Math League 2021 Past Papers.
Part I: Multiple choice questions.
1.There is a triangle abc, where a=60°, bc=8cm, ac=10cm, find the magnitude of b and c.
a. ∠b=60°，∠c=60°
b. ∠b=45°，∠c=75°
c. ∠b=30°，∠c=90°
d. ∠b=60°，∠c=30°
2.The length of a rectangle is 4cm more than the width, and the circumference is 48cm.
a.It is 16cm long and 12cm wide
b.Length 14cm, width 10cm
c.Length 18cm, width 14cm
d.Length 20cm, width 16cm
3.Calculation: 2 3+3 4=?
a. 5/6
b. 5/7
c. 3/7
d. 14.In an isosceles triangle, the length of the base edge is 12 cm, and the length of the leg is 14 cm.
a. 84cm²
b. 48cm²
c. 72cm²
d. 96cm²
5.If the area of a square is 36cm, what is its circumference?
a. 24cm
b. 18cm
c. 12cm
d. 30cm
6.The diameter of a circle is 14cm, find the circumference of the circle.
a. 44cm
b. 28cm
c. 22cm
d. 38cm
Part 2: Answering questions.
1.Solve the following equation: 2x-5=11.
Solution: First convert the equation to 2x=16, then get x=8.
2.The length of a cuboid is 5 cm, the width is 3 cm, and the height is 4 cm, find its volume and surface area.
Solution: The volume of the cuboid is length, width and height = 5 3 4 = 60cm, and the surface area is 2 (length and width + width and height + length and height) = 2 (5 3 + 3 4 + 5 4) = 94cm.
3.In a circular garden, the radius is 8m, find the area and perimeter of this garden.
Solution: The area of the garden is r =314×8×8=200.96m and the circumference is 2 r=2 314×8=50.24m。
4.Solving a system of equations:
2x+3y=11
x-y=5 solution: first convert the second equation to x=5+y, then substitute the first equation to get 2(5+y)+3y=11, simplify to get y=1, and then substitute x=5+y to get x=6.
5.In a planar Cartesian coordinate system, ABCD is a parallelogram with coordinates of A and C (-3,4) and (5,-1), respectively.
Solution: First, find the coordinate representation of the vector ac, get ac=(5-(-3),-1-4)=(8,-5), and then find the coordinate representation of ab, and get ab=(-3-(-3),4-4)=(0,0), because the vector ac and the vector ab are parallel, so the area of the parallelogram abcd is equal to the cross product of ac and ab, that is, 8 5=40.