Oundle School 2018 First Form

IndependentCo-ed

12 questions

Original PDFWorked solutions in progress

Questions

1. 1
  1.a
  John wanted to buy a boat.
  
  Boat $A$ cost $\rtqMathsSymbolPound 34{,}567{,}300$ . Boat $B$ cost $\rtqMathsSymbolPound 23{,}997{,}324$ .
  
  Calculate the difference between the two prices.
  1.b
  Polly's bill in a shop came to $\rtqMathsSymbolPound 374.67$ .
  
  Ellie's bill came to $\rtqMathsSymbolPound 263.21$ .
  
  What was the total they spent altogether?
  1.c
  A box contains $37$ chocolates. How many chocolates would there be in $26$ boxes?
  1.d
  Seven computers cost $\rtqMathsSymbolPound 882$ . Find the cost of one computer.
  1.e
  $650$ calculators need to be shipped in boxes. A maximum of $24$ calculators fit in each box.
  
  How many boxes are needed?
  Worked solution
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2. 2
  Work out the following, obeying the correct order of operations.
  2.a
  $-3 + 0$
  2.b
  $0 \times 4$
  2.c
  $4 - 3 \times 0$
  2.d
  $8 + 0 \div 4$
  2.e
  $-1 \times 4 + 3 \times 5$
  2.f
  $7 - 7 \div 7 + 7$
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3. 3
  Insert brackets to make the following statements correct:
  3.a
  $9 \times 5 \div 2 + 1 = 15$
  3.b
  $3 \times 7 - 6 \times 4 - 3 = 15$
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4. 4
  A pile of food can feed $12$ rabbits for $15 \rtqMathsUnit{days}$ .
  
  For how long could the same pile of food feed $20$ rabbits?
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5. 5
  An iPhone used to cost $\rtqMathsSymbolPound 500$ . Since Brexit the price has increased by $22\%$ .
  
  How much does it cost now?
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6. 6
  $a$ and $b$ are two different, positive whole numbers which make the following statement true:
  
  $3a + 2b = 48$
  
  Find two possible pairs of numbers which make the statement above true.
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7. 7
  The ratio of height to width on an old television screen is $3 \rtqMathsRatioSeparator 4$ .
  
  If the height of a television screen was $21 \rtqMathsUnit{cm}$ , find the perimeter of the screen.
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8. 8
  Write down the missing number in each part.
  8.a
  $23 \times \rtqMathsQuestionMarkPlaceholder = 690$
  8.b
  $2.3 \times \rtqMathsQuestionMarkPlaceholder = 6900$
  8.c
  $6900 \div \rtqMathsQuestionMarkPlaceholder = 23000$
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9. 9
  In this question you may use the grid below to help you answer the questions.
  
  A straight line passes through the points $(1, 2)$ and $(6, 12)$ .
  A blank 20-by-20 square grid has light lines at every unit and darker lines every five units. No points or lines are plotted.
  9.a
  9.a.i
  The point $(3, a)$ also lies on the line. Calculate the value of $a$ .
  9.a.ii
  The point $(7, b)$ also lies on the line. Calculate the value of $b$ .
  9.a.iii
  Give the coordinates of a new point which would form a right angled triangle with the original two points.
  9.b
  Another straight line goes through the point $(5, 1)$ and is parallel to the first line. Give the coordinates of any other point on this second line.
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10. 10
  When the fraction “one thirteenth” is written as a decimal, the first digit after the decimal point is $0$ , the second is $7$ , and the third is $6$ . If fifteen decimal places are calculated then we find:
  
  $\dfrac{1}{13} = 0.076 \rtqMathsDigitGroupSeparator 923 \rtqMathsDigitGroupSeparator 076 \rtqMathsDigitGroupSeparator 923 \rtqMathsDigitGroupSeparator 076 \rtqMathsSequenceEllipsis$
  
  You will notice that after six decimal places the digits begin to repeat, and in fact this pattern continues.
  10.a
  Write down the digits that are in the $4^\text{th}$ and $10^\text{th}$ decimal places.
  10.b
  What number would you find in the $15^\text{th}$ decimal place?
  10.c
  What number would you find in the $2{,}000^\text{th}$ decimal place?
  10.d
  How many $7$ s appear in the first $200$ decimal places?
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11. 11
  You have the numbers $-2, 7, 5$ and $-13$ available.
  
  Any of these numbers can be used in each part of the question.
  11.a
  What is the highest number that can be obtained by adding two of the above numbers?
  11.b
  What is the lowest number that can be obtained by adding two of the above numbers?
  11.c
  What is the highest number that can be obtained by subtracting two of the above numbers?
  11.d
  What is the lowest number that can be obtained by multiplying two of the above numbers?
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12. 12
  This question is about fractions.
  12.a
  Which fraction is bigger, four fifths or eight ninths?
  12.b
  Write down a fraction which is greater than two fifths, but less than four fifths.
  12.c
  Write down a fraction that is greater than three fifths, but less than four fifths.
  12.d
  Write down a fraction which is less than one seventh, but greater than zero.
  12.e
  Calculate half of one sixth.
  12.f
  What is the result if one is subtracted from three fifths?
  Worked solution
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Oundle School 2018 · First Form

Questions

Oundle School 2018 · First Form

Questions

Oundle School 2018 First Form

Oundle School 2018 First Form