高中数学百科知识竞赛题目简单版

Easy

1. (easy) For the scientific notation of 0.00000281, which of the following is correct?

Answer : (b)

856

5

1081.2)(1081.2)(1081.2)(1081.2)(---⨯⨯⨯⨯d c b a

2. (easy) Find the asymptotes of the curve: 231+-=

x y answer: x=3, y=2.

3.(easy) Differentiate with respect to x

(a) 354-+=x x P (b) 2

34x V π=

Answer:3'45x P += 3'38x V π-= (c) )6)(7(-+=x x y (d) )2(2x x y -=

Answer:12'+=x y 23

'251x x y -= 4.(easy) The tangent to the curve 4ax y = at the point (1,b) is parallel to the line x+2y=100, find the value of a and b. Answer: 8

1-==b a 5.( Beginning with the equation x y =, write the new equation after the following transformations have been applied.

(a) (easy) Move 6 units to the right. Answer:6-=x y 6.(easy )Solve the equation 31tan -=x 02≤≤-x π

Sol: 6

7,6ππ--=x 7.(Easy)Determine the exact value of 0cos150 Answer:32

- 8.(Easy)State the natural domain of the function 2142x y x +=

-. Answer:1

2

x ≠ 9.(Easy)What is the gradient of the line that is perpendicular to 6250.x y +-= Answer:13

10.(Easy)How many combinations of 3 shirts to take on a holiday can be made from the 10 shirts available?

Answer:104210C =

11.(Easy)What is the coefficient of the term 22x y in the expansion of

()42x y +? Answer:24

12.(easy) The points (-2,5), (3,k) and (5,12) are collinear. Find the value(s) of k

Answer: K=10

13.(easy) Solve the following equations:

81312=+t 125

152=+t Answer: t=2.5 t=-5

04.02551=⋅-t t 0338312=-⋅++x x Answer: t=0 x=-1

14.(easy) A sequence is defined by the rule n n h h 321-=+ where n=1, 2, 3…for 1h =k. Given that k is a constant, find k if 5984-=h Answer:368

=k

15. (easy) A curve has equation )2)(1(22x x y -+=, show that 2')(cx b ax y += stating the values of a, b and c.

Answer: a=2, b=1, c=-2