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175 students

ST. STEPHEN'S GIRLS' COLLEGE

Mid-Year Examination 2019-2020

Mathematics

Time Allowed: 1 hour 15 minutes

Question/Answer Paper

Please read the following instructions very carefully.

1. This paper consists of TWO sections, A and B.

2. Write your class, class number, name and division in the

spaces provided on this cover.

3. This paper carries 100 marks. Attempt ALL questions in

this paper. Write your answers in the spaces provided in

this Question/Answer Paper.

4. The diagrams in this paper are not necessarily drawn to

For Markers' Use Only

LHK, KAL, YLN, MLY

Form 2 Mathematics Mid-Year Exam 2019-20

In the process of designing the structure of a stadium, the relation among the time for clearing

the crowd (t minutes), the number of people in the stadium (N), the number of passages (n),

the width of each of the passages (w m) is considered, and the following formula is obtained.

It is known that at the end of a match, there are 7200 people leaving the stadium. If 10

passages, each of 6 m wide, are open for people to pass through, how long will it take to

clear all people?

Make n the subject of the formula.

We are going to open the 6m wide passages to clear a crowd of 12000 people in the

stadium after a count-down activity on New Year's Eve. At least how many passages

are required to clear the crowd in 15 minutes?

Form 2 Mathematics Mid-Year Exam 2019-20

28. There is some soda and the volume of the soda is measured as 50.0 L, correct to the nearest

0.5 L. The capacity of a cup is 250 mL, correct to the nearest 10 mL.

(a) Find the percentage error of measurement of the volume of the soda.

(b) Find the lower limit of the capacity of the cup.

Is there enough soda to fill up 210 cups? Explain your answer.

End of Paper

Form 2 Mathematics Mid-Year Exam 2019-20

Section A (51%)

All rough work should be done on the rough work paper provided, but will not be marked.

Round off 0.03499 to 3 significant figures.

How many significant figures are there in each of the

following numbers?

(b) 470 000 (correct to the nearest 100)

(a) The temperature is measured as 20 °C, correct to the

nearest °C. Find the maximum absolute error.

(b) The weight is measured as 2.5 kg, correct to the

nearest 0.1 kg. Find the relative error.

Find the value of the polynomial 2x³-x²y-3xy² +5

when x = -2 and y = 1.

Consider the polynomial 4x²y² - 2xy +9xyz³.

(a) What is the degree of the polynomial?

(b) Arrange the polynomial in descending powers of y.

Simplify (x² − 3x+5)−2(x² −2x+1).

Factorize 8 pq+4p-6q-3.

Expand (-ab- c)².

10. Determine if the following equations are identities. Circle 10.

the correct answer.

(a) (2x - 3)(2x + 3) = 4x² - 9

(b) x–4=5x − 4(x + 1)

Form 2 Mathematics Mid-Year Exam 2019-20

11. It is given that x² - Ax+3x-5=Bx² - 4x+C.

Find the values of A, B and C.

12. If A = P1+

and r = 2.5.

13. For a triangle with sides a, b and c, the area A is

A = √s (sa) (s - b) (sc), where s = (a + b + c).

If a=7, b=8 and c=9, find the value of A.

(Correct your answer to 3 significant figures.)

14. Simplify the following expressions.

find the value of P if A = 1320, n = 4 12.

15. Change the subject of each of the following formulae to

the letter in the square brackets.

(a) p=n+2(k − 3)

16. If P(a, -1) lies on the graph of the equation

=-1, find the value of a.

17. Solve the simultaneous equations

hotel was full and it received $99 600 yesterday, find the

number of adults having the buffet yesterday.

18. A hotel can serve 460 people for a lunch buffet. The price 18.

for an adult is $250 and that for a child is $140. If the

Subtotal: 127

Form 2 Mathematics Mid-Year Exam 2019-20

Section B (49%)

Complete the table so that the corresponding values of x and y satisfy the following

(b) Hence, draw the graph of the equation y=-2x-1 in the following rectangular

coordinate plane.

Form 2 Mathematics Mid-Year Exam 2019-20

20. There are some coins in a bag. The numbers of $1 coins, $2 coins and $5 coins are

(3x³ −4x+7), (2x² +5x−

²x² −3) and (x³ −2x²+x−1) respectively. Express the total value of

the coins in terms of x. (Arrange the answer in descending powers of x.)

21. Simplify the expression

Form 2 Mathematics Mid-Year Exam 2019-20

22. Determine if (5+2x)(5-2x)=20x-(2x-5)² is an identity.

23. If (2x+3y)(4x+Ay)=8x² +16xy+By², find the values of A and B.

Form 2 Mathematics Mid-Year Exam 2019-20

24. The figure shows a garden.

(b) When x = 2, find the area of the garden.

(a) Find the area of the garden in terms of x. (Arrange the answer in descending powers of x.)

Form 2 Mathematics Mid-Year Exam 2019-20

25. (a) Solve the simultaneous equations.

(b) Hence, or otherwise, solve the simultaneous equations

Form 2 Mathematics Mid-Year Exam 2019-20

26. Simplify the following expressions.

x³ - 2x²y 5x-10 y

2x+6y 4xy+12y²