, and more green balls than blue balls. If three balls are chosen at random from the bag, without replacement, the probability that there is one of each colour is Write down the number of green balls in the bag.

9 response sheet Team number School name A1 B1 C1 D1 A2 B2 C2 D2 A3 B3 C3 D3 A4 B4 C4 D4 Bonus 3 Bonus 3 Bonus 3 Bonus 3 A total /15 B total /15 C total /15 D total /15 Circle the mark awarded for each question and cross out the others. At the end of the round, either circle the bonus mark or cross it out. Final score /60

p and q are two different primes greater than 25. Pass on the least possible value of p + q.

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