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

## Questions from the 2023 Mathematics Specimen Paper 1

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

## Question 1: Algebra

## Question 2: Numbers (LCM and HCF)

## Question 3: Numbers (Estimation and standard form)

## Question 4: Algebra – Expand and simplify

## Question 5: Statistics (Pie Chart)

(b) The pie chart only gives us information about the proportion of adults in each age group. The number of adults in any age group, or total number of adults are not given. Hence, it is not possible to calculate the number of adults overs 60 years old.

## Question 6: Algebra (Quadratic Functions)

(a) Part a involve completing the square for a quadratic function. Alternatively, you could expand the “complete- the- square” form, and compare coefficient to find n.

(b) The square of any number must be at least 0. For (x-6)^{2} to be minimum, x = 6. (x-6)^{2} -19 is a minimum when x = 6.

## Question 7: Geometry (Construction of lines)

## Question 8: Algebra

## Question 9: Properties of Circles

⦟BDC = 180^{o} – 124 =56^{o}

⦟ADB =⦟ABD = 37^{o} ( angles in an isos triangle)

⦟ADC = ⦟ADB + ⦟BDC =56^{o} + 37^{o} = 93^{o}

⦟ABC= ⦟ABD + ⦟DBC =37^{o} + 50^{o} = 87^{o}

Since ⦟ABC +⦟ADB = 180^{o}, ⦟ABC and ⦟ADB are opposite angles in a cyclic quadrilateral, A, B, C and D lie on the circumference of a circle, and it is possible to draw a circle passing through them.

## Question 10: Ratio

In this question, student can use a non- algebra or an algebra method to solve this question on ratio.

## Question 11: Numbers (Mean)

(a) 20 x 78 = 1560 kg

(b) Total weight of males = 12 x 84 = 1008 kg

Total weight of females = 1560 – 1008 = 552 kg

Mean weight of females = 552 / 8 = 69 kg

## Question 12: Algebra

## Question 13: Algebra

## Question 14: Coordinate Geometry

## Question 15: Algebra

a(i) 9x^{12}

(ii) 8x^{6}

(b)

## Question 16: Congruent Triangles

## Question 17: Algebra (Factorize)

(a) 9wx + y – 3x -3wy

= 9wx – 3wy – 3x + y

= 3w(3x-y) – (3x-y)

= (3w-1)(3x-y)

(b) 5x^{4} – 80y^{4}

= 5( x^{4} – 16y^{4})

= 5( x^{2} – 4y^{2})( x^{2} + 4y^{2})

= 5( x + 2y)( x – 2y)( x^{2} + 4y^{2})

## Question 18: Matrices

(a)

(b)

(c)

## Question 19: Geometry – Angles of a polygon

## Question 20: Properties of circles

## Question 21: Area and Length of sectors

(a) perimeter of sector = 8.2(2.2) + 8.2 + 8.2 = 34.44 cm

(b) πr(8.2) = ½(8.2)^{2}(2.2)

r= 2.87078 = 2.87 cm (3 s.f.)

## Question 22: Set notation and Venn Diagrams

a(i) A = {17, 19, 23}

(ii) B = { 20, 25}

**ε** = {16, 17, 18, 19, 20, 21, 22, 23, 24, 25}

Hence, (A U B)’ ={16, 18, 21, 22, 24}

b(i) The correct statement is:

(ii) (a) 10 (b) 3

## Question 23: Trigonometry

## Question 24: Statistic

(a)(i) 26/50 = 13/25

(ii) 20- 22 cm

(iii) [4(17) + 21(19) + 20(21) + 5(23) + 1(25)]/50 = 20.54 cm

(b) 1. Median and mode for males occur at the same headspan rage of 22 – 24 cm. For female, they occur at different headspan range. For females, the median headspan occurs at the 20- 22 cm range, while the mode occurs in the 18- 20 cm range.

2. The mean headspan of males are larger than the mean headspan of females.

## Question 25: Similar triangles and figures

(a) x/7.5 = (10-2) / 10

x = 7.5(8/10) = 6 cm

(b) Volume of glass block = (2/10)^{3} [1/3 x 7.5 x 7.5 x 10] = 1.5 cm^{3}

mass = 1.5 x 2.6 = 3.9 g

## Question 26: Number patterns

(a) 4n + 6

(b) 4n + 6 = 264

n = 64.5

Since n should be an interger as it is the term number of a sequence, hence 264 is not a term of this sequence.

(c) 2n^{2} + 8n = 384

2n^{2} + 8n – 384 = 0

n^{2} + 4n – 192 = 0

(n +16)( n – 12) = 0

n = 12 or -16 (reject -16, since n is positive)

Hence, n = 12

## Worked Solutions for 2023 Mathematics Specimen Paper:

2023 Specimen Paper for Mathematics Paper 1

2023 Specimen Paper for Mathematics Paper 2