Highgate School Sample Paper A

IndependentCo-ed

4 questions

Original PDFWorked solutions in progress

Questions

1. 1
  The following questions are about a butcher's shop.
  1.a
  Karim buys $7$ burgers and $5$ steaks. Burgers cost $61 \rtqMathsUnitCurrencyPence$ each and steaks cost $84 \rtqMathsUnitCurrencyPence$ each.
  
  How much did Karim spend in total?
  1.b
  Sausages come in packs of $8$ . Each pack costs $\rtqMathsSymbolPound 1.30$ .
  
  James spends $\rtqMathsSymbolPound 9.10$ on sausages. How many sausages did James get?
  1.c
  Tyler buys $16$ chicken wings, and receives $\rtqMathsSymbolPound 14.72$ change from a $\rtqMathsSymbolPound 20$ note.
  
  What is the price of a chicken wing?
  1.d
  The butcher also sells slices of turkey.
  
  Donald buys three quarters of the slices in the shop. Alisha then buys a sixth of the remaining slices.
  
  Alisha bought $3$ slices. How many more slices than Alisha did Donald buy?
  1.e
  Lamb chops are three times more expensive than pork chops.
  
  Tina buys $2$ lamb chops and $2$ pork chops. She spends $\rtqMathsSymbolPound 9.60$ in total.
  
  How much do lamb chops and pork chops cost?
  Worked solution
  Being written
2. 2
  Mr Green's garden is a mixture of lawn, patio and flower beds. A plan of the garden is shown below, with some (but not all) of the measurements.
  
  The picture is not drawn to scale.
  Three nested rectangles share their bottom-right corner. Their differences form an L-shaped flower bed and lawn around an 8 metre by 3 metre patio. Six guide-to-guide dimensions and boxed arrow callouts identify the plan.
  2.a
  What is the area covered by Mr Green's lawn?
  2.b
  Mr Green buys $6$ flower pots. Flower pots cost $\rtqMathsSymbolPound 4.00$ each.
  
  Mr Green has a voucher for “ $15\%$ off”.
  
  How much does Mr Green spend on flower pots if he uses the voucher?
  2.c
  Mr Green wants to lay paving stones on his patio. The stones are rectangles measuring $50 \rtqMathsUnit{cm} \times 20 \rtqMathsUnit{cm}$ .
  
  How many paving stones are needed to pave the patio?
  2.d
  The area of the flower bed is $60 \rtqMathsUnit{m}^2$ .
  
  Three sacks of fertilizer are needed for every $4 \rtqMathsUnit{m}^2$ of flower bed.
  
  Sacks cost $\rtqMathsSymbolPound 10$ each, but are on offer: “buy four sacks and get a fifth sack free”.
  
  How much does it cost to fertilize the flower bed?
  Worked solution
  Being written
3. 3
  3.a
  Tim is going paintballing. Entry into paintballing costs $\rtqMathsSymbolPound 23$ , but then you also have to pay $\rtqMathsSymbolPound 6$ per $100$ paintballs that you use.
  
  Tim spent $\rtqMathsSymbolPound 65$ in total. How many paintballs did he use?
  3.b
  Janice is running a bath. She mixes hot water with cold water to make sure the temperature is just right.
  
  She uses $5$ times more hot water than cold water. Janice's bath holds $90 \rtqMathsUnit{litres}$ of water in total. How much hot water does she use?
  3.c
  Bob the Builder is filling a hole with a mixture of gravel and sand. $234 \rtqMathsUnit{kg}$ of sand are needed to make $400 \rtqMathsUnit{kg}$ of the mixture.
  
  Bob makes $1000 \rtqMathsUnit{kg}$ of the mixture.
  
  How much gravel does Bob need?
  3.d
  In the picture below, rectangle $A$ has an area of $70 \rtqMathsUnit{cm}^2$ , and rectangle $B$ has an area of $63 \rtqMathsUnit{cm}^2$ . The side lengths of the rectangles are whole numbers.
  
  The sides labelled $X$ and $Y$ are both longer than $1 \rtqMathsUnit{cm}$ .
  Rectangles A and B share a full vertical side and have equal height. A vertical double-headed dimension outside the left edge is labelled X. A horizontal double-headed dimension below rectangle B spans its width and is labelled Y.
  Find the lengths of the sides labelled $X$ and $Y$ .
  3.e
  Victoria the vet is weighing her pets.
  
  Her rabbit and her cat together weigh $10 \rtqMathsUnit{kg}$ .
  
  Her cat and dog together weigh $24 \rtqMathsUnit{kg}$ .
  
  Her dog and rabbit together weigh $20 \rtqMathsUnit{kg}$ .
  
  How much do all $3$ of her pets weigh when weighed together?
  Worked solution
  Being written
4. 4
  4.a
  In the town of Mathsville there are $360$ residents.
  
  $45 \%$ of the residents are children, the rest are adults.
  
  How many adults are there in Mathsville?
  4.b
  Numbertown Primary School has $280$ pupils. $56$ of these pupils are girls.
  
  What percentage of the pupils are boys?
  4.c
  The price of a bus ticket from Mathsville to Numbertown has increased by $50\%$ in the past year. A bus ticket now costs $\rtqMathsSymbolPound 1.80$ .
  
  What did it cost a year ago?
  4.d
  Mathsville Maths Supplies is a shop selling maths equipment.
  
  Tina bought $4$ calculators and $3$ protractors for $\rtqMathsSymbolPound 16.10$ . Ahmed bought $2$ calculators and $1$ protractor for $\rtqMathsSymbolPound 7.50$ .
  
  How much does a calculator cost, and how much does a protractor cost?
  4.e
  Football is very popular in Numbertown.
  
  Two fifths of the population support London Mathletic.
  
  The rest support either Mathsville United or the Counting Crows.
  
  Twice as many people support Mathsville United than support the Counting Crows.
  
  $500$ people support the Counting Crows.
  
  What is the total population of Numbertown?
  Worked solution
  Being written