Here’s the worked solutions for the 2022 H2 A Level Mathematics Paper 1. Click on the question number to go to the question directly.
Worked solutions for 2022 H2 A Level Mathematics Paper 1
Question 1
Given :
iz + 2w = -1 —- (1)
(2-i)z + iw = 6 —- (2)
Find z and w in a + bi form where a and b are real numbers.
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 1. This is a complex number and system of equation question.](https://emilylearning.com/wp-content/uploads/2023/03/image-1.png)
Question 2
This is a question on Maclaurin Series.
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 2a. This is a Maclaurin Series question.](https://emilylearning.com/wp-content/uploads/2023/03/image-2-1024x490.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 2b. This is a Maclaurin Series question.](https://emilylearning.com/wp-content/uploads/2023/03/image-3-1024x376.png)
Question 3
This question is on application of differentiation to tangents and normals.
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 3a. This is a question on application of differentiation to normals and tangents, as well as parametric equations.](https://emilylearning.com/wp-content/uploads/2023/03/image-4.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 3b. This is a question on application of differentiation to normals and tangents, as well as parametric equations.](https://emilylearning.com/wp-content/uploads/2023/03/image-5.png)
Question 4
This question tests students on manipulating Trigonometric identities, and also on integration.
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 4. This question is on manipulation of trigonometric identities, and integration.](https://emilylearning.com/wp-content/uploads/2023/03/image-6.png)
Question 5
This question tests students on their application of differentiation. In addition, concepts from O Level Additional Mathematics topics on discriminant (from quadratic function chapter) is also tested.
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 5a. This question is on tangents and normals, as well as additional mathematics topics on discriminant.](https://emilylearning.com/wp-content/uploads/2023/03/image-7.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 5b. This question is on tangents and normals, as well as additional mathematics topics on discriminant.](https://emilylearning.com/wp-content/uploads/2023/03/image-8.png)
Question 6
Question 6 is on functions and transformation of graphs.
(a)
Students are expected to write a series of transformation to transform y = 1/x to y = (ax+k)/(x-a). Remember to use the recommended transformation order for this question.
![](https://emilylearning.com/wp-content/uploads/2023/06/image.png)
Hence, the required transformation are:
- translate the graph y = f(x) a units in the positive x- direction.
- scale parallel to the y axis by a factor of a² + k
- translate the graph by a units in the positive y- direction
(b)
Let y = f(x)
![](https://emilylearning.com/wp-content/uploads/2023/06/image-1.png)
Range of f = domain of f⁻¹ = ℝ \ a
![](https://emilylearning.com/wp-content/uploads/2023/06/image-2.png)
(c )
Since f(x) = f⁻¹(x),
f²(x) = f f⁻¹(x) = x, x ∈ ℝ, x ≠a
(d)
f²⁰²³(1) = f(1) = (a+k)/(1-a)
Question 7
Question 7 is on differentiation and integration (including their application)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 7a. This question is on differentiation and finding the turning point from differentiation.](https://emilylearning.com/wp-content/uploads/2023/06/image-3.png)
(b)
![](https://emilylearning.com/wp-content/uploads/2023/06/image-4.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 7b. This question is on integration, using integration by parts. Students are required to find the area under the graph by integration.](https://emilylearning.com/wp-content/uploads/2023/06/image-5.png)
Question 8
Question 8 is on integration and its application.
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 8a. This question is on integration.](https://emilylearning.com/wp-content/uploads/2023/06/image-6.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 8b. This question is on integration.](https://emilylearning.com/wp-content/uploads/2023/06/image-7.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 8b. This question is on integration.](https://emilylearning.com/wp-content/uploads/2023/06/image-8.png)
Question 9
Question 9 is on arithmetic and geometric progression.
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 8b. This question is on arithmetic progression.](https://emilylearning.com/wp-content/uploads/2023/06/image-10.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 8b. This question is on geometric progression, with trigonometric manipulation.](https://emilylearning.com/wp-content/uploads/2023/06/image-11.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 8b. This question is on geometric progression.](https://emilylearning.com/wp-content/uploads/2023/06/image-12.png)
Question 10
Question 10 is on application of differentiation, discriminant, curve sketching and inequalities.
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 10. This question is on curve sketching.](https://emilylearning.com/wp-content/uploads/2023/06/image-13.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 10. This question is on curve sketching.](https://emilylearning.com/wp-content/uploads/2023/06/image-14.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 10. This question is on curve sketching.](https://emilylearning.com/wp-content/uploads/2023/06/image-15.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 10. This question is on curve sketching.](https://emilylearning.com/wp-content/uploads/2023/06/image-18-1024x539.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 10. This question is on curve sketching.](https://emilylearning.com/wp-content/uploads/2023/06/image-20.png)
Question 11
This question is on vectors.
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 11. This question is on vectors.](https://emilylearning.com/wp-content/uploads/2023/06/image-31.png)
![](https://emilylearning.com/wp-content/uploads/2023/06/image-32.png)
(b)
Part b involves finding the cartesian equation of plane, given 3 position vectors:
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 11. This question is on vectors.](https://emilylearning.com/wp-content/uploads/2023/06/image-33.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 11. This question is on vectors.](https://emilylearning.com/wp-content/uploads/2023/06/image-34.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 11. This question is on vectors.](https://emilylearning.com/wp-content/uploads/2023/06/image-35-1024x568.png)
Question 12
This question is on differential equations.
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 12. This question is on differential equations.](https://emilylearning.com/wp-content/uploads/2023/06/image-21.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 12. This question is on differential equations.](https://emilylearning.com/wp-content/uploads/2023/06/image-22.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 12. This question is on differential equations.](https://emilylearning.com/wp-content/uploads/2023/06/image-23.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 12. This question is on differential equations.](https://emilylearning.com/wp-content/uploads/2023/06/image-27.png)
![](https://emilylearning.com/wp-content/uploads/2023/06/image-28.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 12. This question is on differential equations.](https://emilylearning.com/wp-content/uploads/2023/06/image-29.png)
![Solutions to 2022 H2 A Level Mathematics Paper 1 Question 12. This question is on differential equations.](https://emilylearning.com/wp-content/uploads/2023/06/image-30.png)
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