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Group 1 Result:

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1. (1 point) Select all Pythagorean triples (n is assumed to be a natural number greater than 1):

A. {2, 3, 4} B. {8, 15, 17} C. {3n, 4n, 5n} D. {2n, n 2 − 1, n 2 + 1}

2. (1 point) log 0.5 2 √

3

2 = A. − 4

3 B. − 3

4 C. 4

3 D. 3

4

3. (1 point) How many real solutions does the equation 31x 2 + x + 2020 = 0

have?

A. 0 B. 1 C. 2 D. infinitely many

(2)

4. (2 points) Consider the following diagram:

O is the centre of the circle. Find the size of the angle BCD.

(3)

5. (4 points) Consider the following figure:

Find the length of the line segment DB

(4)

6. (5 points) Solve the following equations:

(i) 3x 2 + 7x = 0

(ii) x 2 − 4x = 21

(iii) 3x 2 − 7x = 6

(iv) 2x 2 − 4x + 7 =

(v) 2 2x+1 + 5 · 2 x − 3 = 0

(5)

7. (2 points) Consider the following similar triangles:

If the total area of both triangles is 30 cm 2 , find the area of the larger

triangle.

(6)

8. (4 points) Consider the following pyramid ABCDE:

The base of the pyramid is a square of side length 8 cm. The height of the pyramid is 6 cm.

(a) Find the slant height x of the pyramid.

(b) Find the total surface area of the pyramid.

Cytaty

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