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。