National 5 Maths 2023 Paper 1

Answer explanation

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Solve, algebraically, the system of equations: 2x + 3y = 8 5x + 2y = -2.

• x = 2, y = 1

• x = -2, y = 4

• x = 1, y = 2

• x = -1, y = 3

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• 3

• 2

• -3

• -2

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• 3

• -3

• 2

• -2

Answer explanation

P is the point (0, c).

Find the value of c.

• 11

• -11

• 2

• -2

Answer explanation

• 2 Real and distinct roots.

• 2 Real and equal roots.

• No Real Roots

Answer explanation

In triangle ABC:

AC = 5 metres

BC = 6 metres

cos C = 1/5

Calculate the length of AB.

• AB = 7 metres
• AB = 5 metres
• AB = 6 metres
• AB = 8 metres

Answer explanation

A business recorded the salaries of a sample of its employees and the length of time they have worked for the business. The scattergraph shows the relationship between their salary, P pounds, and the length of time, T years, they have worked. A line of the best fit has been drawn.

Find the equation of the line of best fit in terms of P and T.

Give the equation in its simplest form.

• P = 1500T + 12500

• P = 150T + 300

• P = -200T + 500

• P = 200T + 500

Answer explanation

Use your equation from part (a) to estimate the salary of an employee who has worked for the business for 8 years.

• £10,000

• £24,500

• £25,000

• £23,500

Answer explanation