2023 Mathematics Specimen Paper 2

Emily February 4, 2023 O Level

In this post, you’ll find the worked solutions for 2023 Mathematics specimen paper 1.

Questions from the 2023 Mathematics Specimen Paper 2

Click on the question below to go directly to the solutions of each question

Question 1: Algebra

(a) (i)

Question 1 of O Level Mathematics 2023 specimen paper 2 is on algebra.
Here's the worked solution for question 1a(i).

(a)(ii)

Question 1 of O Level Mathematics 2023 specimen paper 2 is on algebra, in particular, making another variable the subject of the algebraic expression.
Here's the worked solution for question 1a(ii).

(b)

Question 1 of O Level Mathematics 2023 specimen paper 2 is on solving simultaneous equations. This is a linear simultaneous equation, which can be solved by both elimination or substitution method.
Here's the worked solution for question 1b.

(c)

Question 1 of O Level Mathematics 2023 specimen paper 2 is on algebra, where students are required to combine the algebraic fractions into a single fraction. Here's the worked solution for question 1c.

(d)

Question 1 of O Level Mathematics 2023 specimen paper 2 is on algebra, where students are expected to solve an algebraic equation involving x.
Here's the worked solution for question 1d.

Question 2: Percentage

(a)

Question 2 of O Level Mathematics 2023 specimen paper 2 is on percentage. Here's the worked solution for question 2a.

(b)

Question 2 of O Level Mathematics 2023 specimen paper 2 is on percentage. Here's the worked solution for question 2b.

(c)

Question 2 of O Level Mathematics 2023 specimen paper 2 is on percentage. Here's the worked solution for question 2c.

(d)

Question 2 of O Level Mathematics 2023 specimen paper 2 is on percentage and currency exchange rate.
Here's the worked solution for question 2d.

Question 3: Graphs

Question 3 of O Level Mathematics 2023 specimen paper 2 is on sketching of graphs. In this diagram, you see a cubic graph, and a linear graph drawn. The point of intersection is the solution to the equation. Here's the worked solution for question 4b.

(a)

Question 3 of O Level Mathematics 2023 specimen paper 2 is on sketching of graphs. This is the table of x and corresponding y values used to plot the cubic graph. Here's the worked solution for question 4a.

(c)

The graph of y = x³/4 – 2x + 3 cuts the x- axis at only one point.

(d)(i)

Question 3 of O Level Mathematics 2023 specimen paper 2 is on sketching of graphs. Here's the worked solution for question 4c.

(ii)

Question 3 of O Level Mathematics 2023 specimen paper 2 is on sketching of quadratic graphs. This is the solution for the cubic equation, obtained graphically.

Question 4: Statistics and Probability

(i)

Question 4 of O Level Mathematics 2023 specimen paper 2 is on cumulative frequency curves, a statistic topic. This question involves median, mode, interquartile range and so on. Here's the worked solution for question 5a.

i(a) 94 g

i(b) 106g

i (c) Interquartile range = 114 – 88 = 26g

Question 4 of O Level Mathematics 2023 specimen paper 2 is on cumulative frequency curves, a statistic topic. This question involves median, mode, interquartile range and so on. Here's the worked solution for question 5b.

(ii) Out of the 200 apples:

164-32 = 132 of Variety B are between 80g to 120g.

180-24 = 156 of Variety A are between 80g to 120g.

Variety A because a larger proportion of variety A apples are within the desired range. 156 out of the 200 apples of Variety A are between 80g – 120 g while only 132 of the 200 apples of Variety B are between 80 to 120 g.

(b)(i)

Probability of 2 same varieties of apples:

= 9/16 x 8/15 + 7/16 x 6/ 15

=19/ 40

(ii)

Question 4 of O Level Mathematics 2023 specimen paper 2 is on probability. Here's the worked solution for question 4b(ii).

Question 5: Geometry (property of circles)

(a)

Question 5 of O Level Mathematics 2023 specimen paper 2 is on properties of circles and triangles. This are part of the topics from the section on geometry. This first part is on proving similar triangles.
Here's the worked solution for question 5a.

(b)(i)

Question 5 of O Level Mathematics 2023 specimen paper 2 is on properties of circles and triangles. This are part of the topics from the section on geometry. This part is on finding the relationship between areas of similar triangles. Here's the worked solution for question 5b(i)

(ii)

Question 5 of O Level Mathematics 2023 specimen paper 2 is on properties of circles and triangles. This are part of the topics from the section on geometry. This part is on angle properties of circles such as angle in a semicircle, angle at circumference, and so on. Here's the worked solution for question 5b(ii).

Question 6: Vectors

(a)

Question 6 of O Level Mathematics 2023 specimen paper 2 is on vectors. HEre is the worked solution of question 6 a(i).

(ii)

Question 6 of O Level Mathematics 2023 specimen paper 2 is on vectors. Here is the worked solution of question 6a(ii).

(b)

Question 6 of O Level Mathematics 2023 specimen paper 2 is on vectors. Here is the worked solution of question 6b.

Question 7: Trigonometry

(a)

Question 7 of O Level Mathematics 2023 specimen paper 2 is on trigonometry and bearings. Here's the worked solutions for question 7a.

Question 7 of O Level Mathematics 2023 specimen paper 2 is on trigonometry and bearings. Here's the worked solutions for question 7a.

(b)

Question 7 of O Level Mathematics 2023 specimen paper 2 is on trigonometry and bearings. Here's the worked solutions for question 7b.

Question 8: Word problems involving Quadratic Equations and Trigonometry

(a)

Question 8 of O Level Mathematics 2023 specimen paper 2 is on Word problems involving Quadratic Equations and Trigonometry. Here's the worked solution of question 8a.

(b)

Question 8 of O Level Mathematics 2023 specimen paper 2 is on Word problems involving Quadratic Equations and Trigonometry. Here's the worked solution of question 8b.

(c)

Question 8 of O Level Mathematics 2023 specimen paper 2 is on Word problems involving Quadratic Equations and Trigonometry. Here's the worked solution of question 8c.

Question 9: Data Analysis & Speed, Distance and Time

a(i)

Question 9 of O Level Mathematics 2023 specimen paper 2 is on Question 9: Data Analysis & Speed, Distance and Time. Here's the worked solution of question 9a (i).

(ii)

Question 9 of O Level Mathematics 2023 specimen paper 2 is on Question 9: Data Analysis & Speed, Distance and Time. Here's the worked solution of question 9a (ii).

(b)

No. Although both Zhao and Mei met their target for each week, the calories burnt by Zhao is not 50% more than that of Mei’s.

Working:

Question 9 of O Level Mathematics 2023 specimen paper 2 is on Question 9: Data Analysis & Speed, Distance and Time. Here's the worked solution of question 9b.

Worked Solutions for 2023 Mathematics Specimen Paper:

2023 Specimen Paper for Mathematics Paper 1

2023 Specimen Paper for Mathematics Paper 2

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