Tonbridge School Paper 1

IndependentBoys

17 questions

Original PDFWorked solutions in progress

Questions

1. 1
  The bar chart shows the number of pupils in the four year $7$ classes at a certain school.
  The classes are 7A, 7B, 7C and 7D. The darker Boys bars show 14, 12, 7 and 5 respectively; the lighter Girls bars show 12, 8, 7 and 4. The vertical Frequency scale runs from 0 to 15.
  1.a
  How many girls in class $\text{7D}$ ?
  1.b
  How many boys in total in all four classes?
  1.c
  What is the ratio of boys to girls in class $\text{7B}$ ? Give your answer in its simplest form.
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2. 2
  Four friends are shopping in their local supermarket.
  2.a
  Anton buys a chocolate bar for $\rtqMathsSymbolPound 0.84$ and a can of drink for $\rtqMathsSymbolPound 0.78$ .
  
  How much do they cost in total?
  2.b
  Boris buys a tube of suncream that costs $\rtqMathsSymbolPound 8.62$ .
  
  How much change does he receive from a $\rtqMathsSymbolPound 10$ note?
  2.c
  Bottles of vintage lemonade cost $\rtqMathsSymbolPound 1.37$ . Charles buys $5$ of these.
  
  What is the total cost?
  2.d
  Danny buys six doughnuts which cost a total of $\rtqMathsSymbolPound 2.76$ .
  
  How much does each doughnut cost?
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3. 3
  Calculate:
  3.a
  $4 + 5 \times 3 - 2$
  3.b
  $3 \times 2^2$
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4. 4
  From the list of numbers:
  
  $5, \rtqMathsListSeparator 6, \rtqMathsListSeparator 8, \rtqMathsListSeparator 23, \rtqMathsListSeparator 27, \rtqMathsListSeparator 45, \rtqMathsListSeparator 72$
  
  (You may use each number more than once or not at all).
  4.a
  A factor of $12$
  4.b
  A multiple of $15$
  4.c
  A prime number bigger than $10$
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5. 5
  5.a
  Write $0.2$ as a fraction in its lowest terms.
  5.b
  Write these numbers in order from the smallest to the largest:
  
  $0.3, \rtqMathsListSeparator \dfrac{8} {25}, \rtqMathsListSeparator 33\%, \rtqMathsListSeparator \dfrac {1} {3}$
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6. 6
  A packet of sweets contains $15$ red, $25$ blue and $10$ green. A larger packet of sweets has the colours in the same ratio and contains $22$ green.
  
  How many blue are there in the larger packet?
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7. 7
  The number of goals scored by a Tonbridge hockey team in their four matches last season were:
  
  $4, \rtqMathsListSeparator 6, \rtqMathsListSeparator 1, \rtqMathsListSeparator 6$
  7.a
  Find the mean number of goals scored.
  7.b
  Find the median number of goals scored.
  7.c
  What is the range of the number of goals scored?
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8. 8
  If $a = 3$ , $b = 5$ and $c = -2$ , find the value of:
  8.a
  $ab^2$
  8.b
  $(bc)^2$
  8.c
  $\dfrac{a+b}{c}$
  8.d
  $\dfrac{2b-c} {a}$
  8.e
  $a - \dfrac{b} {c}$
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9. 9
  Calculate, giving your answers as fractions or mixed numbers:
  9.a
  $\dfrac{1} {4} + \dfrac{1} {3}$
  9.b
  $3\dfrac{1} {4}-1\dfrac{2} {5}$
  9.c
  $2\dfrac{1} {2}\times1\dfrac{3} {5}$
  9.d
  $\dfrac{4} {5}\div\dfrac{3} {10}$
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10. 10
  Simplify:
  10.a
  $7a - 4a + 2a - a$
  10.b
  $3b \times b^2$
  10.c
  $\dfrac{4c^2}{8}$
  10.d
  $\dfrac{3d+3d}{4}$
  10.e
  $3 - 2(e - 1)$
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11. 11
  Write down the next two terms of the following sequences:
  11.a
  $2, \rtqMathsListSeparator 4, \rtqMathsListSeparator 7, \rtqMathsListSeparator 11, \rtqMathsListSeparator \rtqMathsSequenceEllipsis \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  11.b
  $\dfrac {2} {3}, \rtqMathsListSeparator 2, \rtqMathsListSeparator 6, \rtqMathsListSeparator 18, \rtqMathsListSeparator \rtqMathsSequenceEllipsis \rtqMathsListSeparator \rtqMathsSequenceEllipsis$
  11.c
  A sequence follows the rule: Treble and add one.
  
  Explain why if the first term is $-\dfrac{2} {9}$ the second term is $\dfrac{1} {3}$ .
  11.d
  Find the fourth term.
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12. 12
  12.a
  A tennis racket costs $\rtqMathsSymbolPound 85$ originally. In a sale it is reduced by $15\%$ .
  
  What is the sale price?
  12.b
  I score $42$ out of $48$ on a test.
  
  What percentage is that?
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13. 13
  In the diagram below the straight lines $ABG$ and $DEF$ are parallel. Lines $CB$ and $EG$ are also parallel.
  
  Find the angles marked $a$ , $b$ , $c$ in the diagram.
  
  The diagram is not drawn accurately.
  Horizontal lines ABG and DEF are parallel. Sloping lines CB and EG are parallel. A further segment DB crosses CB at B. The marked angles are 50 degrees at D, a at E, b and c at B, and 28 degrees at G.
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14. 14
  Solve the equations (showing clear working):
  14.a
  $3𝑥 - 4 = 20$
  14.b
  $2 - 𝑥 = 3(1 - 𝑥)$
  14.c
  $\dfrac {𝑥} {3} =\dfrac {𝑥-4} {2}$
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15. 15
  Draw:
  15.a
  A quadrilateral with no line of symmetry but order two rotational symmetry.
  15.b
  A trapezium with a line of symmetry.
  15.c
  A rhombus with the two diagonals having lengths $6 \rtqMathsUnit{cm}$ and $4 \rtqMathsUnit{cm}$ .
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16. 16
  Using some or all of the digits $1,3,5,7,0$ make:
  
  (each digit may only occur once so the three digit number $113$ is not allowed but $507$ is).
  16.a
  A three digit even number.
  16.b
  The smallest three digit multiple of $5$ .
  16.c
  The largest possible multiple of $3$ (this does not have to be a three digit number and may have more digits).
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17. 17
  Find the total area of the shaded regions.
  
  The diagram is not drawn accurately.
  The rectangle is 12 cm wide and 8.3 cm high. A left triangle with top span 3.784 cm and a right triangle with top span 2.216 cm are shaded.
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