Maths: Full Practice Paper (Additional, Level 3, Set 2)
This is the second full practice paper for Additional Mathematics (Level 3), the further 13+ Common Entrance paper sat only by candidates entered for it, giving a complete timed paper of algebra, trigonometry, proportion and standard form questions beyond the Core syllabus.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read every question fully before starting, since Additional Mathematics questions often combine two topics, such as Pythagoras' theorem inside a proportion problem.
- Revise right-angled trigonometry (SOHCAHTOA), Pythagoras' theorem, direct and inverse proportion, standard form and factorising quadratics before attempting the paper, since these appear repeatedly.
- Show full algebraic working for every step, since method marks are awarded for correct working even when a final answer is wrong.
- For proportion problems, always state the constant of proportionality explicitly, rather than trying to scale directly between two given values.
- Keep full accuracy through a multi-step calculation and round only the final answer, to the degree of accuracy the question asks for.
- Spend time in proportion to the marks available, so a 5 or 6 mark question near the end gets more time than an early 2 mark one.
- Check any quadratic solution by substituting it back into the original equation before moving on.
Worked example
A ramp has a horizontal length of 8 m and rises at an angle of 15 degrees to the horizontal. Work out the vertical height the ramp rises, giving your answer to 1 decimal place.
- Label the triangle: the horizontal length (8 m) is adjacent to the 15 degree angle, and the height needed is opposite.
- Since opposite and adjacent are involved, use tangent: tan(15) = height / 8.
- Rearrange and substitute: height = 8 x tan(15).
- Evaluate: 8 x 0.2679 = 2.1436.
- Round to 1 decimal place. Final answer: 2.1 m.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A right-angled triangle has shorter sides of 5 cm and 12 cm. Work out the length of the hypotenuse.Show answer
Answer: 13 cm (5^2 + 12^2 = 169, sqrt(169) = 13)
Q2y is directly proportional to x. When x = 6, y = 15. Work out y when x = 10.Show answer
Answer: 25 (the multiplier is 15 / 6 = 2.5, so y = 2.5 x 10 = 25)
Q3Write 3.6 x 10^-3 as an ordinary number.Show answer
Answer: 0.0036
Q4Solve x^2 - 5x + 6 = 0.Show answer
Answer: x = 2 or x = 3 (factorises to (x - 2)(x - 3) = 0)
Q5In a right-angled triangle, the angle at A is 32 degrees and the adjacent side is 9 cm. Work out the length of the hypotenuse, to 1 decimal place.Show answer
Answer: 10.6 cm (hypotenuse = 9 / cos(32) = 10.6126, which rounds to 10.6)
Q6p is inversely proportional to q. When q = 3, p = 20. Work out p when q = 12.Show answer
Answer: 5 (the constant is 3 x 20 = 60, so p = 60 / 12 = 5)
Exam-style questions
Written in the style of a 13+ Common Entrance exam paper, with a full mark scheme.
Solve the equation x^2 + 2x - 15 = 0.
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The height h (in metres) of a cone-shaped tent of fixed volume is inversely proportional to the square of its base radius r. When r = 2, h = 6. (a) Find h when r = 4. (b) State what happens to h if r is tripled.
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A right-angled triangle has a hypotenuse of 20 cm and one angle of 35 degrees. (a) Find the length of the side opposite the 35 degree angle, to 1 decimal place. (b) Find the length of the side adjacent to the 35 degree angle, to 1 decimal place.
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Free printable worksheet
Want more practice on paper? Download the maths: full practice paper (additional, level 3, set 2) worksheet pack - 9 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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