Download Mathematics - IB/M/Jun23/8300/3H - Exam Paper and more Cheat Sheet Performing arts in PDF only on Docsity!
jun2383003H01
IB/M/Jun23/E8 8300/3H
For Examiner’s Use Pages Mark 2 – 3 4 – 5 6 – 7 8 – 9 10 – 11 12 – 13 14 – 15 16 – 17 18 – 19 20 – 21 22 – 23 24 – 25
TOTAL
Wednesday 14 June 2023 Morning Time allowed: 1 hour 30 minutes
Materials
For this paper you must have:
- a calculator
- mathematical instruments
- the Formulae Sheet (enclosed).
Instructions
- Use black ink or black ball-point pen. Draw diagrams in pencil.
- Fill in the boxes at the top of this page.
- Answer all questions.
- You must answer the questions in the spaces provided. Do not write outside the box around each page or on blank pages.
- If you need extra space for your answer(s), use the lined pages at the end of this book. Write the question number against your answer(s).
- Do all rough work in this book. Cross through any work you do not want to be marked.
Information
- The marks for questions are shown in brackets.
- The maximum mark for this paper is 80.
- You may ask for more answer paper, graph paper and tracing paper. These must be tagged securely to this answer book.
Advice
In all calculations, show clearly how you work out your answer.
GCSE
MATHEMATICS
Higher Tier Paper 3 Calculator
Please write clearly in block capitals.
Centre number Candidate number
Surname
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Candidate signature I declare this is my own work.
H
Do not write outside the Answer all questions in the spaces provided. box
1 The line with equation y = 2 x + 7 intersects the y - axis at A.
Complete the coordinates of A. [1 mark]
Answer ( (^0) , )
2 Write down a fraction equivalent to 1. [1 mark]
Answer
3 Solve 5 x + 11 = 3 x + 19
[2 marks]
x =
Do not write outside the 6 Here is cuboid A. box
Cuboid B is made from two of cuboid A.
volume of A : volume of B = 1 : 2
Matthew says, “surface area of A : surface area of B must be 1 : 2 because B is made of 2 of A.”
Is Matthew correct? Tick one box.
Yes No Cannot tell
Give a reason for your answer. [2 marks]
Turn over ►
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7 (a) Complete the table of values for y = x^2 + 2 x box
[2 marks]
x –^3 –^2 –^1 0
y^3 –^1
7 (b) Draw the graph of^ y^ =^ x^2 +^2 x^ for values of^ x^ from^ – 3 to 1
[2 marks]
Turn over for the next question
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Do not write outside the 9 The pie chart shows information about people at a fair during three days. box
There were 132 more people on Friday than on Thursday.
Work out the number of people on Saturday. [3 marks]
Answer
Turn over for the next question
Not drawn accurately
Do not write outside the
10 Use trigonometry to work out the value of x. box
[3 marks]
x = cm
Not drawn accurately
Do not write outside the 12 Here is a biased spinner. box
12 (a) Ali, Ben and Cary want to know the probability of spinning red on the biased spinner.
They each spin it and count how many times it lands on red and divide by the total number of spins.
Ali says I spun red the most times
Ben says I spun the spinner the most times
Cary says My relative frequency of red is 0.
Who had the best estimate for the probability of spinning red? Give a reason for your answer. [1 mark]
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Do not write outside the 12 (b) Dev spins the spinner 80 times. box
He says, “My relative frequency of red is 0.185”
Give a reason why his relative frequency must be wrong. [1 mark]
12 (c) Elena spins the spinner 125 times.
The relative frequency of red is 0.
Work out how many times the spinner landed on green. [2 marks]
Answer
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Do not write outside the 14 Kiran paid Income Tax and National Insurance on her annual salary. box
Kiran paid £5186 Income Tax.
How much National Insurance did she pay? [4 marks]
Answer £
Income Tax 0% of the first £12 570 of her annual salary 20% of the rest of her annual salary
National Insurance 0% of the first £9880 of her annual salary 13.25% of the rest of her annual salary
Do not write outside the 15 180 runners started a marathon. box
Some of the runners did not complete it.
15 (a) The histogram represents the times of the runners who did complete the marathon.
How many runners did not complete the marathon? [3 marks]
Answer
Do not write outside the 16 box
In this right-angled triangle,
a = 16 cm
a : c = 4 : 5
Work out the area of the triangle. [4 marks]
Answer cm^2
Not drawn accurately
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Do not write outside the box 17 Solve
x + − x
[4 marks]
x =
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Do not write outside the 19 Two integers have a difference of 6 box
The integers are multiplied together. 9 is then added.
Prove algebraically that the result is always a square number. [3 marks]
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Do not write outside the box
20 (a) Sunil thinks that E and D are linked by the equation E =
D
The graph shows the values of D and E for 2 ⩽ D ⩽ 6
Choose one point on the graph and state if Sunil’s equation is correct for that point. [1 mark]
