中二 數學試卷 (F2 Maths Past Paper)

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Class: S. 2
Attempt ALL questions.
The total marks of this paper is 80.
SECTION A: MULTIPLE CHOICE (30 marks)
Mark your answers on the multiple choice answer sheet provided. Choose the BEST answer for each.
1. Which of the following is NOT an identity ?
FIRST TERM UNIFORM TEST 2021-2022
SECONDARY II MATHEMATICS
²-y²=(x+y)(x−y)
C. (x + y)² = x² + y² + 2xy
2. Simplify (a-b)²(a²-b²).
III. 3x + 2
3. If A, B and C are constants such that Ax² + C = (x+2)(x+B) + 6, then B =
4. Which of the following is/are factors(s) of 9x² + 12x + 4?
(x + y)² = -x² - y² - 2xy
D. (-x-y)² = x² + y² - 2xy
B. III only
C. I and II only
5. Which of the following expression(s) has/have a factor x - 3?
II. 2(x² - 6x + 9)
III. (x - 3+ y)²
B. I and II only
6. Which of the following cannot be factorized?
B. 8a²-18b²
C. 4ab+2b²
Date: 1-11-2021
Time: 1 hour
No. of pages: 3
C. II and III only
C. a² + 2ab + b²
D. 2b² - 2ab
D. II and III only
D. All of them.
D. b²a² + 2ab
Simon and Jonathan share a sum of $ 18 000 in the ratio 3: 2. By how much is Simon's share
more than Jonathan's share?
C. $ 10 800
8. The scale of a map is 1 : 20 000. If two buildings are 3.8 cm apart on the map, then the actual
distance between the two buildings is
9. The price of wine of brand X is $ 150/L. If 4L of wine of brand X and 3L of brand Y are mixed so
that the cost of the mixed wine is $ 300/L, find the cost of wine of brand Y.
10. Which of the following cars has the lowest speed?
Car A: 50 km/h
Car C: 15 m/s
11. If a is 25% less than 250 and b is 25% greater than 250, then a : b =
13. Let a, b, c and d be non-zero numbers. If a
C. 0.76 km.
12. It is given that x is inversely proportional to y. When x = 4, y = 12. Find the value of y
when x = 6.
15. Factorize -b²-4ab + 4b + 16a.
A. (b-4)(b + 4a)
C. (4-b)(b-4a)
Car B: 800 m/min
Car D: 0.015 km/s
14. Given that (a + b)² = 25 and (a - b)² = 15, find the value of a² + b².
D. $ 12 000
C. I and III only
, which of the following must be true?
(4+ b) (4a - b)
(4-b) (4a + b)
II and III only
SECTION B: CONVENTIONAL QUESTIONS (50 marks)
Write all answers on the single-lined papers provided. All working should be clearly shown.
1. Expand the following expressions by using Identities only.
(a) (2a − 3b)²
(b) (-5x + 7y)(7y + 5x)
(c) [(a + 2b) - c] [(a + 2b) + c]
2. Evaluate 999² without using a calculator.
3. Factorize the following expressions.
(a) 3a² - 2a² - 2a
(b) b(a − 2) + 3(2 − a)
(c) 4a² - 64
(d) 6c(5c-2d) - 6(2d-5c)²
4. (a) Factorize x² - 2xy + y².
(b) Hence, factorize (a + 3b)² -2(a +3b)(a + d) + (a + d)².
5. If a 15:27 8:5: b, find the values of a and b.
6. Find a b c in each of the following.
2:3 and b: c= 2:7
3:2 and c: b=3:4
9. If a b 5: 6, find
( = + b) = (a + 1).
END OF PAPER
7. David earns $8 400 working for 25 days while John earns $9 450 working for 30 days. It is given that
David and John work 8 hours and 7 hours each day respectively.
(a) Find the hourly wages of David and John respectively.
(b) The employer has $12 000. Do you think he has enough money to pay for their 20-day wages?
Explain your answer.
8. Four identical water pipes discharge water into a tank at the same time and fill up in 10 hours. It is
given that all pipes have the same rate of water flow. If the tank is to be filled up with water within 6
hours, how many more pipes are needed?
Section A(@ 2 marks)
FIRST TERM UNIFROM TEST 2021-2022
SECONDARY II MATHEMATICS
Marking Scheme
= (7y)² - (5x)²
= 49y² - 25x²
(2a - 3b)²
= (2a)² – 2(2a)(3b) + (3b)²
= 4a²-12ab +9b²
(-5x + 7y)(7y + 5x)
[(a + 2b) - c] [(a + 2b) +c]
= (a + 2b)²-c²
= (a)² + 2(a)(2b) + 4b²c²
= a² + 4ab + 4b²-c²
= (1000-1)²
= (1000)² - 2000 + 1
= 1 000 000 - 2000 + 1
3a³-2a² - 2a
= a(3a²-2a-2)
b(a − 2) + 3(2 − a)
=b(a-2)-3(a-2)
= (b − 3)(a - 2)
= (2a)²-(8)²
= (2a-8)(2a + 8)
= 4(a − 4)(a + 4)
= 4(a − 4)(a + 4)
6c(5c-2d)-6(2d - 5c)²
= 6(5c - 2d) [c (5c2d)]
= 6(5c-2d) (c- 5c + 2d)
= 6(5c-2d) (-4c+ 2d)
= 12(5c2d) (d-2c)
= (x - y)²
(a + 3b)² = 2(a +3b)(a + d) + (a + d)²
[(a + 3b)(a + d)]²
x² - 2xy + y²
a: 15:27 8:5:b
a = 24, b=9
a: b= 2:3 and b: c= 2:7
a:b: c = 4:6:21
= 3:2 and c: b=3:4
a:b=2:3 and b:c=4:3
a:b:c = 8:12:9
4x3:3x3 = 12:9
3a = 4b = 5c
a: b c = 20:15:12
20-day wages of David
20-day wages of John
5x 3:4x3= 15:12
Hourly wage of David = $8 400/(25 x 8 hr)
Hourly wage of John
= $9 450/ (30 x 7 hr)
Total salary expenses = $6 720 + $6 300
.. The employer does not have enough money to pay for their 20-day wages.
= $42 x 8 × 20
= $45 x 7 × 20
Let n be the number of pipes needed for filling up the water tank in 6 hours.
.. 3 more pipes are needed.
Let a 5k and b = 6k where k#0.
( ₁ + b ) : (a + 1 ) = ( ² + + 6k) : ( SK + + 2)
(+ / + 6k) : ( SK + 1 )
= { 1 + 6) = (₁ + ! )