Unfortunately, each of them properly identi…ed two of the colours but occasionally mixed up the other two colours: one person sometimes mixed up red and orange, another person sometimes [r]
(1)36 JUNIOR HIGH SCHOOL MATHEMATICS CONTEST May 2, 2012
NAME: GENDER:
PLEASE PRINT (First name Last name) M F
SCHOOL: GRADE:
(7,8,9)
You have 90 minutes for the examination The test has two parts: PART A — short answer; and PART B — long answer The exam has pages including this one Each correct answer to PART A will score points You must put the answer in the space provided No part marks are given
Each problem in PART B carries points You should show all your work Some credit for each problem is based on the clarity and completeness of your answer You should make it clear why the answer is correct PART A has a total possible score of 45 points PART B has a total possible score of 54 points
You are permitted the use of rough paper Geome-try instruments are not necessary References includ-ing mathematical tables and formula sheets are not
permitted Simple calculators without programming or graphic capabilities are allowed Diagrams are not drawn to scale They are intended as visual hints only When the teacher tells you to start work you should read all the problems and select those you have the best chance to …rst You should answer as many problems as possible, but you may not have time to answer all the problems
MARKERS’USE ONLY PART A B1 B2 B3 B4 B5 B6 TOTAL (max: 99)
BE SURE TO MARK YOUR NAME AND SCHOOL AT THE TOP OF THIS PAGE
THE EXAM HAS PAGES INCLUDING THIS COVER PAGE Please return the entire exam to your supervising teacher
(2)PART A: SHORT ANSWER QUESTIONS (Place answers in the boxes provided)
A1 The sum of three diÔerent prime numbers is 12 What are the numbers?
A2 Peter buys a pizza and eats half of it on the …rst day On the second day he eats one-third of the remaining part What fraction of the original pizza is still uneaten?
A3 What whole number is equal to
(1 2) 1
1
2 + (2 3)
1
3 + (3 4)
1
4 + + (99 100) 99
1 100 ?
A4 You have a giant spherical ball of radius metres sitting on level ground You put a red dot on the top of the ball, then you roll the ball13 metres north How far from the ground (in metres) is the red dot?
(3)A6 Four identical cubes are stacked up as in the diagram The length of each edge of each cube is2cm The straight-line distance (in cm) from cornerAto cornerB can be written in the form
p
N whereN is a positive integer What is N?
A7 Andrew, Belinda, Cameron and Danielle gather every day for 30 days to play tennis Each day, the four of them split oÔ into two teams of two to play a game and one of the teams is declared the winning team If Andrew, Belinda, and Cameron were on the winning team for 12, 13, and 14 of the games respectively, for how many of the games was Danielle on the winning team?
A8
3 x
31
Each box in the diagram contains a number, some of which are shown The number in each box above the bottom row is obtained by adding up the numbers in the two boxes connected to it in the row below For example,3 + = What number is in the box marked x?
A9 A B C D E F G H I J K L M N O X
The diagram shows a regular 15-sided polygon
ABCDEF GHIJ KLM N O, so that all sides are equal and all angles are equal Extend the sides
(4)PART B: LONG ANSWER QUESTIONS
(5)(6)(7)B4 ABCD is a quadrilateral with AB = BC = cm and AD=DC = cm, and with
\BAD=\BCD= 90 Find the length of AC (in cm)
J J J J J J J J J J
Q Q
Q Q
A
B
C
D
3
(8)B5 There is a basket containing marbles of four colours (red, orange, yellow and green) Alice, Bob and Cathy each counted the marbles in the basket and wrote down their results (see the table) Unfortunately, each of them properly identi…ed two of the colours but occasionally mixed up the other two colours: one person sometimes mixed up red and orange, another person sometimes mixed up orange and yellow, and the third person sometimes mixed up yellow and green How many marbles of each colour were there in the basket? Which colours did each of Alice, Bob and Cathy mix up?
Red Orange Yellow Green Alice
Bob
(9)