高中数学百科知识竞赛中等难度

Medium

1.Find the 11th term of the geometric sequence that commences 1, 3, 3, ...

Answer : 243 2.Determine the gradient function :

223132x x x

-+ Answer: 3342632--++-x x x 3. Find the centre and radius of the circle with equation: x y y x 10622=++. Answer: centre (5, -3), radius : 34 4. Write down the domain and range of the function 2656y x x =+-+. Answer: domain: 3,x ≥or 2x ≤.

Range: 6.y ≥

5.Fourteen girls and seven boys are applying for five student council positions. Determine how many ways the council positions can be filled if at least four girls are selected.

Answer: 5

1471441C C C +=9009 6.What number could be added to each of the three numbers 3, 11 and 27 so that the resulting numbers form a geometric sequence?

Answer: 5

7.$4000 is invested into an account paying interest at 8%, compounded annually and $200 is withdraw from the account after each 12 months .

determine (nearest cent) the amount in the account at the end of ten years, after the $200 for the year has been withdrawn. Answer: $8635.69

8.Find the equation of the quadratic function that has exactly the same shape as that of 1232+-=x x y , has the same line of symmetry as 742+-=x x y and that cuts the y-axis at the point ()15,0

Sol: 3)2(32+-=x y

9.State the range of the function

21+=x y for the given domain:{}23:-<≤-∈x R x .

Sol: 1:-≤∈y R y

10.For the sequence -1,0,7,26,63,… determine the sixth term

Answer:124

11.Determine the equation of the function for the table below x

1 2 3 4 5 y

-60 -30 -20 -15 -12

Answer: x y 60-= 12.A card is randomly drawn from a normal pack. What is the probability that the card is a red or a two?

Answer: 13

7 13.In triangle ABC ?=60A , a=3.5, b=4 Find the size of B to the nearest degree.

Answer:??98,82

14.Determine whether the two circles with equations

()()93222=-+-y x and ()()15222=-++y x have two points in common, just one point in common or no point in common. Answer: no point in common