DURATION: 2 hours INSTRUCTIONS TO CANDIDATES Answer all questions. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks in this paper is 80. The use of approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For �, use either your calculator value or 3.142, unless the question requires the answer in terms of �. (A list of mathematical formulae is given on the last page of the solutions booklet.) O-LEVEL ADDITIONAL MATHEMATICS MOCK EXAMINATION 1 PAPER 1 Name Class Date 80
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DURATION: 2 hours
INSTRUCTIONSTOCANDIDATES
Answer all questions.
The number of marks is given in brackets [ ] at the end of each question or part question.The total number of marks in this paper is 80.
The use of approved scientific calculator is expected, where appropriate.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For �, use either your calculator value or 3.142, unless the question requires the answer in terms of �.
(A list of mathematical formulae is given on the last page of the solutions booklet.)
O-LEVELadditiOnaL MatHEMatiCS
MOCK EXaMinatiOn 1PaPEr 1
Name Class Date
80
01 MExam 1_OL Add Math MExam.ind1 1 8/1/2016 10:26:15 AM
1 (a) Are the points A(–130, – 127), B(2, 5), C(7, 10) and D(100, 97) collinear? [3] (b) Prove that the points A(0, 3), B(4, 0), C(1, –4) and D(–3, –1) are the vertices of
a square. [4]
� Solve the following equations. (i) 2x + 5 √
__ x – 3 = 0 [3]
(ii) 2(lg x)2 + lg x5 – 3 = 0 [3] (iii) 2e2x + 5ex – 3 = 0 [3]
01 MExam 1_OL Add Math MExam.ind2 2 8/1/2016 10:26:15 AM
DURATION: 2 hours 30 minutes
INSTRUCTIONSTOCANDIDATES
Answer all questions.
The number of marks is given in brackets [ ] at the end of each question or part question.The total number of marks in this paper is 100.
The use of approved scientific calculator is expected, where appropriate.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For �, use either your calculator value or 3.142, unless the question requires the answer in terms of �.
(A list of mathematical formulae is given on the last page of the solutions booklet.)
O-LEVELadditiOnaL MatHEMatiCS
MOCK EXaMinatiOn 1PaPEr �
Name Class Date
100
01 MExam 1_OL Add Math MExam.ind9 9 8/1/2016 10:26:16 AM
1 Find the equation of the circle if A(–3, –4), B(–3, 6) and C (8, 6) are on the circumference of the circle. [5]
� Sketch the graph of y = –2 sin 2x – 1 for –� < x < �. [5]
01 MExam 1_OL Add Math MExam.ind10 10 8/1/2016 10:26:16 AM
DURATION: 2 hours
INSTRUCTIONSTOCANDIDATES
Answer all questions.
The number of marks is given in brackets [ ] at the end of each question or part question.The total number of marks in this paper is 80.
The use of approved scientific calculator is expected, where appropriate.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For �, use either your calculator value or 3.142, unless the question requires the answer in terms of �.
(A list of mathematical formulae is given on the last page of the solutions booklet.)
Name Class Date
O-LEVELadditiOnaL MatHEMatiCS
MOCK EXaMinatiOn 2PaPEr 1
80
02 MExam 2_OL Add Math MExam.ind1 1 8/1/2016 10:26:04 AM
1 The equation of a curve is y = 1 + x _____ 1 – x . Find the values of d2y
___ dx2 when the rate at which y
is changing is twice the rate at which x is changing. [5]
2 Evaluate ∫ (ex + 1)2
_______ ex – 1 dx. [4]
02 MExam 2_OL Add Math MExam.ind2 2 8/1/2016 10:26:04 AM
Name Class Date
DURATION: 2 hours 30 minutes
INSTRUCTIONSTOCANDIDATES
Answer all questions.
The number of marks is given in brackets [ ] at the end of each question or part question.The total number of marks in this paper is 100.
The use of approved scientific calculator is expected, where appropriate.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For �, use either your calculator value or 3.142, unless the question requires the answer in terms of �.
(A list of mathematical formulae is given on the last page of the solutions booklet.)
O-LEVELadditiOnaL MatHEMatiCS
MOCK EXaMinatiOn 2PaPEr 2
100
02 MExam 2_OL Add Math MExam.ind9 9 8/1/2016 10:26:05 AM
2 (a) Without using a graph, solve the equation ||5x – 5| – 5| = 10. [4] (b) solve the inequality 6 – x – x2 < 0. [3]
02 MExam 2_OL Add Math MExam.ind10 10 8/1/2016 10:26:05 AM
DURATION: 2 hours
INSTRUCTIONSTOCANDIDATES
Answer all questions.
The number of marks is given in brackets [ ] at the end of each question or part question.The total number of marks in this paper is 80.
The use of approved scientific calculator is expected, where appropriate.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For �, use either your calculator value or 3.142, unless the question requires the answer in terms of �.
(A list of mathematical formulae is given on the last page of the solutions booklet.)
Name Class Date
O-LEVELadditiOnaL MatHEMatiCS
MOCK EXaMinatiOn 3PaPEr 1
80
03 MExam 3_OL Add Math MExam.ind1 1 8/1/2016 10:25:52 AM
1 (i) solve the simultaneous inequalities. [4] (x – 1)2 36 | x – 6 | < 5 (ii) Sketch the graphs of y = (x – 1)2 and y = |x – 6| on the same diagram and label
03 MExam 3_OL Add Math MExam.ind2 2 8/1/2016 10:25:52 AM
Name Class Date
DURATION: 2 hours 30 minutes
INSTRUCTIONSTOCANDIDATES
Answer all questions.
The number of marks is given in brackets [ ] at the end of each question or part question.The total number of marks in this paper is 100.
The use of approved scientific calculator is expected, where appropriate.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For �, use either your calculator value or 3.142, unless the question requires the answer in terms of �.
(A list of mathematical formulae is given on the last page of the solutions booklet.)
O-LEVELadditiOnaL MatHEMatiCS
MOCK EXaMinatiOn 3PaPEr �
100
03 MExam 3_OL Add Math MExam.ind7 7 8/1/2016 10:25:52 AM
03 MExam 3_OL Add Math MExam.ind8 8 8/1/2016 10:25:53 AM
Name Class Date
DURATION: 2 hours
INSTRUCTIONSTOCANDIDATES
Answer all questions.
The number of marks is given in brackets [ ] at the end of each question or part question.The total number of marks in this paper is 80.
The use of approved scientific calculator is expected, where appropriate.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For �, use either your calculator value or 3.142, unless the question requires the answer in terms of �.
(A list of mathematical formulae is given on the last page of the solutions booklet.)
O-LEVELadditiOnaL MatHEMatiCS
MOCK EXaMinatiOn 4PaPEr 1
80
04 MExam 4_OL Add Math MExam.ind1 1 8/1/2016 10:25:26 AM
1 (i) Find the value of m for which the coefficient of x3 in the expansion of (1 + x)5 + (3 + mx)4 + (2 – x)3 is 105. [4] (ii) What is the coefficient of x4 in the expansion? [2]
� Prove that cos A – sin A ___________ sin A + cos A = tan 2A – sec 2A. [4]
04 MExam 4_OL Add Math MExam.ind2 2 8/1/2016 10:25:26 AM
Name Class Date
DURATION: 2 hours 30 minutes
INSTRUCTIONSTOCANDIDATES
Answer all questions.
The number of marks is given in brackets [ ] at the end of each question or part question.The total number of marks in this paper is 100.
The use of approved scientific calculator is expected, where appropriate.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For �, use either your calculator value or 3.142, unless the question requires the answer in terms of �.
(A list of mathematical formulae is given on the last page of the solutions booklet.)
O-LEVELadditiOnaL MatHEMatiCS
MOCK EXaMinatiOn 4PaPEr �
100
04 MExam 4_OL Add Math MExam.ind9 9 8/1/2016 10:25:27 AM
04 MExam 4_OL Add Math MExam.ind10 10 8/1/2016 10:25:27 AM
Name Class Date
DURATION: 2 hours
INSTRUCTIONSTOCANDIDATES
Answer all questions.
The number of marks is given in brackets [ ] at the end of each question or part question.The total number of marks in this paper is 80.
The use of approved scientific calculator is expected, where appropriate.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For �, use either your calculator value or 3.142, unless the question requires the answer in terms of �.
(A list of mathematical formulae is given on the last page of the solutions booklet.)
O-LEVELadditiOnaL MatHEMatiCS
MOCK EXaMinatiOn 5PaPEr 1
80
05 MExam 5_OL Add Math MExam.ind1 1 8/1/2016 10:25:15 AM
� (a) Express sin 8A in terms of sin A. [4] (b) Express cos 4A in terms of cos A. [4]
05 MExam 5_OL Add Math MExam.ind2 2 8/1/2016 10:25:15 AM
Name Class Date
DURATION: 2 hours 30 minutes
INSTRUCTIONSTOCANDIDATES
Answer all questions.
The number of marks is given in brackets [ ] at the end of each question or part question.The total number of marks in this paper is 100.
The use of approved scientific calculator is expected, where appropriate.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For �, use either your calculator value or 3.142, unless the question requires the answer in terms of �.
(A list of mathematical formulae is given on the last page of the solutions booklet.)
O-LEVELadditiOnaL MatHEMatiCS
MOCK EXaMinatiOn 5PaPEr �
100
05 MExam 5_OL Add Math MExam.ind9 9 8/1/2016 10:25:16 AM
y – 5 = x – 2 y = x + 3 When x = –130, y = –130 + 3 = –127 Points A, B and C are collinear. When x = 100, y = 100 + 3 = 103 ≠97 Points A,B,CandDarenotcollinear.
(b) Length of AB = √______________
(0 – 4)2 + (3 – 0)2 = 5 Length of BC = √
_______________ (4 – 1)2 + (0 + 4)2
= 5 Length of CD = √
________________ (1 + 3)2 + (–4 + 1)2
= 5 Length of DA = √
________________ (–3 – 0)2 + (–1 – 3)2
= 5 Since all the sides are equal in length, ABCD is either
a rhombus or a square. gradient of AB × gradient of BC
4 (i) Let f(x) = x4 + x3 – 13x2 – x + 12 When x = 1, f(1) = 1 + 1 – 13 – 1 + 12 = 0 When x = –1, f(–1) = 1 – 1 – 13 + 1 + 12 = 0 (x + 1)(x – 1) or x2 – 1 is a factor of f(x). By inspection, x4 + x3 – 13x2 – x + 12 = (x2 – 1)(x2 + x – 12)
–x2
–12x2 _____ –13x2
(x2 – 1)(x2 + x – 12) = 0 (x – 1)(x + 1)(x + 4)(x – 3) = 0 x=–4,–1,1,3 (ii) tan4 x + tan3 x – 13tan2 x – tan x+ 12 = 0 From (i), (tan x – 1)(tan x + 1)(tan x + 4)(tan x – 3) = 0 When tan x = –4, x=180º–75.96º,360º–75.96º ≈104.0º,284.0º When tan x = –1, x=180º–45º,360º–45º =135º,315º When tan x = 1, x=45º,180º+45º =45º,225º When tan x = 3, x=71.57º,180º+71.57º ≈71.6º,251.6º x=45º,71.6º,104.0º,135º,225º,251.6º,284.0º,315º