UniGeniusFunctional Skills Maths · Level 2

Questions and answers

Functional Skills Maths Level 2 questions with answers

Twenty questions in the paper's style, from a 2-mark warm-up to a 6-mark floor plan. Try one, have it marked, then read the worked answer.

Question 1

2 marksNo calculator

A cold store is at −7°C. After a fault, its temperature is 5°C.

By how many degrees has the temperature risen?

Worked answer

12°C

  1. The rise is 5 − (−7).
  2. Subtracting a negative adds: 5 + 7 = 12°C.

Marks: M1 5 − (−7), or 7 + 5; A1 12°C.

Question 2

2 marksNo calculator

A shop receives 18 boxes. Each box contains 24 notebooks. It sells 37 notebooks.

How many notebooks are left?

Worked answer

395 notebooks

  1. 18 × 24 = 18 × 20 + 18 × 4 = 360 + 72 = 432.
  2. 432 − 37 = 395 notebooks.
  3. Check: 395 + 37 = 432, and 18 × 24 = 432.

Marks: M1 18 × 24 = 432; A1 395.

Question 3

2 marksNo calculator

A sensor's battery indicator reads 0.375.

Write 0.375 as a fraction in its simplest form, and as a percentage.

Worked answer

3/8 and 37.5%

  1. 0.375 = 375/1,000 = 3/8.
  2. 0.375 × 100 = 37.5%.

Marks: B1 3/8; B1 37.5%.

Question 4

3 marksNo calculator

A maker has two pieces of fabric. One is 1¾ metres long and the other is 2⅚ metres long.

Find the total length. Give your answer as a fraction or mixed number in its simplest form.

Worked answer

4 7/12 m

  1. Common denominator 12: 1¾ = 1 9/12 and 2⅚ = 2 10/12.
  2. 3 + 19/12 = 3 + 1 7/12.
  3. Total: 4 7/12 m.

Marks: M1 Twelfths: 1 9/12 and 2 10/12; M1 3 + 19/12, or 55/12; A1 4 7/12 m.

Question 5

3 marksCalculator

Blue paint and white paint are mixed in the ratio 3:2. A decorator needs 35 litres of the mixture.

How much of each colour is needed?

Worked answer

21 litres blue, 14 litres white

  1. 3 + 2 = 5 parts.
  2. 35 ÷ 5 = 7 litres a part.
  3. Blue 3 × 7 = 21 litres; white 2 × 7 = 14 litres. Check: 21 + 14 = 35.

Marks: M1 5 parts, 7 litres a part; A1 21 litres blue; A1 14 litres white.

Question 6

3 marksCalculator

A machine uses the formula F = 4n² − 3n.

Find F when n = 5.

Worked answer

85

  1. Square first: 5² = 25.
  2. 4 × 25 = 100 and 3 × 5 = 15.
  3. 100 − 15 = 85.

Marks: M1 5² = 25; M1 4 × 25 − 3 × 5 = 100 − 15; A1 85.

Question 7

3 marksCalculator

Six staff pack an order in 8 hours. They all work at the same rate. Four staff will pack an identical order.

How long will the four staff take?

Worked answer

12 hours

  1. The work needs 6 × 8 = 48 staff-hours.
  2. Four staff: 48 ÷ 4 = 12 hours.
  3. Fewer staff take longer, which checks the direction.

Marks: M1 6 × 8 = 48 staff-hours; M1 Dividing the 48 staff-hours by 4; A1 12 hours.

Question 8

5 marksCalculator

A learner has a budget of £490. Shop A sells a laptop at £480 before VAT. It takes 15% off that price, then adds VAT at 20% to the discounted price. Shop B sells the same laptop for £495 including VAT, with no discount.

Which shop, if either, can the learner buy from within the budget? Show your working.

Your decision
Worked answer

Shop A only, at £489.60.

  1. Shop A after discount: 480 × 0.85 = £408.
  2. With VAT: 408 × 1.20 = £489.60, which is £0.40 under £490.
  3. Shop B: £495 is £5 over the budget.
  4. So only Shop A is within budget.

Marks: M1 Discounted price £408; A1 Shop A with VAT £489.60; M1 Shop A compared with the budget: £0.40 under; M1 Shop B compared with the budget: £5 over; C1 Shop A only.

Question 9

3 marksCalculator

A ticket costs £60 after a 25% discount.

What was its original price?

Worked answer

£80

  1. After 25% off, £60 is 75% of the original price.
  2. 60 ÷ 0.75 = £80.
  3. Check: 80 × 0.75 = 60.

Marks: M1 £60 is 75% of the original; M1 60 ÷ 0.75; A1 £80.

Question 10

4 marksCalculator

£800 is put in an account paying 4% compound interest each year. Nothing is taken out and there are no charges.

Find the balance after 2 years and the total interest earned.

Worked answer

£865.28 balance, £65.28 interest

  1. Year 1: 800 × 1.04 = £832.
  2. Year 2: 832 × 1.04 = £865.28.
  3. Interest: 865.28 − 800 = £65.28.

Marks: M1 Multiplier 1.04, or £832 after one year; M1 A second year of growth on £832, or 800 × 1.04²; A1 £865.28; A1 £65.28.

Question 11

4 marksCalculator

A worker is paid £12.80 an hour for 37.5 ordinary hours. They also work 6 overtime hours paid at 1.5 times the ordinary rate. Their travel this week costs £27.60. Ignore tax and other deductions.

How much of this week's earnings is left after travel?

Worked answer

£567.60

  1. Ordinary pay: 37.5 × 12.80 = £480.
  2. Overtime rate: 12.80 × 1.5 = £19.20.
  3. Overtime pay: 6 × 19.20 = £115.20.
  4. Left: 480 + 115.20 − 27.60 = £567.60.

Marks: M1 Ordinary pay £480; M1 Overtime rate £19.20; M1 Overtime pay £115.20; A1 £567.60.

Question 12

3 marksCalculator

1 mile = 1.6 km. A conversion graph goes through (0 miles, 0 km), (5, 8), (10, 16) and (15, 24). A van uses 5 litres of fuel per 100 km.

Change 12.5 miles to kilometres with the conversion. Find the fuel used on a 12.5-mile journey.

Worked answer

20 km and 1 litre

  1. 12.5 × 1.6 = 20 km (the graph reads 20 at 12.5 miles).
  2. Fuel: 20 ÷ 100 × 5 = 1 litre.

Marks: B1 20 km; M1 20 ÷ 100 × 5 or 0.05 litres per km; A1 1 litre.

Question 13

5 marksCalculator

A delivery van travels 126 km in 1 hour 45 minutes, not counting stops. It carries a block of material with mass 18 kg and volume 0.06 m³. Density = mass ÷ volume.

Find the van's average speed in km/h, and the density of the block in kg/m³.

Worked answer

72 km/h and 300 kg/m³

  1. 1 h 45 min = 1.75 h.
  2. Speed: 126 ÷ 1.75 = 72 km/h.
  3. Density: 18 ÷ 0.06 = 300 kg/m³.

Marks: M1 1 hour 45 minutes = 1.75 hours; M1 126 ÷ 1.75 set up; A1 72 km/h; M1 18 ÷ 0.06 set up; A1 300 kg/m³.

Question 14

6 marksCalculator

A room would be an 8 m by 5 m rectangle, but a 3 m by 2 m rectangular corner is cut out. A triangular platform in the room has base 2.4 m and perpendicular height 1.5 m and will not be carpeted. Carpet costs £18.75 per m², charged for exactly the area needed.

Find the cost of carpeting the floor around the platform.

Worked answer

£603.75

  1. Rectangle: 8 × 5 = 40 m². Cut-out: 3 × 2 = 6 m².
  2. Room: 40 − 6 = 34 m².
  3. Platform: ½ × 2.4 × 1.5 = 1.8 m².
  4. Carpet: 34 − 1.8 = 32.2 m².
  5. Cost: 32.2 × 18.75 = £603.75.

Marks: M1 Whole rectangle 40 m²; M1 Cut-out 6 m²; M1 Room 34 m²; M1 Platform 1.8 m²; M1 Carpet 32.2 m²; A1 £603.75.

Question 15

6 marksCalculator

A closed cylindrical tank has internal radius 0.4 m and internal height 1.2 m. Ignore the wall thickness. Use π = 3.142 and 1 m³ = 1,000 litres.

Find its capacity in litres to the nearest litre, and its total surface area including both ends, in m² to 2 decimal places.

Worked answer

603 litres and 4.02 m²

  1. Volume: 3.142 × 0.4² × 1.2 = 0.603264 m³ = 603.264 litres, so 603 litres.
  2. Ends: 2 × 3.142 × 0.4² = 1.00544 m².
  3. Curved: 2 × 3.142 × 0.4 × 1.2 = 3.01632 m².
  4. Total: 4.02176 m², so 4.02 m².

Marks: M1 π × 0.4² × 1.2; M1 0.603264 m³; A1 603 litres; M1 Both ends: 1.00544 m²; M1 Curved surface 3.01632 m²; A1 4.02 m².

Question 16

4 marksCalculator

A rectangular deck is 6 m by 4 m. It is drawn at a scale of 1:50. On a separate site grid, where 1 unit is 1 metre, three corners of the deck are A(−2, −1), B(4, −1) and C(4, 3), in order round the deck.

Give the drawing's length and width in centimetres, and the coordinates of the fourth corner, D.

Worked answer

12 cm by 8 cm; D = (−2, 3)

  1. 6 m = 600 cm and 4 m = 400 cm.
  2. 600 ÷ 50 = 12 cm; 400 ÷ 50 = 8 cm.
  3. D has A's x-coordinate and C's y-coordinate: (−2, 3).

Marks: M1 600 cm and 400 cm; A1 12 cm and 8 cm; B1 x = −2; B1 y = 3.

Question 17

3 marksCalculator

A display is made of identical cubes. Each number in the table is the height of a solid stack. A viewer looks from the front.

Stacks of cubes (plan view)
LeftCentreRight
Back row121
Front row, nearest viewer213

How many cubes are in the display, and how many squares are in the front elevation?

Worked answer

10 cubes; front elevation 2, 2, 3 = 7 squares

  1. Cubes: 1 + 2 + 1 + 2 + 1 + 3 = 10.
  2. Front view: the taller stack in each column: 2, 2 and 3.
  3. 2 + 2 + 3 = 7 squares.

Marks: M1 Every stack added; A1 10 cubes; A1 7 squares (heights 2, 2, 3).

Question 18

5 marksCalculator

A supervisor records the number of completed jobs per worker in one day. The target is a mean of at least 9.

Completed jobsNumber of workers
0 to 44
5 to 98
10 to 146
15 to 192

Estimate the mean. Does the estimate meet the target? Show your working.

Your decision
Worked answer

No. The estimated mean is 8.5.

  1. Midpoints: 2, 7, 12, 17.
  2. 2 × 4 + 7 × 8 + 12 × 6 + 17 × 2 = 170.
  3. 170 ÷ 20 = 8.5, below 9, so no.

Marks: M1 Midpoints 2, 7, 12, 17; M1 Total 170; M1 Dividing 170 by 20; A1 8.5; C1 No, with 8.5 compared with 9.

Question 19

2 marksCalculator

Arrival delays in minutes for five buses: route A 4, 6, 6, 8, 11; route B 5, 6, 7, 8, 9.

Find the mean and range of each route. Which route's delays are more consistent?

Your decision
Worked answer

Route B: both means are 7, but B's range is 4 against A's 7.

  1. Both totals are 35, so both means are 35 ÷ 5 = 7.
  2. Ranges: A = 11 − 4 = 7; B = 9 − 5 = 4.
  3. Same mean, smaller range: route B is more consistent.

Marks: M1 Totals of 35, so both means are 7; C1 Route B, because its range (4) is smaller than A's (7).

Question 20

3 marksCalculator

A survey of 120 learners: each is in exactly one cell of the table. One learner is chosen at random, the name is put back, and a second choice is made independently.

TravelMorning classAfternoon classTotal
Walk243660
Bus421860
Total6654120

Find the probability that the first learner walks and is in the afternoon class, and the probability that both learners chosen travel by bus.

Worked answer

3/10 (0.3 or 30%) and 1/4

  1. Walk and afternoon: 36 out of 120 = 3/10 = 0.3 = 30%.
  2. Bus each time: 60/120 = 1/2.
  3. Independent choices: 1/2 × 1/2 = 1/4.

Marks: B1 3/10, 0.3 or 30%; M1 1/2 × 1/2; A1 1/4.

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