Highgate School Sample Paper B

IndependentCo-ed

4 questions

Original PDFWorked solutions in progress

Questions

1. 1
  Some animals are being sold at a pet shop.
  1.a
  Hamsters cost $\rtqMathsSymbolPound 7.50$ each and gerbils cost $\rtqMathsSymbolPound 3.20$ each. Javier buys $4$ hamsters and $3$ gerbils.
  
  How much did Javier spend in total?
  1.b
  Goldfish are kept in large tanks. Each tank can hold up to $13$ fish. There are $193$ goldfish in the shop.
  
  How many tanks are needed to hold all of these goldfish?
  1.c
  Chickens and chicks all have $2$ wings. There are $8$ chickens in the shop, and each of these $8$ chickens has $5$ chicks.
  
  How many wings are there in total?
  1.d
  $7$ cat bowls cost the same as $4$ dog leads. $3$ cat bowls cost $\rtqMathsSymbolPound 72$ .
  
  What does a dog lead cost?
  1.e
  The shop has a sale on stick insects: “buy $3$ stick insects and get a $4 ^\text{th}$ stick insect free”.
  
  Ahmed paid $\rtqMathsSymbolPound 17.85$ for $20$ insects. What is the cost of $1$ stick insect?
  Worked solution
  Being written
2. 2
  2.a
  In a charity fun run, one sixth of the runners were adults, and the rest were children. There were $120$ adults in the race.
  
  How many children were running the race?
  2.b
  Tickets to enter a fairground cost $\rtqMathsSymbolPound 7.00$ for adults and $\rtqMathsSymbolPound 3.00$ for children. Once inside the fairground, each ride costs $\rtqMathsSymbolPound 3.00$ for adults and $\rtqMathsSymbolPound 1.50$ for children.
  
  Joe and his $2$ grandchildren, Amy and Peter, go to the fairground. Joe goes on $2$ rides, and Peter goes on four times as many rides as Amy.
  
  In total they spend $\rtqMathsSymbolPound 34.00$ between them. How many rides did Peter go on?
  2.c
  A watch shop has a $2$ day winter sale. On the first day, two thirds of all the watches are sold. On the second day, a quarter of the remaining watches are sold.
  
  The shop sold $72$ watches on the first day. How many watches were sold on the second day?
  2.d
  A rectangle is split into two smaller rectangles, labelled $A$ and $B$ . Rectangle $A$ is shaded. One seventh of the original rectangle is shaded.
  A long rectangle is divided vertically into two parts. The left one-seventh is labelled A and shaded. The remaining six-sevenths is labelled B and unshaded. The partition between them is dashed.
  With scissors, I cut off and remove a third of rectangle $B$ . What fraction of the remaining shape is now shaded?
  Worked solution
  Being written
3. 3
  3.a
  A bag contains $600$ sweets. Sweets are either red, blue or green. There are $8$ more red sweets than blue sweets. $30\%$ of the sweets are blue. How many sweets are green?
  3.b
  In a sale, the price of a toy car is reduced by $40\%$ .
  
  I buy the toy car for $\rtqMathsSymbolPound 42$ . What did it cost before the sale?
  3.c
  Fido the Dog ate $16$ pork sausages and $24$ lamb sausages.
  
  What percentage of Fido's sausages were lamb?
  3.d
  Jack and Jill are buying chocolates in a Chocolate Shop.
  
  Jack bought $6$ chocolate frogs and $5$ truffles for $\rtqMathsSymbolPound 9.55$ .
  
  Jill bought $3$ chocolate frogs and $3$ truffles for $\rtqMathsSymbolPound 5.25$ .
  
  How much does a chocolate frog cost, and how much does a truffle cost?
  3.e
  An artist mixes red, yellow and white paint to create a new shade of orange.
  
  Two fifths of the mixture is yellow paint.
  
  The artist uses three times as much red paint as white paint.
  
  In total, the artist mixes $180 \rtqMathsUnit{ml}$ orange paint.
  
  How much red paint does the artist need?
  Worked solution
  Being written
4. 4
  4.a
  James has $15$ sweets in his pocket. He has $7$ red sweets, $6$ blue sweets, and $2$ pink sweets. Without looking, he removes some sweets from his pocket and places them on the table. What is the smallest number of sweets he should remove to guarantee that he has at least one sweet of each colour?
  4.b
  Four identical rectangles are joined together to form a larger rectangle, as shown below.
  Three identical horizontal rectangles are stacked on the left. A fourth congruent rectangle is rotated vertically and placed to their right, sharing the full height. A vertical double-headed dimension outside the right edge is labelled X.
  The area of the larger rectangle is $192 \rtqMathsUnit{cm}^2$ Find the length of the side labelled $X$ .
  4.c
  Karen wants to find the value of $1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10$ . Rather than just doing the calculation, she notices that she can reorder the numbers in a clever way:
  
  $1 + 10 + 2 + 9 + 3 + 8 + 4 + 7 + 5 + 6$ . She does this because $1 + 10, 2 + 9, 3 + 8$ etc all add up to $11$ , and so her sum simplifies to $11 + 11 + 11 + 11 + 11$ , which equals $55$ .
  
  Using Karen's method, add up all of the whole numbers from $1$ to $20$ .
  4.d
  Tina is an athlete, and she is completing a difficult training session. Her coach makes her run $5 \rtqMathsUnit{metres}$ forwards, then $5 \rtqMathsUnit{metres}$ back, then $10 \rtqMathsUnit{metres}$ forwards, then $10 \rtqMathsUnit{metres}$ back, then $15 \rtqMathsUnit{metres}$ forwards, then $15 \rtqMathsUnit{metres}$ back, and this continues until she has run $100 \rtqMathsUnit{metres}$ forwards, then $100 \rtqMathsUnit{metres}$ back.
  
  How far does Tina run in total?
  Worked solution
  Being written