third level revision - st peter the apostle high school · third level revision all numeracy...

St Peter the Apostle High School Numeracy and Mathematics

Third Level Revision

St Peter the Apostle

High School

Numeracy and Mathematics


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All numeracy questions are highlighted in bold font

Questions E&Os 1.

a) Round 56.7957 to 3 decimal places. b) Round 100.99213 to 3 decimal places. c) Round 2.18065 to 3 decimal places. d) Round 246.98213 to 3 decimal places. Digital resource: www.mathsworkout.co.uk - Number/12.Rounding&Estimation/Targets3 www.sptamaths.co.uk - Numeracy Ninjas/key skills/rounding/decimal places

MNU 3-01a

2. a) A fruit shop has 105 bags of apples. They can fit 6 bags of apples in a crate. How many crates are needed to fit all the apples? b) The 900 workers in a factory do the lottery. They win the top prize of £3600000. How much should each person receive? c) Frank made 1018 minutes of calls on his mobile phone last year. He was charged at the rate of 8 pence per minute. What was his total phone bill for the year? Give your answer in pounds and pence. d) A luxury coach can seat 62 passengers. How many coaches are needed to take 325 school pupils on their summer trip? e) Calculate 7.26 × 1.4 f) Calculate 25.12 × 2.7 Digital resource: www.mathsworkout.co.uk - Number/1.Arithmetic/Targets5 and Number/5.Decimals/Targets2-5 www.sptamaths.co.uk - Numeracy Ninjas/key skills/Whole Numbers/Decimals

MNU 3-03a MNU 3-03b

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3. a) 25 x (-40) b) 300 ÷ (-20) c) (-5) x 80

d) It was -5oC at 6am. The temperature rises by 4oC every hour. What is the

temperature at 10am? e) It was 9oC at 6pm. The temperature falls 2oC every hour. What is the

temperature at 12 midnight? Digital resource: www.mathsworkout.co.uk - Number/6.Integers/Targets2-5 www.sptamaths.co.uk - Numeracy Ninjas/key skills/Integers

MNU 3-04a

4.

a) Find the highest common factor of 6 and 10 b) Find the highest common factor of 30 and 45 c) Find the lowest common multiple of 6 and 8 d) Find the lowest common multiple of 2, 3 and 4 e) Write 12 as a product of prime factors. f) Write 30 as a product of prime factors. g) Write 32 as a product of prime factors. h) Jamie has a set of flashing disco lights. The red light flashes every 9 seconds, the yellow light flashes every 12 seconds and the blue light flashes every 6 seconds. When Jamie switches all of them on, the yellow, red and blue flash together. After how many seconds will all the lights flash at the same time again?

Digital resource: www.mathsworkout.co.uk - Number/7.Factors/8.Prime/9.Multiples www.sptamaths.co.uk - Numeracy Ninjas/key skills/Special Numbers/Multiples/Factors

MTH 3-05a MTH 3-05b







5. a) Evaluate 42

b) Evaluate 23

c) Evaluate 33

d) Evaluate 24

Digital resource: www.mathsworkout.co.uk - Number/10.Powers/Targets1&3 www.sptamaths.co.uk - Numeracy Ninjas/key skills/Special Numbers/Squares/Cubes

MTH 3-06a

6.

a) Change 32

5 to an Improper Fraction (Top Heavy)

b) Increase £620 by 15% c) Decrease £900 by 30% Evaluate:

d) 5

8+

4

5

e) 4

7+

5

6

Leave your answers as a mixed number fraction

f) 8

9−

3

4

Digital resource: www.mathsworkout.co.uk - Number/17.Fractions1/Target 4 and Number/18.Fractions2 and Number/19.Percentage1 www.sptamaths.co.uk - Numeracy Ninjas/key skills/FracPerc/Converting

MNU 3-07a MTH 3-07b MTH 3-07c







7.

a) Simplify the ratio 3 : 9 b) Simplify the ratio 10 : 25 c) A model Ferarri has a scale of 1 : 43 i) The model has a tyre diameter of 2 cm. What will the tyre diameter be on the real Ferarri? ii) The real Ferarri has a height of 129 centimetres. What is the height of the model? d) Fares on the Subway Trains are expected to rise soon by 8%. What will be the new cost of a ticket which just now is priced £6? e) In a sale, a designer shirt, normally priced at £120, is reduced by 30%. What is the sale price of the shirt? Digital resource: www.mathsworkout.co.uk - Number/21.Ratio www.sptamaths.co.uk – Courses/Old Courses/S1/2 5-14 Levels/LevelE/Ratio

MNU 3-08a

8.

a) A shop is offering 2 payment options for a Sofa. They have a ‘Pay it up’ option with a deposit payment of £175 followed by 9 monthly direct debit payments of £95 or you can pay £950 cash. How much extra would it cost to pay for the Sofa on ‘Pay it Up’ scheme compared to buying it cash? b) The ‘Pram Store’ is offering 2 payment options for a Double Pushchair. They have a ‘Pay it up’ option with a deposit payment of £20 followed by 26 monthly direct debit payments of £7.50 or you can pay £199 cash. How much extra would it cost to pay for the Double Pushchair on ‘Pay it Up’ scheme compared to buying it cash?

If the exchange rate for pounds to euros is £1 = €1.44 c) What is £200 in euros? d) What is £400 in euros? e) What is £500 in euros? Digital resource: www.sptamaths.co.uk – Courses/Old Courses/S1/2 5-14 Levels/LevelE/Money

MNU 3-09a MNU 3-09b






9.

a) A car travels 180 kilometres and takes 3 hours. Calculate the speed of the car. b) A plane flying for 8 hours and travelling 3200 miles. Calculate the speed of the plane? c) A bird flying 20 kilometres and taking 2 hours. Calculate the speed of the bird. d) A car travelled for 4 hours at an average speed of 50mph. How far did the car travel? e) Dan drove his motorbike at an average speed of 40mph and travelled a distance of 200 miles. How long was Dan travelling for?

Digital resource: www.mathsworkout.co.uk – Geometry & Measure/18.Speed, Distance, Time www.sptamaths.co.uk – Courses/S1 to S3/S1/L3/October to Christmas/SDT

MNU 3-10a

10

a) Joiners tend to measure the length of objects in millimetres. i) If a joiner measures 25mm how many metres is this? ii) If a joiner measures 98mm how many metres is this? b) Calculate the AREA of these composite 2D shapes: i) ii) c) Calculate the VOLUME of this composite 3D shape:

Digital resource: www.mathsworkout.co.uk – Geometry&Measure/2.Measure2 and Geometry&Measure/11.Area/Target3 and Geometry&Measure/13.Volume/Target1 www.sptamaths.co.uk – Courses/Old Courses/Intermediate1/Topic Questions/Geometry

MNU 3-11a MTH 3-11b







11. a)

i) Copy and complete this table, showing the cost of buying books.

ii) Copy and complete:- “the total cost of books = ? x the number of books”. iii) Write the formula using symbols connecting C and B. iv) Use this formula to find the cost of 15 books.

b) This pattern is made up of equilateral triangles:-

i) Draw neatly the next pattern with 5 triangles.

ii) Copy the following table and complete it:-

iii) Write down the formula using symbols L = ? x T + ?. iv) Use your formula to decide how many lines/matches are needed to place 30 triangles in a row.

Digital resource: www.mathsworkout.co.uk – Algebra&Problem Solving/14.Sequences1 and Algebra & Problem Solving/15.Sequences2 www.sptamaths.co.uk – Courses/Old Courses/S1/2 5-14 Levels/Level F/Pattern

MTH 3-13a





12.

a) Collect like terms: 3r + 8s + 5r – 2s b) Collect like terms: y + 4x – 3y + x + 5y

c) Collect like terms: 9p + 12p + p – 22p

d) Collect like terms: 6z2 + 5z – 2z2 + 12z e) If a = 2 and b = –3 evaluate 2b + a f) If a = 2 and b = –3 evaluate 5a – 2b

g) If a = 2 and b = –3 evaluate a2 + b Digital resource: www.mathsworkout.co.uk – Algebra&Problem Solving/3.LikeTerms and Algebra & Problem Solving/8.Substitution www.sptamaths.co.uk – Courses/Old Courses/S1/2 5-14 Levels/Level F/Algebra

MTH 3-14a

13. In the diagrams below, the weighing scales are perfectly balanced: Use the diagrams to create equations and solve to find out the value of a box in each question:-

d) Find the value of x by solving the equation 5x – 1 = 24

e) Find the value of x by solving the equation 4x + 7 = 19

f) Find the value of x by solving the equation 6x – 3 = 27

Digital resource: www.mathsworkout.co.uk – Algebra&ProblemSolving/6.SolvingEquations1/Targets1&2 www.sptamaths.co.uk – Courses/Old Courses/S1/2 5-14 Levels/Level E/Algebra

MTH 3-15a MTH 3-15b







14. Using mathematical instruments to accurately draw the following triangles:

a) Draw ΔABC where AB = 10 cm, ∠CAB = 50° and ∠CBA = 65°

b) Draw ΔRYT where RY = 5 cm, ∠TRY = 35° and ∠TYR = 125° c) Use a ruler and protractor to draw a rhombus of side 5 cm which has one of its

angles of 100°

Digital resource: www.mathsworkout.co.uk – Geometry&Measure/16.ScaleDrawings/Target5 www.sptamaths.co.uk – Courses/Old Courses/S1/2 5-14 Levels/Level E/Drawings

MTH 3-16a

15. a) Use 3 LETTERS to name the following angle

b) Find the size of the angle labelled x°

c) Find the size of the angle labelled x° d) Calculate the bearing from Ackton to Dunston.





e) Calculate the bearing from Ackton to Enton. f) 2 Doll’s Houses are mathematically similar. Shown here are the front faces of both of the houses. Calculate the height of the Large Doll House.

Digital resource: www.mathsworkout.co.uk – Geometry&Measure/8.Angles and Geometry&Measure/16.ScaleDrawings/Targets3&4 and Geometry&Measure/21.Similarity/Targets1&2 www.sptamaths.co.uk – Courses/Old Courses/S1/2 5-14 Levels/Level E/Angles and Courses/Old Courses/S1/2 5-14 Levels/Level E/ScaleDrawings and

MTH 3-17a MTH 3-17b MTH 3-17c





16. Draw a 5 by 5 coordinate grid as shown. (a) Plot the points P(2,3), Q(3,1) and R(4,3). (b) S is a point to be put on the grid so that figure PQRS is a rhombus (diamond). On your diagram plot the point S and write down its coordinates. (c) Join P to R and join Q to S. You now have the two diagonals of the rhombus. Write down the coordinates of the point X where the two diagonals meet. Digital resource: www.sptamaths.co.uk – Courses/Old Courses/S1/2 5-14 Levels/LevelD/Coordinates and Courses/Old Courses/S1/2 5-14 Levels/LevelE/Negatives/Exercise4 www.mathsworkout.co.uk - Algebra&Problem /17.StraightLine1/Targets1&2 www.numeracyworkout.co.uk – Statistics&Probability /1.Coordinates

MTH 3-18a

17. a) How many lines of Symmetry does the following shapes have? i) ii) b) Copy each of the following shapes neatly and complete each one such that the bold line is a line of symmetry. i) ii)

Digital resource: www.mathsworkout.co.uk – Geometry&Measure/3.LineSymmetry

www.sptamaths.co.uk – Courses/Old Courses/(S1/2)5-14Levels/Level/Symmetry

MTH 3-19a



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18. a) The pie chart shows the different type of houses a group of 36 families stay in. i) Calculate the size of the missing angle representing those living in a flat. ii) What fraction of the 36 families stay in a detached villa? iii) of the 36 families, how many of them stay in a:

bungalow

flat

semi - detached villa ? b) The pie charts below show the grades awarded in a recent exam for two classes. At first glance, it appears that there were more A passes in Class 1 than in Class 2. Assuming that the pie charts are accurate, why might this not actually be the case? Digital resource: www.sptamaths.co.uk – Courses/Old Courses/S1/2 5-14 Levels/LevelE/Statistics www.mathsworkout.co.uk - Statistics&Probability/5.BarCharts/6.LineGraphs/7.ScatterGraphs/8.PieCharts/14.FrequencyTables/16.Histograms

MNU 3-20a MTH 3-20b MTH 2-21a MTH 3-21a





19.

A toy box contains building bricks. There are 3 green, 1 black, 9 blue, 12 orange, and 15 white bricks. (a) What is the Probability of picking a green brick? (b) What is the Probability of picking a blue brick? (c) What is the Probability of picking an orange brick? (d) What is the Probability of picking a white brick? Give your answer in its simplest form Digital resource: www.mathsworkout.co.uk - Statistics&Probability/10.IntroductionToProbability/11.ProbabilityLab /19.Probability1 www.numeracyworkout.co.uk – Statistics&Probability /10.Probability and 11.GamesofChance

MNU 3-22a


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Holistic Question 1 Skye has just purchased a new house and decides to have her garden designed as demonstrated in the diagram. She has sourced two companies to lay the grass. She is provided with the following prices:

The premium hardwood timber decking she wants costs £35 per square metre. The labour cost to fit the decking is £350. She has managed to get the pond priced and fitted for £300.

Skye has set herself a budget of £1600. However, she has her heart set on astrograss. She is willing to go 20% over budget if she can get the astrograss. Can she afford to get everything including the astrograss? If so, which company should she go with? If not, what is her best option?

MNU 3-01a MNU 3-03a MNU 3-07a MNU 3-09a MNU 3-09b MNU 3-11a MTH 3-11b



Holistic Question 2

The senior hospitality class are making shortbread to sell at the interval of the school show.

The recipe they are given is a ratio as shown below:

Butter : Sugar : Plain Flour

60g : 30g : 90g This is enough to make 6 large biscuits. The ingredients are purchased from the local supermarket Waitco:

Plain Flour: 500g = 40p 1.5kg = 75p Butter: 250g = £1.18 Caster Sugar: 500g = £1.10 2kg = £2.68 The class are optimistic and think they can sell 240 biscuits at 25p each. If they achieve their goal what is the maximum profit that the class will make?

MNU 2-11b MNU 3-01a MNU 3-08a MNU 3-09a MNU 2-09b



Solutions

1.

a) 56.796 b) 100.992 c) 2.181 d) 246.982

2. a) 105 ÷ 6 = 17.5, 18 crates b) £3 600 000 ÷ 900, £4000 c) 1018 x 8p = 8144p, £81.44 d) 325 ÷ 62 = 5.2.., 6 coaches e) 10.164 f) 67.824

3. a) -1000 b) -15 c) -400 d) -5°C + 16°C = 11°C e) 9°C – 12°C = -3°C

4. a) 2 b) 15 c) 24 d) 12 e) 2, 2, 3 f) 2, 3, 5 g) 2, 2, 2, 2, 2 h) 36 seconds

5. a) 16 b) 8 c) 27 d) 16

6. a) 17

5

b) 15% = £93, £620 + £93 = £713 c) 30% = £270, £900 - £270 = £630

d) 57

40 = 1

17

40

e) 59

42 = 1

17

42

f) 5

36

7. a) 1 : 3 b) 2 : 5 c) (i) 2 x 43cm = 86cm (ii) 129cm ÷ 43 = 3cm d) 8% = 48p, new cost £6.48 e) 30% = £36, new cost £84

8. a) ‘Pay it up’ cost = £175 + (9 x £95) = £1030, Difference in price is £80 b) ‘Pay it up’ cost = £20 + (26 x £7.50) = £215, Difference in price is £16 c) €288 d) €576 e) €720



9. a) S = 180 ÷ 3 = 60 km/h b) S = 3200 ÷ 8 = 400 mph c) S = 20 ÷ 2 = 10 km/h d) D = 4 X 50 = 200 miles e) T = 200 ÷ 40 = 5 hours

10. a) (i) 0.025 metres (ii) 0.098 metres b) (i) Total Area = 48 cm2 (ii) Total Area = 298 cm2

c) Total Volume = 171 cm3

11. a) (i) 12, 18, 24, 30, 36 (ii) the total cost of books = 6 x the number of books (iii) C = 6 x B (iv) £90 b) (i) (ii) 9, 11, 13 (iii) L = 2 x T + 1 (iv) 61 lines

12. a) 8r +6s b) 3y + 5x c) 0 d) 4z2 + 17z e) -4 f) 16 g) 1

13. a) B + 5 = 12, B = 7 b) B + 2 = 9, B = 7 c) 2B = 16, B = 8 d) 5x = 25, x = 5 e) 4x = 12, x = 3 f) 6x = 30, x = 5

14.

15. a) WFP or PFW b) x° = 144° c) x° = 77° d) 070° e) 098° f) h = 40 x 6 = 240 cm



16.

a) P, Q and R plotted (see diagram) b) S plotted (see diagram), (3,5) c) X (3,3)

17. a) (i) 0 (ii) 1 b) c)

18. a) (i) 30° (ii) 1

4 or equivalent (iii) bungalow 9, flat 3, semi-detached 15

b) You cannot assume that both classes have the same number of students

19. a) Pr (green) = 3

40

b) Pr (blue) = 9

40

c) Pr (orange) = 12

40 =

3

10

d) Pr (white) = 15

40 =

3

8

third level revision - st peter the apostle high school · third level revision all numeracy...

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