Fryer Contest 2016年真题

1. Three schools each sent four students to a competition. The scores earned by nine of the students are given in the table below. The scores of the remaining three students are

represented by x, y and z. The total score for any school is determined by adding the scores of the four students competing from the school.

(a) What is the total score for School A?

(b) The total scores for Schools A and B are the same. What is the value of x, the score for Student 4 at School B?

(c) The total scores for Schools A and C are the same. If the score for Student 4 at School C is twice that of Student 3 at School C, determine these two scores.

2. When Esther and her older brother Paul race, Esther takes 5 steps every 2 seconds, and each of her steps is 0.4 m long. Paul also takes 5 steps every 2 seconds, but each of his

steps is 1.2 m long.

(a) In metres, how far does Esther travel in 2 seconds?

(b) In metres per second, what is Paul’s speed?

(d) If Esther begins a race 3 minutes before Paul, how much time does it take Paul to catch Esther?

3. A median is a line segment drawn from a vertex of a triangle to the midpoint of the opposite side of the triangle.

(a) In the diagram, 4ABC is right-angled and

has side lengths AB = 4 and BC = 12. If AD

is a median of ∆ABC, what is the area

of ∆ACD?

(b) In rectangle EF GH, point S is on F H

with SG perpendicular to F H. In ∆FGH,

median FT is drawn as shown. If FS = 18,

SG = 24 and SH = 32, determine the area

of ∆FHT.

to LN at R. Medians KP and KQ are drawn in

∆KLM and ∆KMN respectively, as shown. If

LR = 6, RN = 12, KR = x, RM = 2x + 2, and the

area of KPMQ is 63, determine the value of x.

4. A BINGO card has twenty-five different integers arranged into five rows and five columns labeled B, I, N, G, and O such that:

• The middle integer is always 0.

• Integers in column B are between 1 and 15 inclusive.

• Integers in column I are between 16 and 30 inclusive.

• Integers in column N are between 31 and 45 inclusive

(other than the middle integer being 0).

• Integers in column G are between 46 and 60 inclusive.

• Integers in column O are between 61 and 75 inclusive.

(a) What is the smallest possible sum of the numbers in a row on a BINGO card?

(b) Carrie’s BINGO card has a row and a diagonal each with the same sum. What is the smallest possible such sum? Show that there is a BINGO card with this sum and explain why there is no BINGO card with a smaller such sum.