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Additional Mathematics, Summaries of Mathematics

Mathematics

This is a additional Mathematics pamphlet

Typology: Summaries

2024/2025

Available from 04/12/2025

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Additional Mathematics/4030/1 2 0 2 4 Chinyama Kaumba J 0971887395
MINISTRY OF EDUCATION
SICHILI SECONDARY SCHOOL
MATHEMATICS DEPARTMENT
Grade 12 Aggregate Exam
Additional Mathematics 4030/1
Paper 1
Tuesday 29 OCTOBER 2024
Additional materials:
Answer Booklet
Silent Electronic Calculator (non programmable)
Time: 2 hours Marks: 80
Instructions to Candidates
1 Write your names on every page of the Answer Booklet provided.
2 There are twelve questions in this paper. Answer all questions.
3 Write your answers in the Answer Booklet provided.
4 If you use more than one Answer Booklet, fasten the Answer Booklets together.
5 Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the
case of angles in degrees, unless a different level of accuracy is specified in the question.
Information for candidates
1 The number of marks is shown in brackets [ ] at the end of each question or part question.
2 The use of a non programmable electronic calculator is expected, where appropriate.
3 You are reminded of the need for clear presentation in your answers.
4 Cell phones and other electronic devices are not allowed in the examination room.
5 Check the formulae overleaf.
JKC/2024 This question paper consists of 5 printed pages
pf3
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pf5

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Download Additional Mathematics and more Summaries Mathematics in PDF only on Docsity!

Page 1 of 5

Additional Mathematics/4030/1 2 0 2 4 Chinyama Kaumba J 0971887395

MINISTRY OF EDUCATION

SICHILI SECONDARY SCHOOL

MATHEMATICS DEPARTMENT

Grade 12 Aggregate Exam

Additional Mathematics 4030/

Paper 1

Tuesday 29 OCTOBER 2024

Additional materials:

Answer Booklet

Silent Electronic Calculator (non programmable)

Time: 2 hours Marks: 80

Instructions to Candidates

1 Write your names on every page of the Answer Booklet provided.

2 There are twelve questions in this paper. Answer all questions.

3 Write your answers in the Answer Booklet provided.

4 If you use more than one Answer Booklet, fasten the Answer Booklets together.

5 Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the

case of angles in degrees, unless a different level of accuracy is specified in the question.

Information for candidates

1 The number of marks is shown in brackets [ ] at the end of each question or part question.

2 The use of a non programmable electronic calculator is expected, where appropriate.

3 You are reminded of the need for clear presentation in your answers.

4 Cell phones and other electronic devices are not allowed in the examination room.

5 Check the formulae overleaf.

JKC/2024 This question paper consists of 5 printed pages

CHINYAMA K

AUMBA

J

MATHEMATICS FORMULAE

1 ALGEBRA

Quadratic Equation

For the equation 𝑎𝑥

2

−𝑏±√𝑏

2

− 4 𝑎𝑐

2 𝑎

𝑛

𝑛

𝑛− 1

𝑛− 2

2

𝑛−𝑟

𝑟

𝑛

where 𝑛 is a positive integer and (

𝑛!

(𝑛−𝑟)!𝑟!

2 TRIGONOMETRY

Identities

Sin

2

A + cos

2

A = 1

Sec

2

A = 1 + tan

2

A

Cosec

2

A = 1 + cot

2

A

Formula for ∆ ABC

𝑎

sin 𝐴

𝑏

sin 𝐵

𝑐

sin 𝐶

2

2

2

− 2 𝑏𝑐 cos 𝐴

𝑏𝑐 sin 𝐴

6 Prove the identity

𝟏

𝐬𝐞𝐜 𝛉+𝐭𝐚𝐧 𝛉

𝟏+𝐬𝐢𝐧 𝛉

𝐜𝐨𝐬 𝛉

≡ 𝟐 𝐬𝐞𝐜 𝛉. [4]

7 (a) Find the middle term in the expansion of (𝑥 −

1

𝑥

10

. [4]

(b) Expand

2

5

in ascending powers of 𝑎 up to the term containing 𝑎

2

. [5]

8 (a) Given that 𝑦 =

3

√ 2 𝑥

2

  • 5

, find an expression for

𝑑𝑦

𝑑𝑥

. [3]

(b) Given that 𝑦 =

𝑥− 2

2 𝑥+ 5

, where 𝑥 ≠ − 1. 5 , find the approximate change in 𝑦 as 𝑥 increases

from 2 to 2.35. [6]

9 Find all the angles between 0° and 360° which satisfy the equation

cos 𝑥

= 4 sin 𝑥. [5]

10 The position vector r of a point on a straight line is given by r = 2i + 3j + 𝜆(𝐢 − 4 𝐣) where

𝜆 is a constant.

(a) Find the position vector when 𝜆 = 5. [3]

(b) The line with vector equation r intersects the line joining points with position vectors

5 i + 3j and i – 2 j at a point P. Find the position vector of P. [7]

11 (a) Given that ∫

𝟑

𝒂

𝒙

𝟐

𝒃𝒙

𝟒

𝟓

𝟐

𝒙

, find the values of 𝑎 and 𝑏. [3]

(b) The diagram below shows part of the curve 𝑦 = 𝑥

2

intersecting the line 𝑦 = 𝑝𝑥 at

(0, 0) and A.

Find

(i) the coordinates A in terms of P, [3]

(ii) the value of 𝑝 for which the area of the shaded region is 36 𝑢𝑛𝑖𝑡𝑠

2

. [4]

A

𝟐

12 Solutions to this question by scale drawing will not be accepted.

In the diagram below, BPCR is a rhombus. P is (0, 6), C is ( 6 , 𝑡) and B is (2, 0). The lines

PR and BC bisect at Q, PR = 2BC and PR = 8 √

Find

(a) the value of 𝑡, [2]

(b) the coordinates of R, [3]

(c) the equation of PR, [3]

(d) the area of the rhombus. [2]

B

R

C (𝟔, 𝒕)

P(0, 6)

Q