中二 數學試卷 (F2 Maths Past Paper)

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Section A-Multiple Choice Questions (2 marks each, 10 marks)
Please put your answers in the boxes provided on P.2
1. It is given that 3(Px − Q)(x + 2) = 6x² + 3x + R, find the value of R.
2. 2p² - pq+qr - 2pr +3q - 6p
A. (2pq) (p - r + 3).
B. (2p+q) (p − r + 3).
C. (2pq) (p -r-3).
(2p+q) (p - r - 3).
If p³q = −4 and 3p – 2q = 6, then 20p6q³ — 30p7q² =
(x + y = 12
The sum of the units digit and the tens digit of a two-digit number is 12. If the two digits are interchanged,
the new number is greater than the original number by 54. Let x be the tens digit and y be the units digit
of the original number, which of the following pairs of simultaneous equations can be formed from the
information given above?
10x + y = 12
(10y + x) − (10x + y) = 54
First Term Test (2020-2021)
Form Two Mathematics
+ y) − (10y + x) = 54
(10y + x) − (10x + y) = 54
2020 2021 First Form Test
Form 2 Mathematics
Page 1 of 8
Qu | Solutions
6x + y = 15 ... ... (1)
(4x - 5y = 27.
(1) × 5+ (2),
(30x + 5y) + (4x - 5y) = 15 x 5+27
Sub x 3 into (1),
6(3) + y = 15
y³ + xy² - 7y²
= y² (y + x - 7)
y³ + xy² - 7y²-y-x+7
= y²(y + x-7) - (y + x −7)
= (y + x-7)(y² − 1)
= (y + x-7)(y + 1)(y − 1)
50a³ 18a(a - 2)²
= 2a[25a² — 9(a − 2)²]
= 2a [(5a)² – (3(a − 2))²¹]
= 2a(5a + 3(a − 2))(5a – 3(a − 2))
= 2a (5a + 3a − 6) (5a − 3a + 6)
= 2a(8a - 6) (2a + 6)
= 8a(4a − 3)(a + 3)
rewriting into two
For simplifying the equation.
For eliminating x/y
For 25a² = (5a)² or
9(a − 2)² = (3(a − 2))²
For(A²-B²) = (A + B)(A - B)
Qu | Solutions
12 (1/3²-34) (-34-²²)
= 12 [94² - D²
12a. (a - 2x)²
a² - 4ax + 4x²
12b. Let x=b2c
(a − 2b + 4c)²
= (a − 2(b − 2c))²
= (a − 2x)²
= a² - 4ax +4x²
a² − 4a(b − 2c) + 4(b − 2c)²
a²-4ab+8ac + 4(b² − 4bc + 4c²)
a²-4ab+8ac + 4b² − 16bc + 16c²
13a. 4x² - 12xy +9y²
= (2x − 3y)²
13b. Let x = 4pq and y=p+q
4(4p — q)² — 12(4p − q)(p + q) + 9(p + q)²
= 4x² - 12xy +9y²
= (2x - 3y)²
= [2(4p —
q) — 3(p+q)]²
= (8p - 2q - 3p - 3q)²
= (5p - 5q)²
= 25(p - q)²
For identifying A A and B
For (p5)² = p¹⁰
Can be absorbed.
Sub x 4pq and y=p+q
Qu | Solutions
(2x + 11y = 57... ... (1)
3x - 5y = 21... ... (2)
(1) × 3 − (2) × 2,
6x +33y - 6x +10y = 57 x 3 - 21 x 2
Sub y 3 into (2),
3x - 5(3) = 21
14b. Let x = a + b and y = a - b.
(2(a + b) + 11(a - b) = 57
( 3(a + b) — 5(a - b) = = 21
(2x + 11y = 57
3x - 5y = 21
From (a), we have x = 12 and y = 3.
(a + b = 12...... (1)
a-b= 3...... (2)
Sub a 7.5 into (2),
Let x and y be the number of $2 coins and $5 coins
Dennis has.
x - 2y = 2...... (2)
(2x + 5y = 49
(1)-(2) × 2,
2x + 5y - 2x + 4y = 49 - 2x2
Sub y 5 into (2),
x = 2(5) = 2
Therefore, the total number of coins Dennis his
= 5 + 12 = 17.
For elimination/substitution
For substitution
For elimination/substitution
For substitution
Qu Solutions
16. Sub (5,3) into the equations.
( a(5) + b(3) = 19
(3a(5) - (2b − 1)(3) = 15
5a + 3b5a + 2b = 19 – 4
Sub b 3 into (1),
5a + 3(3) = 19
5a + 9 = 19
5a + 3b = 19
5a + 3b = 19... ... (1)
5a 2b = 4...... (2)
4x + 2y = 15
4x + 2y = 15
The solution is x = 4.5, y = -1.5.
-x + 3y = −9
For substituting the point
For simplifying the equations
For elimination/substitution
-x + 3y = -9
Table: 1M for any pair correct
1A for all correct
1M for a line plotted according to table
1A for a correct line.
1A for all (Include labelling)
The graph of the equation 3x - 2y + k = 0 passes through the points (3,2) and (1, a). Find the
values of k and a.
k = -5, a = 1
k = 5, a = −4
k = -5, a = −1
Section B-Short Questions (31 marks)
6. Determine, with explanation, whether
(x+1)(2x-1)
Form 2 Mathematics
is an identity.
Section A Total
Page 2 of 8
(2x - 5y = 42
Solve the simultaneous equations 15x - 3y = 29 by the method of substitution.
8. Solve the simultaneous equations
= 3 by the method of elimination.
Form 2 Mathematics
Page 3 of 8
(a) Factorize y³ + xy² - 7y².
(b) Hence, factorize y³ + xy² − 7y² − y - x + 7.
10. Factorize 50a³ - 18a(a − 2)².
11. Expand 12 (²-3)(-³2-²²).
Form 2 Mathematics
Page 4 of 8
12. (a) Expand (a − 2x)².
(b) Using the result of (a), expand (a − 2b + 4c)².
Section C-Long Questions (29 marks)
13. (a) Factorize 4x² - 12xy +9y².
(b) Using the result of (a), factorize 4(4p — q)² – 12(4p − q)(p + q) + 9(p + q)².
Form 2 Mathematics
Page 5 of 8
Solve the simultaneous equations (2x + 11y = 57
3x - 5y = 21
(b) Using the result of (a), solve the simultaneous equations (2(a + b) + 11(a − b) = 57 . (3 marks)
3(a + b) 5(a − b) = 21
Form 2 Mathematics
Page 6 of 8
Dennis has some $2 coins and some $5 coins in his pocket. The total value of the coins is $49. If the
number of $2 coins is higher than 2 times the number of $5 coins by 2, find the total number of coins
Dennis has.
If the graphs of the equations ax + by = 19 and 3ax - (2b − 1)y = 15 intersect at (5,3), find the
values of a and b.
Form 2 Mathematics
Page 7 of 8
17. By filling in ALL THE BOXES in the tables below, solve
4x + 2y = 15
Therefore, the solution is
END OF PAPER
Form 2 Mathematics
4x + 2y = 15
-x + 3y = -9 graphically.
-x + 3y = -9
Page 8 of 8
Section A-Multiple Choice Questions
Section B & C-Short Questions & Long Questions
Qu Solutions
(x + 1) (2x − 1)
2x² + x - 1
2x = 42 + 5y
L.H.S. R. H. S.
.. It is an identity.
First Term Test (2020-2021) Form Two Mathematics
Suggested Solution
(2x - 5y = = 42 (1)
- 3y = 29. (2)
Sub (3) into (2),
5 (42 + 5y)
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x = 1, y = −8
5(42 + 5y) - 6y = 58
210 + 25y6y = 58
Sub y8 into (3)
1M + 1A For making x or y as subj.
For expanding
For adding brackets
(Can be absorbed)
For substitution