Senior Team Maths Challenge Regional Final 2008 Mini Relay Round
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- Winifred Flowers
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1 A1 Solve the simultaneous equations: 2x 5y 2z 4 7x y 2z 13 9x 4 y 1 Write down the value of. 2 z yx 2
2 A2 T is the number that you will receive The expression T x 4 1 2x 2 Tx 7x 5 can be written in the form px q 2x 2 7x 5. Write down the value of p.
3 A3 T is the number that you will receive The ratio of the volumes of these two similar cuboids, shown similarly situated, is 64:1. (T 1 ) cm P (T + 3) cm (T 5) cm (Diagram not to scale) Calculate the perimeter of face P.
4 A4 T is the number that you will receive A solid is formed by joining a right circular cone with base of radius 3cm, to a hemisphere of radius 3cm, as shown. The cone has a slant height of (T 7) cm. Calculate the volume of the solid in terms of.
5 B1 Given that x 1 calculate the value of x.
6 B2 T is the number that you will receive The equation ( 2 2 x x ) 5(2 ) 4 solutions, a and b. 0 has two Using the substitution y 2 x or otherwise, calculate T(a + b).
7 B3 T is the number that you will receive Let x 2 3 T T 2 T 3 T. x Calculate the value of.
8 B4 T is the number that you will receive Let A 11T 75 T 12. A can be written in the form, where a, b and c are integers. a b c a b Write A in the form. c
9 C1 2y + x + 4 = 0 is the equation of the line L 1 y + 5x = 2 is the equation of the line L 2 y = ax + b is the equation of the line L 3 The line L 3 passes through the y-intercept of L 1 and the x-intercept of L 2. Calculate ab.
10 C2 T is the number that you will receive The coordinates T, T,, 2 0, T 10 0, T 10 and (T, 0) give the vertices of a quadrilateral. Calculate the area of this quadrilateral.
11 C3 T is the number that you will receive The graphs with equations y 2x x and y 6x 33intersect at two points, x, y and x,y T Calculate the difference between and. x 1 x 2
12 C4 T is the number that you will receive The circle x 2 y 2 8Tx y 2x 6Ty 8 intersects the line at points x, y and 1 1,y. x2 2 0 Calculate x. x. 1 2
13 D1 The digits of 2008 can be arranged in different orders, for example In how many different orders can these digits be arranged?
14 D2 T is the number that you will receive A combination lock has (T 3) digits, where each digit is one of 0-9. Burglar Bill attempts every possible combination in sequence. It takes him 2 seconds to try each combination. Calculate, to the nearest hour, the longest time it could take him to open the safe.
15 D3 T is the number that you will receive Worthington-upon-Mud has a tug-of-war squad of 10 men. A team of (T + 2) men is needed for their next event. How many different teams could be selected?
16 D4 T is the number that you will receive (T 5) people are in a room. Everyone shakes everyone else s hand once. Calculate the total number of handshakes.
17 E1 Triangle ABC has a right-angle at A. Semicircles are drawn with BA, AC and BC as diameters as shown. Given that AC = 8 and BC = 10, write down the value of one third of the total shaded area.
18 E2 T is the number that you will receive T The value of 3 5 form a b can be expressed in the 5, where a and b are integers. Write down the value of 8(a b).
19 E3 T is the number that you will receive A parallelogram ABCD is such that DAB 2w 70, BCD w 30, and ABC CDA x T. Write down the value of. x 6
20 E4 T is the number that you will receive The angles of a certain hexagon form an arithmetic sequence with common difference ½T. Write down the size, in degrees, of the smallest angle of the hexagon.
21 F1 Write down the value of
22 F2 T is the number that you will receive A cylinder of radius 4cm and height (T + 6)cm has the same volume as a different cylinder of radius (4 + y)cm and height (T 2)cm. Calculate the value of y.
23 F3 T is the number that you will receive Given that T 16 c 7d 4 d e 20 e f 36 f 5c 15 find the value of c.
24 F4 T is the number that you will receive In the diagram, all angles are measured in degrees. Write down the value of x. (6 + T)x 3x 7Tx (3 T)x 6x (Diagram not to scale)
25 Answers Question 1 Question 2 Question 3 Question 4 Relay A π Relay B ½ Relay C or 5 Relay D Relay E o Relay F
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