### National 5 Mathematics Paper 1 With Solutions

**There is a total of 15 questions for the National 5 mathematics paper 1 of 2018. so you can all the solutions here. more National 5 mathematics Paper solutions will be shared soon.**

**1. A baking company will reject cakes if they do not weigh 400 g ± 3%.**

**The weights of a sample of 13 cakes are shown below.**

**385, 391, 409, 403, 386, 412, 413, 407, 400, 390, 387, 405, 388**

**Calculate the fraction of cakes that will be rejected.**

**Use your working to justify your answer.**

**2. Jennifer is planning to go on a 4-night city break.**

**The costs are shown in the table below.**

Flights £270

Accommodation £90 per night

Spending money £450

Insurance £30

**She earns £400 per week.**

**She saves 1/****8**

**of her earnings each week towards her city break.**

**Calculate the minimum number of weeks it will take Jennifer to save enough**

**money for her city break.**

**4. Lynn is flying an aircraft and has been told that the outside temperature is**

**34 °C lower than the ground temperature.**

**The ground temperature is 6 °C.**

**Calculate the outside temperature and mark it on the gauge below.**

**5. Guests at a wedding were asked to choose their main course.**

** 3/7 of the guests chose chicken**

**1/3 of the guests chose beef**

**• the remaining guests chose the vegetarian option.**

**Calculate the fraction of guests that chose the vegetarian option.**

**6. Tom thinks that the answer to the following calculation is 8∙7.**

**Is Tom correct?**

**Use your working to justify your answer.**

**8. Ian buys a new sofa.**

**The original price was £700.**

**The shop is having a sale with 25% off the price of all sofas.**

**When he goes to the shop he finds there is an additional 5% off the sale price.**

**Calculate the price Ian pays for his sofa.**

**9. Steven flew to Hong Kong to start a new job.**

**The flight included a stop in Doha.**

**He flew from Edinburgh to Doha then from Doha to Hong Kong.**

**• The flight from Edinburgh to Doha took 6 hours 35 minutes.**

**• The flight from Doha to Hong Kong took 7 hours 20 minutes.**

**• Hong Kong is 8 hours ahead of Edinburgh.**

**Steven’s plane took off from Edinburgh at 9:15 am local time.**

**It landed in Hong Kong at 8:50 am local time.**

**How long was the stop in Doha?**

**10. David sat a class test.**

**His results are shown in the table below.**

**Marks available Percentage achieved**

**Paper 1 35 80%**

**Paper 2 65 60%**

**(a) Calculate the number of marks he achieved in paper 1.**

**(b) Calculate his overall percentage for this test**

**11. Ribbon has to be placed around the outside of the love heart cake shown**

**below.**

**The top of the cake is in the shape of an isosceles triangle with two identical**

**semi-circles.**

**The ribbon needs to be the length of the perimeter of the top of the cake**

**plus an extra 2·8 cm.**

**Calculate the length of ribbon needed for the cake.**

**Take π = 3 14 ·**

**12. A helicopter flew from Aberdeen airport to transport workers to oil rig 1 and**

**then continued on to oil rig 2.**

**It flew 82 km on a bearing of 042° to oil rig 1.**

**It then flew 46 km on a bearing of 194° to oil rig 2.**

**(a) Construct a scale drawing to illustrate this journey.**

**Use a scale of 1 cm : 10 km.**

**The helicopter then returns to Aberdeen airport from oil rig 2.**

**13. A lawn is to be created in the shape of an isosceles triangle with dimensions**

**as shown below.**

**Calculate the area of the lawn.**

**14. Michael runs a stall at the school fayre.**

**His game requires two spinners to be spun and allowed to come to rest.**

**The spinners are shown below.**

**The numbers on which the spinners come to rest are multiplied together.**

**To win a prize the answer to this multiplication must be less than 5.**

**Calculate the probability of winning a prize.**

**15. A ramp to allow wheelchair access to a school has the dimensions shown**

**below.**

**The maximum gradient allowed for a ramp with a horizontal distance of**

**4 m is 1/****14 .**

**Does the gradient of this ramp meet the regulations?**

**Use your working to justify your answer.**

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