Maths: Full Practice Paper (Additional, Level 3, Set 4)
This is the fourth full practice paper for Additional Mathematics (Level 3), the further 13+ Common Entrance paper sat only by candidates entered for it, giving a further complete timed paper of algebra, trigonometry, proportion and standard form beyond the Core syllabus.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the whole question through before starting, since Additional Mathematics questions often disguise a Pythagoras, trigonometry or proportion question inside a worded context.
- Keep trigonometry (SOHCAHTOA), Pythagoras' theorem, direct and inverse proportion, standard form and quadratic factorising secure, since these recur across every Additional Mathematics paper.
- Write out every algebraic step in full, since method marks are given for correct working even when the final answer is wrong.
- In a proportion question, find and state the constant of proportionality explicitly before using it to answer the question.
- Carry full accuracy through a multi-step calculation, rounding only the final answer to the accuracy requested.
- Check a quadratic solution by substituting it back into the original equation before finalising your answer.
- Give the highest-mark questions, usually near the end of the paper, more time than an early, low-mark question.
Worked example
A flagpole casts a shadow of 12 m when the sun's rays make an angle of 38 degrees with the ground. Work out the height of the flagpole, giving your answer to 1 decimal place.
- Label the triangle: the shadow (12 m) is adjacent to the 38 degree angle, and the flagpole's height is opposite.
- Since opposite and adjacent are involved, use tangent: tan(38) = height / 12.
- Rearrange and substitute: height = 12 x tan(38).
- Evaluate: 12 x 0.7813 = 9.3756.
- Round to 1 decimal place. Final answer: 9.4 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 9 cm and 40 cm. Work out the length of the hypotenuse.Show answer
Answer: 41 cm (9^2 + 40^2 = 1681, sqrt(1681) = 41)
Q2y is directly proportional to x^2. When x = 4, y = 32. Work out y when x = 6.Show answer
Answer: 72 (the constant is 32 / 16 = 2, so y = 2 x 36 = 72)
Q3Write 5.4 x 10^4 as an ordinary number.Show answer
Answer: 54000
Q4Solve x^2 - 2x - 24 = 0.Show answer
Answer: x = 6 or x = -4 (factorises to (x - 6)(x + 4) = 0)
Q5In a right-angled triangle, the angle at A is 27 degrees and the opposite side is 6 cm. Work out the length of the hypotenuse, to 1 decimal place.Show answer
Answer: 13.2 cm (hypotenuse = 6 / sin(27) = 13.2161, which rounds to 13.2)
Q6p is inversely proportional to q. When q = 8, p = 9. Work out p when q = 6.Show answer
Answer: 12 (the constant is 8 x 9 = 72, so p = 72 / 6 = 12)
Exam-style questions
Written in the style of a 13+ Common Entrance exam paper, with a full mark scheme.
Solve the equation x^2 + x - 20 = 0.
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The number of days D needed to build a wall is inversely proportional to the number of identical workers n. When n = 4, D = 15. (a) Find D when n = 6. (b) Find n when D = 5.
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A right-angled triangle has a hypotenuse of 18 cm and one angle of 55 degrees. (a) Find the length of the side opposite the 55 degree angle, to 1 decimal place. (b) Find the length of the side adjacent to the 55 degree angle, to 1 decimal place. (c) Use your rounded answers to (a) and (b) to estimate tan(55 degrees), to 2 decimal places.
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Free printable worksheet
Want more practice on paper? Download the maths: full practice paper (additional, level 3, set 4) 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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