Best Buy Questions: Higher Tier Practice (Part 2) - Worksheets, Questions and Revision

8 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

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3.12HB Best Buy Questions: Higher Tier Practice (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A hardware shop in Leeds sells a strimmer. The price shown includes VAT at 20%. The price shown is 99.50 pounds.
Work out the price of the strimmer before VAT was added. Give your answer to the nearest penny.

(Total for Question 1 is 3 marks)

Amelia is comparing three bags of basmati rice at a supermarket in Cardiff.
Bag A: 500 g for 1.20 pounds.
Bag B: 1.5 kg for 3.30 pounds.
Bag C: 2 kg for 4.60 pounds.
Work out the price per kilogram for each bag, giving each answer to 2 decimal places where needed, and state which bag gives the best value for money.

(Total for Question 2 is 5 marks)

Oliwia is choosing between two shops for a jacket that has a full price of 60 pounds at both shops.
Northgate Fashion: 10% off, then a further 10% off the reduced price at the till.
Willowbrook Clothing: a single discount of 20% off.
Work out the final price at each shop and state which shop is cheaper, and by how much.

(Total for Question 3 is 5 marks)

Yusuf is comparing two boxes of cereal in a supermarket in Bristol.
Box X: 750 g for 2.85 pounds.
Box Y: 500 g for 1.95 pounds.
Yusuf's working is shown below.
Box X: 2.85 / 700 * 100 = 40.71 pence per 100 g (to 2 dp)
Box Y: 1.95 / 500 * 100 = 39 pence per 100 g
Since 39 is less than 40.71, Yusuf concludes that Box Y is better value.
Identify the mistake in Yusuf's working, then work out the correct price per 100 g for Box X and state which box actually gives better value.

(Total for Question 4 is 5 marks)

A sofa has a full price of 640 pounds at two furniture branches.
Ashworth Furniture: the sofa is reduced by 1/4, plus a 35 pound delivery charge.
Bellhaven Home: the sofa is reduced by 20%, with free delivery.
Callum wants to buy the sofa as cheaply as possible. Work out the total cost at each branch and state which is cheaper, and by how much.

(Total for Question 5 is 5 marks)

Oliwia runs a market stall in Nottingham selling loose-leaf tea.
Standard tea costs 8.40 pounds per kg. Premium tea costs 15.60 pounds per kg.
Oliwia mixes Standard and Premium tea in the ratio 5:3 by weight to make a house blend.
Work out the cost per kg to Oliwia of making the house blend. She plans to sell the blend for 12.00 pounds per kg: state, with a reason, whether this price covers the cost of making it, and give the profit margin per kg if it does.

(Total for Question 6 is 6 marks)

A shop increases the price of an item, P pounds, by a%, then decreases the new, increased price by the same percentage, a%.
(a) Show that the final price after both changes is P(1 - a²/10000) pounds.
(b) A shop increases the price of a games console, originally 250 pounds, by 10%, then decreases the new price by 10% in a January sale. Use the result from part (a), or otherwise, to work out the final price and the overall percentage change from the original price.
Show all working.

(a)(a) Show that the final price after both changes is P(1 - a²/10000) pounds.(3)

(b)(b) The original price is 250 pounds and a = 10. Work out the final price and the overall percentage change from the original price.(3)

(Total for Question 7 is 6 marks)

A photo-printing shop charges 12 pence for each of the first 20 photos in an order. Every additional photo beyond the 20th costs 60% of the standard 12 pence rate. Nia orders n photos, where n > 20.
(a) Show that the total cost, C pence, of an order of n photos is given by C = 240 + 7.2(n - 20).
(b) A rival print shop charges a flat rate of 9 pence per photo, for any order size. Find the range of values of n for which Nia's local shop is cheaper than the rival flat-rate shop. Give your answer as an inequality, and state the smallest whole number of photos for which the local shop is cheaper.

(a)(a) Show that the total cost, C pence, of an order of n photos (n > 20) is given by C = 240 + 7.2(n - 20).(2)

(b)(b) Find the range of values of n for which Nia's local shop is cheaper than a rival shop charging a flat rate of 9 pence per photo. Give your answer as an inequality, and state the smallest whole number of photos for which the local shop is cheaper.(5)

(Total for Question 8 is 7 marks)

Mark scheme · 3.12HB Best Buy Questions: Higher Tier Practice (Part 2)

Question 1

M1 use 99.50 / 1.2 or equivalent (recognising the VAT-inclusive price is 120% of the price before VAT)
A1 82.9166... seen or implied
B1 82.92 pounds cao, correctly rounded to the nearest penny
Answer: 82.92 pounds. (99.50 / 1.2 = 82.9166... which rounds to 82.92 pounds to the nearest penny.) Working check: 82.92 * 1.2 = 99.504, which rounds to 99.50 pounds.

Question 2

M1 convert Bag A to price per kg: 1.20 / 0.5 (recognising 500 g = 0.5 kg)
A1 Bag A = 2.40 pounds per kg cao
M1 find price per kg for Bag B and Bag C: 3.30 / 1.5 and 4.60 / 2
A1 Bag B = 2.20 pounds per kg AND Bag C = 2.30 pounds per kg, both cao
B1 correctly identify Bag B as the best value, with a valid comparison of all three prices per kg
Answer: Bag A = 2.40 pounds per kg. Bag B = 2.20 pounds per kg. Bag C = 2.30 pounds per kg. Bag B gives the best value for money, being the cheapest per kilogram. Working check: 1.20 / 0.5 = 2.40; 3.30 / 1.5 = 2.20; 4.60 / 2 = 2.30; 2.20 is the smallest of the three.

Question 3

M1 apply the first discount at Northgate Fashion: 60 * 0.9, or a complete method 60 * 0.9 * 0.9
A1 Northgate Fashion final price = 48.60 pounds cao
M1 apply the single discount at Willowbrook Clothing: 60 * 0.8
A1 Willowbrook Clothing final price = 48.00 pounds cao
B1 state Willowbrook Clothing is cheaper, by 0.60 pounds, cao (ft from the two totals)
Answer: Northgate Fashion: 60 * 0.9 * 0.9 = 48.60 pounds. Willowbrook Clothing: 60 * 0.8 = 48.00 pounds. Willowbrook Clothing is cheaper, by 0.60 pounds. (Two successive 10% discounts give an overall reduction of 19%, not 20%: 1 - 0.9*0.9 = 0.19.) Working check: 48.60 - 48.00 = 0.60.

Question 4

B1 identify that Yusuf used 700 g instead of the correct mass of 750 g for Box X
M1 recalculate Box X using the correct mass: 2.85 / 750 * 100
A1 Box X = 38 pence per 100 g cao
B1 Box Y correctly confirmed as 39 pence per 100 g
A1 correct conclusion: Box X is actually the better value (cheaper per 100 g), not Box Y as Yusuf claimed, cao
Answer: Yusuf used 700 g instead of 750 g for Box X. Correct calculation: Box X = 2.85 / 750 * 100 = 38 pence per 100 g. Box Y = 1.95 / 500 * 100 = 39 pence per 100 g. Box X is actually the better value, not Box Y as Yusuf concluded. Working check: 2.85 / 750 = 0.0038, * 100 = 0.38 pounds = 38 pence; 1.95 / 500 = 0.0039, * 100 = 0.39 pounds = 39 pence; 38 is less than 39.

Question 5

M1 a complete method to find Ashworth Furniture's total cost, e.g. 640 * 3/4 + 35
A1 Ashworth Furniture total = 515 pounds cao
M1 a method to find Bellhaven Home's total cost, e.g. 640 * 0.8
A1 Bellhaven Home total = 512 pounds cao
B1 state Bellhaven Home is cheaper, by 3 pounds, cao (ft from the two totals)
Answer: Ashworth Furniture: 640 * 3/4 = 480, plus 35 delivery = 515 pounds. Bellhaven Home: 640 * 0.8 = 512 pounds. Bellhaven Home is cheaper, by 3 pounds. Working check: 515 - 512 = 3.

Question 6

M1 recognise the ratio 5:3 as 8 total parts, e.g. use 5 kg Standard and 3 kg Premium
M1 cost of 5 kg Standard = 5 * 8.40 (= 42.00) and cost of 3 kg Premium = 3 * 15.60 (= 46.80)
M1 divide total cost by total mass: (42.00 + 46.80) / 8
A1 blend cost = 11.10 pounds per kg cao
M1 compare 11.10 pounds per kg with the selling price of 12.00 pounds per kg
A1 correct conclusion with reason: 12.00 pounds covers the cost, giving a margin of 0.90 pounds per kg cao
Answer: Cost of blend = (5*8.40 + 3*15.60) / 8 = (42.00 + 46.80) / 8 = 88.80 / 8 = 11.10 pounds per kg. Selling at 12.00 pounds per kg covers the cost, with a margin of 12.00 - 11.10 = 0.90 pounds per kg. Working check: 5 + 3 = 8 parts; 42.00 + 46.80 = 88.80; 88.80 / 8 = 11.10.

Question 7

(a) M1 increased price = P(1 + a/100), or equivalent
(a) M1 multiply by (1 - a/100) to apply the decrease: P(1 + a/100)(1 - a/100)
(a) A1 expand using difference of two squares to P(1 - a²/10000) cso
(a) Answer: P(1 + a/100)(1 - a/100) = P(1 - (a/100)²) = P(1 - a²/10000), as required.
(b) M1 substitute a = 10 and P = 250, either into part (a)'s formula or by computing 250 * 1.1 * 0.9
(b) A1 final price = 247.50 pounds cao
(b) B1 state the overall change is a decrease of 1% (or -1%) cao
(b) Answer: Final price = 250 * 1.1 * 0.9 = 247.50 pounds. This is a decrease of 1% on the original 250 pounds.