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Question 1 3A Error intervals
[2 marks]
Karim rounds a number, n, to 1 decimal place.
The result is 23.8
Complete the error interval for n.
Worked Solution & Answer
Half the unit of rounding: 0.1 ÷ 2 = 0.05 M1
Lower bound = 23.8 – 0.05 = 23.75
Upper bound = 23.8 + 0.05 = 23.85. A1
Answer: 23.75 ≤ n < 23.85
Question Paper (PDF) • Mark Scheme (PDF)
Question 2 3B Operations with fractions AQA Jun 2018 1F Q7
[2 marks]
A rectangular carpet measures 8 m by 6 m
Part of the carpet is covered by a square rug of length 2 m
8 m6 m2 mNot drawnaccurately
Show that 112 of the carpet is covered by the rug.
Worked Solution & Answer
Area of carpet = 8 × 6 = 48 m2 M1
Area of rug = 2 × 2 = 4 m2
Fraction of carpet covered = 448 = 112 C1
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 3D Writing and simplifying ratio AQA Nov 2020 1F Q5
[2 marks]
The diagram shows Shape A and Shape B on a centimetre grid.
Shape AShape B
Work out area of Shape A : area of Shape B
Give your answer in its simplest form.
Answer
Worked Solution & Answer
Area of Shape A = 4 × 6 = 24 cm2 M1
Area of Shape B = (4 × 2) + (3 × 4) = 8 + 12 = 20 cm2
Ratio = 24 : 20 = 6 : 5 A1
Shape AShape BArea A = 24 squares, Area B = 8 + 12 = 20 squares → 24 : 20 = 6 : 5
Answer: Answer 6 : 5
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Question 6 3E Ratio Eduqas Jun 2017 2F Q16
[2 marks]
Boris has made this pattern out of black and white squares:
4 black squares and 1 white square.
Boris has to add more squares to make a new pattern.
He has to use the smallest possible number of extra squares.
25 of the new pattern is black.
How many black squares and white squares will there be in the new pattern?
Worked Solution & Answer
To minimize extra squares, keep the 4 black squares already present M1
If 4 black squares represent 25 of the new pattern:
Total squares = 4 ÷ 25 = 4 × 52 = 10 squares
White squares = 10 - 4 = 6 white squares
(Extra white squares added = 6 - 1 = 5). A1
Answer: Black squares: 4, White squares: 6
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 3Q Straight line graphs IGCSE Jan 2020 1FR Q11
[3 marks]
On the grid, draw the graph of y = 3x + 2 for values of x from -2 to 4
yx−2−11234O−5−4−3−2−11234567891011121314
Worked Solution & Answer
Points: (–2, –4), (–1, –1), (0, 2), (1, 5), (2, 8), (3, 11), (4, 14) M2 A1
yx−2−11234O−5−4−3−2−11234567891011121314
Answer: Straight line drawn from (−2, −4) to (4, 14)
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Question 8 3G Percentages IGCSE Jun 2023 1FR Q4
[3 marks]
Here is a shape made of squares.
(a) Shade 45 of the shape. [1 mark]
(b) Write 0.7 as a percentage. [1 mark]
%
(c) Write these decimals in order of size.
Start with the smallest decimal.
0.49   0.459   0.4   0.049   0.14 [1 mark]
Worked Solution & Answer
(a)
(4/5) × 20 = 16 squares B1
Answer (a): 16 squares shaded
(b)
0.7 × 100 = 70% B1
Answer (b): 70 %
(c)
0.049, 0.140, 0.400, 0.459, 0.490 B1
Answer (c): 0.049, 0.14, 0.4, 0.459, 0.49
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 3H Percentage change AQA Nov 2020 3F Q29 / 3H Q14
[4 marks]
A rectangle has length 60 cm and width 40 cm
The length decreases by 15%
The width decreases by 10%
Not drawnaccurately60 cm40 cm
Is she correct?
You must show calculations to support your answer.
Sue says,
‘‘The perimeter decreases by 25% because 15% + 10% is 25%’’
Conclusion:
Worked Solution & Answer
Original perimeter = 2(60 + 40) = 200 cm M1
New length = 60 × 0.85 = 51 cm
New width = 40 × 0.90 = 36 cm M1
New perimeter = 2(51 + 36) = 174 cm
Decrease in perimeter = 200 - 174 = 26 cm M1
Percentage decrease = 26200 × 100% = 13%
She is incorrect because percentages cannot simply be added
the actual decrease is 13%. A1
Answer: Conclusion: No (perimeter decreases by 13%)
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Question 10 3C Estimation
[4 marks]
A cone has a volume of 98 cm3.
The radius of the cone is 5.13 cm.
Volume of cone =13πr2hrh
(a) Work out an estimate for the height of the cone. [3 marks]
cm
(b) Will your estimate be more than John's answer or less than John's answer?
Give reasons for your answer. [1 mark]
Worked Solution & Answer
(a)
Estimate V ≈ 100, r ≈ 5, π ≈ 3. 100 = (1/3) × 3 × 5² × h M1
⇒ 100 = 25h M1
⇒ h = 4 cm A1
Answer (a): 4 (accept 3.5 to 4.5) cm
(b)
Numerator increased and denominator decreased, so the estimate is larger C1
Answer (b): More than John's answer, because the numerator (98 -> 100) was rounded up and the denominator (π -> 3 and 5.13 -> 5) was rounded down.
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Score: 0 / 10 (0 / 26 marks)

Grade 3 Quizzes by Topic

24 Topics
3A - Error intervals3B - Operations with fractions
3C - Estimation3D - Writing and simplifying ratio
3E - Ratio3F - Proportion recipes
3G - Percentages3H - Percentage change
3J - Exchange rates3K - Conversions and units
3L - Scale drawings3M - Best buy questions
3N - Substitution3P - Solving linear equations
3Q - Straight line graphs3R - Area and circumference
3S - Rotations3T - Reflections
3U - Enlargements3V - Translations
3W - Mixed transformations3X - Area of compound shapes
3Y - Frequency trees3Z - Two way tables