Maths: Full Practice Paper (Additional, Level 3, Set 3)
This is the third full practice paper for Additional Mathematics (Level 3), the further 13+ Common Entrance paper sat only by candidates entered for it, giving another 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 before starting, since Additional Mathematics problems frequently combine two skills, such as a quadratic equation set inside a worded context.
- Keep your trigonometry, Pythagoras' theorem, proportion, standard form and quadratic factorising secure, since these topics form the bulk of every Additional Mathematics paper.
- Write out full algebraic steps for every question, since method marks are given for correct working even if the final answer is wrong.
- State the constant of proportionality explicitly in any direct or inverse proportion question, rather than scaling between values directly.
- Carry full accuracy through each stage of a calculation and round only the final answer to the accuracy asked for.
- Substitute a solution back into the original equation to check it before writing your final answer.
- Prioritise higher-mark questions near the end of the paper, since these are worth spending more time on than an early, low-mark question.
Worked example
A right-angled triangle has a hypotenuse of 26 cm and one shorter side of 10 cm. Work out the length of the other shorter side.
- Use Pythagoras' theorem: since the hypotenuse is known, the missing shorter side is found by subtracting the squares: b^2 = c^2 - a^2.
- Substitute the known values: b^2 = 26^2 - 10^2.
- Calculate: 676 - 100 = 576.
- Take the square root: sqrt(576) = 24.
- So the other shorter side is 24 cm.
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 7 cm and 24 cm. Work out the length of the hypotenuse.Show answer
Answer: 25 cm (7^2 + 24^2 = 625, sqrt(625) = 25)
Q2y is directly proportional to x^2. When x = 3, y = 45. Work out y when x = 5.Show answer
Answer: 125 (the constant is 45 / 9 = 5, so y = 5 x 25 = 125)
Q3Write 0.000078 in standard form.Show answer
Answer: 7.8 x 10^-5
Q4Solve x^2 + 4x - 21 = 0.Show answer
Answer: x = 3 or x = -7 (factorises to (x - 3)(x + 7) = 0)
Q5In a right-angled triangle, the angle at A is 50 degrees and the hypotenuse is 14 cm. Work out the length of the side opposite angle A, to 1 decimal place.Show answer
Answer: 10.7 cm (opposite = 14 x sin(50) = 10.7246, which rounds to 10.7)
Q6p is inversely proportional to q^2. When q = 2, p = 18. Work out p when q = 3.Show answer
Answer: 8 (the constant is 18 x 4 = 72, so p = 72 / 9 = 8)
Exam-style questions
Written in the style of a 13+ Common Entrance exam paper, with a full mark scheme.
Solve the equation x^2 - 7x + 12 = 0.
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The time T (in minutes) taken to fill a tank is inversely proportional to the number of identical pumps n used. When n = 3, T = 20. (a) Find T when n = 5. (b) Find n when T = 12.
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A right-angled triangle has a hypotenuse of 15 cm and one angle of 42 degrees. (a) Find the length of the side opposite the 42 degree angle, to 1 decimal place. (b) Find the length of the side adjacent to the 42 degree angle, to 1 decimal place. (c) State which trigonometric ratio would use these two shorter sides to check the answer.
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Free printable worksheet
Want more practice on paper? Download the maths: full practice paper (additional, level 3, set 3) 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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