# 中二 數學試卷 (F2 Maths Past Paper)

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First Term Test (2020-2021) Form Two Mathematics

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## 中二數學試卷 PDF 下載

Date: Time allowed :
Section A-Multiple Choice Questions (2 marks each, 10 marks)
2p²pq+qr2pr+ 3q - 6p =
(2pq) (p - r + 3).
(2p+q) (p −r + 3).
C. (2p-q) (p - r - 3).
(2p+q) (p=r-3).
It is given that 3(Px − Q)(x + 2) = 6x² + 3x + R, find the value of R.
4. 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?
yx - xy = 54
If p³q = -4 and 3p - 2q = 6, then 20p6q³-30p²q² =
10x + y = 12
First Term Test (2020-2021)
Form Two Mathematics
10y + x) − (10x + y) = 54
{(10x + y) = (10y + x) = 54
(10y + x) − (10x + y) = 54
6x + y = 15 ... ... (1)
(4x5y = 27... ... (2)
(1) × 5+ (2),
(30x + 5y) + (4x - 5y) = 15 x 5 + 27
9a y³ + xy²2-7y²
= y² (y + x-7)
Sub x 3 into (1),
6(3) + y = 15
9b. 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))²]
= 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)
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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)
12 ( P²5-34) (-34-²²)
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
(8p2q3p - 3q)²
= (5p - 5q)²
= 25(p = q)²
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For identifying A and B
For (p5)² = p¹0
For (=)² ==
Can be absorbed.
Sub x 4p q and y=p+q
Qu Solutions
(2x + 11y = 57... ... (1)
3x - 5y = 21...... (2)
(1) x 3 (2) × 2,
6x +33y - 6x +10y = 57 x 3 - 21 x 2
Sub y 3 into (2),
3x - 5(3) = 21
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)
la-b= 3...... (2)
Sub a 7.5 into (2),
Let x and y be the number of \$2 coins and \$5 coins
Dennis has.
(2x + 5y = 49...... (1)
x - 2y = 2...... (2)
(1)-(2) × 2,
2x + 5y - 2x + 4y = 49 - 2x2
Sub y 5 into (2),
Therefore, the total number of coins Dennis his
= 5 + 12 = 17.
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For elimination/substitution
For substitution
For elimination/substitution
For substitution
Qu Solutions
Sub (5,3) into the equations.
( a(5) + b(3) = 19
(3a(5) (2b-1)(3) = 15
= { 5a + 3b = 19
Sa + 3b5a + 2b = 19-4
Sub b 3 into (1),
5a + 3(3) = 19
5a + 9 = 19
(5a + 3b = 19........ (1)
5a-2b4....... (2)
4x + 2y = 15
4x + 2y = 15
The solution is x = 4.5, y = -1.5.
For substituting the point
-x + 3y = -9
For simplifying the equations.
For elimination/substitution
Table: IM for any pair correct
1A for all correct
IM for a line plotted according to table
IA for a correct line.
1A for all (Include labelling)
17. By filling in ALL THE BOXES in the tables below, solve
4x + 2y = 15
Therefore, the solution is
2020 2021 First Form Test
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END OF PAPER
Form 2 Mathematics
(4x + 2y = 15
graphically.
-x + 3y = -9
Page 8 of 8
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 = -1
k = 5, a = 4
k = 5, a = -4
2020 2021 First Form Test
Section B-Short Questions (31 marks)
Determine, with explanation, whether (x+¹)(2x-1)=x²-1-x is an identity.
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Form 2 Mathematics
Section A Total
Page 2 of 8
7. Solve the simultaneous equations
Solve the simultaneous equations
2020 2021 First Form Test
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(2x - 5y = 42
(5x - 3y = 29
by the method of substitution.
= 3 by the method of elimination.
Form 2 Mathematics
Page 3 of 8
(a) Factorize y³ + xy² - 7y².
(b) Hence, factorize y² + xy²-7y²-y-x+7.
Factorize 50a³-18a(a - 2)2.
Expand 12 (²-3) (-32-²)
2020 2021 First Form Test
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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.
2020 2021 First Form Test
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Form 2 Mathematics
Page 5 of 8
Solve the simultaneous equations (2x+11y = 57
3x - 5y = 21
2020 2021 First Form Test
(b) Using the result of (a), solve the simultaneous equations 3(a + b)-5(a - b) = 21
(2(a + b) + 11(a - b) = 57 (3 marks)
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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.
16. 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.
2020 2021 First Form Test
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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
2020 2021 First Form Test
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END OF PAPER
Form 2 Mathematics
(4x + 2y = 15
graphically.
-x + 3y = -9
Page 8 of 8
Section A-Multiple Choice Questions
Section B & C-Short Questions & Long Questions
Qu Solutions
2x² - (1-x)
.. It is an identity.
First Term Test (2020-2021) Form Two Mathematics
Suggested Solution
(x + 1) (2x − 1)
2x² + x - 1
2x = 42 + 5y
Sub (3) into (2),
(2x - 5y = 42... ... (1)
3y = 29...... (2)
5(42+5y) - 6y = 58
210 + 25y6y = 58
Sub y = -8 into (3)
x = 1, y = -8
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For expanding