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    Pick 'N' Mix Paper - Crossover Paper 3 - Solutions

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    skye.maclean2279

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    © All Rights Reserved
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    Pick 'N' Mix Paper - Crossover Paper 3 - Solutions

    Uploaded by

    skye.maclean2279
    17 views7 pages

    Original Title

    Pick-'n'-Mix-paper---Crossover-Paper-3---Solutions

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    17 views7 pages

    Pick 'N' Mix Paper - Crossover Paper 3 - Solutions

    Uploaded by

    skye.maclean2279

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 7

    Q Topic My Max

    Mark Marks
    1 Venn diagrams 5
    Calculator
    Non

    2 Standard form 5

    3 Pythagoras’ Theorem and Trigonometry 6

    4 Ratio 8
    Calculator

    5 Sequences and nth term 8

    6 Reverse percentages 3

    35

    Revision list: What I need to remember:


    Question 1

    a) 50 students were asked in a survey whether they use texts or social media.

    • 20 students said they only use texts


    • 8 students said they only use social media
    • 17 students said they use both texts and social media

    Put this information on the Venn diagram.

    𝟐𝟎 𝟏𝟕 𝟖 [𝟏]

    [1]
    b) How many of the students in the survey do not use texts or social media?

    𝟐𝟎 + 𝟏𝟕 + 𝟖 = 𝟒𝟓 [𝟏]

    𝟓𝟎 − 𝟒𝟓 = 𝟓 [𝟐]

    .........𝟓.........[𝟐]........
    [2]

    c) One of the students in the survey is chosen at random.

    What is the probability that this student uses texts?

    𝟐𝟎 + 𝟏𝟕 = 𝟑𝟕 [𝟏]
    𝟑𝟕
    ......... ...........[𝟐]..........
    𝟓𝟎
    [2]
    Question 2

    a) The table below shows the number of tonnes of corn produced in a year in five
    countries.

    Country Corn produced (tonnes)


    Mexico 2.65 × 107
    Ethiopia 6.50 × 107
    USA 3.71 × 108
    Brazil 9.45 × 107
    China 2.15 × 108

    Which country produced the most corn?

    .....................𝐔𝐒𝐀 [𝟏].......................
    [1]

    b) Write 2.65 × 107 as an ordinary number.

    ...............𝟐𝟔 𝟓𝟎𝟎 𝟎𝟎𝟎 [𝟏].................


    [1]

    c) How many more tonnes of corn did USA produce than Ethiopia?
    Give your answer in standard form.

    𝟑. 𝟕𝟏 × 𝟏𝟎𝟖 − 𝟔. 𝟓𝟎 × 𝟏𝟎𝟕 [𝟏]

    = 𝟑. 𝟕𝟏 × 𝟏𝟎𝟖 − 𝟎. 𝟔𝟓 × 𝟏𝟎𝟖 [𝟐] 𝒐𝒓 𝟑𝟕. 𝟏 × 𝟏𝟎𝟕 − 𝟔. 𝟓𝟎 × 𝟏𝟎𝟕


    𝒐𝒓 𝟑𝟎. 𝟔 × 𝟏𝟎𝟕 𝐨𝐫 𝟑𝟎𝟔 𝟎𝟎𝟎 𝟎𝟎𝟎 𝐨𝐞

    = 𝟑. 𝟎𝟔 × 𝟏𝟎𝟖 [𝟑]

    ............ 𝟑. 𝟎𝟔 × 𝟏𝟎𝟖 [𝟑]............ tonnes


    [3]
    Question 3

    a) A boy scout ties a rope from the top of a flag pole to the ground to secure it.
    The flag pole is 9 metres tall and he anchors it 5.5 metres away from the
    bottom of the flag pole. How long must the rope be to do this?

    𝑹𝒐𝒑𝒆𝟐 = 𝟗𝟐 + 𝟓. 𝟓𝟐 [𝟏] 𝒂𝒏𝒚 𝒄𝒐𝒓𝒓𝒆𝒄𝒕 𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒊𝒐𝒏


    𝒊𝒏𝒕𝒐 𝑷𝒚𝒕𝒉𝒂𝒈𝒐𝒓𝒂𝒔′ 𝑻𝒉𝒆𝒐𝒓𝒆𝒎

    𝑹𝒐𝒑𝒆 = √𝟗𝟐 + 𝟓. 𝟓𝟐 [𝟐 ]

    𝑹𝒐𝒑𝒆 = 𝟏𝟎. 𝟓 𝒎 [𝟑 ]

    ……𝟏𝟎. 𝟓……[𝟑]…m
    [3]

    b) Calculate the size of the angle marked x.


    Give your answer to 3 significant figures.

    𝑥0
    8.5𝑐𝑚

    7.1𝑐𝑚 Diagram NOT drawn accurately

    𝒔𝒊𝒏(𝒙) = 𝟕. 𝟏 ÷ 𝟖. 𝟓 [ 𝟏]

    𝒙 = 𝒔𝒊𝒏−𝟏 (𝟕. 𝟏 ÷ 𝟖. 𝟓) [ 𝟐]

    𝒙 = 𝟓𝟔. 𝟔𝟎 [ 𝟑]

    𝑥 = …… 𝟓𝟔. 𝟔……0
    [3]
    Question 4

    a) Write 8 mm to 12 cm as a ratio in its simplest form.

    𝟖 ∶ 𝟏𝟐𝟎 [𝟏]

    𝟏 ∶ 𝟏𝟓 [𝟐]
    .........𝟏 ∶ 𝟏𝟓 [𝟐]..........
    [2]

    b) Pat and Julie share some money in the ratio 2 : 5


    Julie gets £45. How much money did Pat get?

    𝑷∶𝑱
    𝟐∶𝟓
    [𝟏] 𝟒𝟓 ÷ 𝟓 = 𝟗
    𝟏𝟖 ∶ 𝟒𝟓

    £......... 𝟏𝟖 [𝟐]..............
    [2]

    c) Last year Kerry’s take home pay was £15 000


    She spent 40% of her take home pay on rent.
    She used the rest of her take home pay for living expenses, clothes and
    entertainment in the ratio 3 : 1 : 2
    How much did Kerry spend on entertainment last year?

    𝟒𝟎% 𝒐𝒇 £𝟏𝟓𝟎𝟎𝟎 = £𝟔𝟎𝟎𝟎


    £𝟏𝟓𝟎𝟎𝟎 − £𝟔𝟎𝟎𝟎 = £𝟗𝟎𝟎𝟎 [𝟏]

    𝑳 ∶ 𝑪 ∶ 𝑬
    𝟑 ∶ 𝟏 ∶ 𝟐
    [𝟏] 𝟑 + 𝟏 + 𝟐 = 𝟔
    [𝟏] 𝟗𝟎𝟎𝟎 ÷ 𝟔 = 𝟏𝟓𝟎𝟎
    𝟒𝟓𝟎𝟎 ∶ 𝟏𝟓𝟎𝟎 ∶ 𝟑𝟎𝟎𝟎

    £ ….......𝟑𝟎𝟎𝟎 [𝟒]............
    [4]
    Question 5

    a) The nth term of a sequence is given by 2n2 + 1.

    Write down the first three terms of this sequence.

    [𝟏] 𝒇𝒐𝒓 𝒕𝒘𝒐 𝒕𝒆𝒓𝒎𝒔 𝒄𝒐𝒓𝒓𝒆𝒄𝒕

    ...........𝟑............, .........𝟗.............., .........𝟏𝟗..............[𝟐]


    [2]

    b) Here are the first four terms of a different sequence.

    8 11 14 17

    i. Write an expression for the nth term of this sequence.

    [𝟏] 𝒇𝒐𝒓 𝟑𝒏 𝒔𝒆𝒆𝒏

    ...........𝟑𝒏 + 𝟓 [𝟐]..............
    [2]

    ii. Explain why 36 is not a term in this sequence.

    𝟑𝒏 + 𝟓 = 𝟑𝟔 [𝟏]𝒐𝒓 𝒇𝒐𝒓 𝟑𝟓 𝒂𝒏𝒅 𝟑𝟖 𝒔𝒆𝒆𝒏

    𝟑𝟏
    𝒏= 𝒘𝒉𝒊𝒄𝒉 𝒊𝒔 𝒏𝒐𝒕 𝒂𝒏 𝒊𝒏𝒕𝒆𝒈𝒆𝒓 [𝟐]
    𝟑
    [2]

    c) Here are the first four terms of a different sequence.

    2 5 10 17

    i. What is the next term of this sequence?

    ............... 𝟐𝟔 [𝟏].....................
    [1]

    ii. Explain how you can work out the next term of this sequence.

    [𝟏] 𝑽𝒂𝒍𝒊𝒅 𝒆𝒙𝒑𝒍𝒂𝒏𝒂𝒕𝒊𝒐𝒏


    𝑬. 𝒈. 𝒊𝒕 𝒈𝒐𝒆𝒔 𝒖𝒑 𝒃𝒚 𝒕𝒘𝒐 𝒎𝒐𝒓𝒆 𝒆𝒂𝒄𝒉 𝒕𝒊𝒎𝒆
    𝒐𝒓 𝒊𝒕 𝒊𝒔 𝒕𝒉𝒆 𝒔𝒒𝒖𝒂𝒓𝒆 𝒏𝒖𝒎𝒃𝒆𝒓𝒔 𝒂𝒅𝒅 𝒐𝒏𝒆

    [1]
    Question 6

    Bethenny buys a house.


    3 years later, the house is worth 4% less than she paid for it.
    The house is now worth £203520.
    What was the original price of the house?

    𝟗𝟔% = £𝟐𝟎𝟑𝟓𝟐𝟎 [𝟏]

    𝟏% = £𝟐𝟏𝟐𝟎 [𝟐] 𝒐𝒓 𝒂𝒏𝒚 𝒇𝒂𝒄𝒕𝒐𝒓 𝒐𝒇 𝟏𝟎𝟎%

    𝟏𝟎𝟎% = £𝟐𝟏𝟐𝟎𝟎𝟎 [𝟑]

    𝒐𝒓

    𝟐𝟎𝟑𝟓𝟐𝟎 ÷ 𝟎. 𝟗𝟔 [𝟐] [𝟏] 𝒇𝒐𝒓 𝟎. 𝟗𝟔 𝒔𝒆𝒆𝒏

    = £𝟐𝟏𝟐𝟎𝟎𝟎 [𝟑]
    £ ……𝟐𝟏𝟐𝟎𝟎𝟎……[𝟑]…
    [3]

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