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PLC Papers

Created For:

PiXL PLC 2017 Certification

Adding and subtracting fractions 2 Grade 4 Objective: Add and subtract fractions including improper fractions and mixed numbers. Question 1 Work these out:

+

(2)

3 − 1 =

(2) Question 2

In a race, Matt took of a 50 seconds and Dom took of a minute to complete.

a) Who won the race?

(2)

b) What was the difference in time between the two reaching the finish line?

(2)


Question 3 Work out:

732 − 3

(2)

Total /10


Checking Calculations 2 Grade 4

Objective: Check calculations using approximation and estimation (including using technology)

Question 1.

For each calculation write down the solution you consider to be the best estimate.

(a) 56.987 ÷ 7.876 (i) 6 (ii) 7 (iii) 9

………………….. (1)

(b) 1.11 x 27.8 (i) 20 (ii) 30 (iii) 40

..……………….. (1)

(c) 82.1 ÷ 0.99

(i) 8 (ii) 80 (iii) 800

.………………….. (1)

(d) 9.992

(i) 20 (ii) 100 (iii) 1000

..………………….. (1)

(Total 4 marks)


Question 2 Use an estimate to show if these answers are correct and explain your answer

(a) 48% of £3244.45 = £1557.34

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

.…………………... (2)

(b) 11% of £49.76 = £9.87

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

……………………. (2)

(c) 23% of £103.87 = £ 50.67

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

……………………. (2)

(Total 6 marks)


Total /10


Compound Measures 2 Grade 4

Objective: Use Compound Measures

Question 1.

Convert the following units

(a) 2.5 hrs to mins

………………….. (1)

(b) 252 mins to hours

..……………….. (1)

(c) 0.25 hours to mins

.………………….. (1)

(d) 48480 minutes to hours

………………….. (1)

(Total 4 marks)


Question 2

(a) A car travels 75mph for 90minutes. Calculate the distance travelled.

…………………….. (2)

(b) It takes a bus 30 minutes to travel 15 miles. Calculate the average speed.

…………………….. (2)

(Total 4 marks)

Question 3.

Eleanor leaves for work at 8.45am. She lives 15 miles from work and travels at a speed of 30mph. At what

time does she arrive for work?

……………. (2)

(Total 2 mark)

Total /10


Converting Metric Units 2 Grade 4

Objective: Know and use metric conversions of length, area, volume and capacity

Question 1.


(a) A triangle has a base of 2m and a height of 2m. Calculate the area of the rectangle in centimetres.

…………………��.. (2)

(b) A square has an area of 100c�2. What is the area in metres?

..……………… ��.. (2)

(c) A square has an area of 4900��2. Find the length of one side in metres.

.…………………m.. (2)

(d) A cube has a volume has a 300��3. Find the volume in �3

..…………………�3.. (2)

(Total 8 marks)


Question 2

(a) The perimeter of an octagon is 40 metres. Find the length of one side in cm.

……………………cm.. (2)

(Total 2 marks)

Total /10


Decimals 2 Grade 3

Objective: Understand adding, subtracting multiplying and dividing decimals.

Question 1

Work out a) 0.3 × 0.2

b) 0.03 × 0.12 (2)

Question 2 Work out 0.8965 ÷ 0.05

(2)

Question 3

Electricity is 41p per unit.

Helen’s household uses 250 units.

Work out the total cost of the electricity. (2)


(b) Gas is 31p per unit. Helen’s household uses 225 units. Work out the total cost of the gas.

(2)

Question 4 Evaluate:

(2)

Total /10


Estimation 2 Grade 4

Objective: Estimate answers

Question 1.

Use approximations to estimate the solution to the following

(a)

14.867

2.7

…………………….. (2)

(b)

989.087

99

…………………….. (2)

(Total 4 marks)

Question 2

Estimate the solution to

0.09 x 41

…………………….. (Total 2 marks)


3. Question 3.

Use approximations to find estimates to the following

(a)

1.24358 × 101

……………. (2)

(b) √35.98

……………. (2)

(Total 4 marks)

Total /10


Fractions and percentages 2 Grade 4

Objective: Interpret fractions and percentages as operators.

Question 1 Work out five eights of 512.

(2)

Question 2 At ‘Amazing Maths Academy’ (AMA) there are 1500 students and 150 teachers.

25% of the students are left-handed.

18% of the teachers are left-handed.

How many left-handed students and teachers are there altogether? (2)

Question 3 a) Nisa scored 13 marks out of 40 in her Science test. What percentage is this?

(2) b) John buys a watch for £20.00 and sold it for £15.00. Find John’s percentage loss?

(2) Question 4 Alex scored 18 out of 20 in a maths test. What percentage did she score?

(2)

Total /10


Fractions and ratio problems 2 Grade 4 Objective: Identify and work with fractions in ratio problems. Question 1 Share £729 in the ratio 3:4:2. Find the value of largest share. (2) Question 2 In similar triangles PST and PQR side PS = 9 cm, side ST = 8cm, side PT = 7 cm and side SR=2 cm. Find a) Side RQ. Give your answer to 1 decimal place.

(2) b) Side TQ. Give your answer to 1 decimal place.

(2)

P

R Q

8cm S T

9cm

NOT TO SCALE


Question 3 a) The ratio of boys to girls in a class is 3 : 17

What fractions of students are boys? (2) b) The ratio of yellow balls to blue balls in a bag is 13 : 40 What fraction of the balls are yellow? (2)

Total /10


Interpret calculator displays 2 Grade 4 Objective: Interpret calculator displays. Question 1 Find the value of: (2.8 x 10 9) ÷ (4 x 10 5). Give your answer in standard form. (2) Question 2 Find the area of the circle with the radius of 7.2 cm. Give your answer correct to 1 d.p . (2) Question 3 Find the circumference’ of the circle with a radius of 9.4 cm. Give your answer as a multiple of π. (2) Question 4 Find the value of: (2.8 x 10 9) x (4 x 10 5) . Give your answer in standard form. (2)


Question 5 Using a calculator work out the answers to these questions give your final answers correct to 2.d.ps

√(7.3 2 – 2.5 2)

√(17.3 2 – 6.3 2)

(2)

Total /10


LCM and HCF 2 Grade 4 Objective: Understand and find LCM and HCF.

Question 1

Find the HCF of 36 and 42. (2)

Question 2

Find the LCM of 52 and 78. (2)

Question 3 Express 60 as a product of its prime factors using any method.

Question 4 (2) Which of the numbers 3, 6, 13, 12, 18, and 8 are factors of 48?

(2)


Question 5

Christmas cards are sold in packs of 30

Postage stamps are sold in packs of 12

John needs the same number of Christmas cards and Postage stamp.

What is the smallest number of each pack he can buy? (2)

Total /10


Listing Outcomes 2 Grade 3 Objective: Applying systematic listing strategies.

Question 1 How many numbers between 20 and 100 have at least one digit that is 6? (2) Question 2 At ‘The Amazing Maths Academy’, a fruit shop sells Apples (A), Pears (P) and Bananas (B).

Gaurav buys 3 fruits at random.

(a) List all the possible pairs of fruits he could buy.

(2)

(b) Find the probability that two out of the three fruits are the same.

(2)


Question 3

Luca has 5 shirts, 4 pairs of trousers and 5 pairs of socks.

a) How many different combinations of shirt, trousers and socks does he have?

(2)

b) He chooses a shirt, trouser and a pair of socks.

How many combinations are there now?

(2)

Total /10


Multiples and factors 2 Grade 4 Objective: Understand and find multiples and factors.

Question 1

a) Which of the numbers 3,15,18, 36, 72. 100 and 108 are multiples of 12.

b) Which of the numbers 3,15, 6, 8, 3, 7, 2. 48 and 18 are factors of 42. (2)

Question 2 Write 96 as the product of its prime factors.

Give your answer in index form.

(2)

Question 3 Find LCM of 16 and 24.

(2)

Question 4 Find HCF of 32 and 48.

(2)


Question 5

Is 51 a prime number? Explain your answer.

(2)

Total /10


Multiplying fractions 2 Grade 4 Objective: Multiply fractions including improper fractions and mixed numbers. Question 1 Work out these questions always give your answer in the simplest form:

732 x 3

(2)

3 x 2

(2)

x

(2)


Question 2 Which is smaller? You must show your working out.

3 x 8 or 5 x 2

(2)

Which is bigger? You must show your working out.

4 x 5 or 3 x 6

(2)

Total /10


Operations 2 Grade 4 Objective: Understand the relationships between operations e.g. Inverse operations.

Question 1

Work out the value of (152 −102)2 (2)

Question 2 Emma says that

16 + 4 x 8 = 160

Jack says that

16 + 4 x 8 = 48

Who is correct? Explain your answer.

(2)

Question 3 Find the missing number in the following

(64 ÷ 8) + (-3 +

) = 24 (2)


Question 4

Which is smaller : 15+ 4 x 3 or (15+4) x 3 (2)

Question 5

Ravi thinks of a number. He divides the number by 3 and takes away 2. His answer is 7. What number did he think of?

(2)

Total /10


Order of operations 2 Grade 4 Objective: Understand and use the order of operations. Question 1 A cup of coffee costs £1.50 . A cup of tea costs £1.30 .

I buy 2 cups of coffee and two cups of tea.

How much change should I get from a £20 note?

(2) Question 2 Use all of the numbers 9, 5, 9 and 2 and any operations to write a numerical expression which is equal to 2.

(2)

Question 3 Which is larger

7+8÷2 or (-5+3) ÷ 2 (2)

Question 4

Find the value of (44 −1)2

(2)


Question 5 Insert brackets, if needed, to make the answer correct: 7+5 x 9-3=37 (1) 9+ 52 – 7 x 2=182 (1)

Total /10


Powers 2 Grade 4 Objective: Understand and use powers, including square numbers up to 15 x 15.

Question 1

Solve 3x = 243

(2)

Question 2

Write down the value of 82, 53, 25 (2) Question 3 Work out the value of 86 ÷ 85

(2) Question 4 Estimate the value of (9.08) 2

(2)

Question 5

Solve 2x = 1024 (2)

Total /10


Prime numbers 2 Grade 3 Objective: Understand prime numbers. Question 1 Write down all the prime numbers between 90 and 112. (2) Question 2 Is 57 prime number?

Explain your answer: (2)

Question 3 a) 17,13,111, 14, 16, 57, 91, 15 and 1

Which two numbers when added together equals a prime number?

(1)

NO YES


b) Write down all the prime numbers: (2)

Question 4

Give an example of prime number whose digit sum is 2 less than than a square number. (1)

Question 5

Write 111 as a product of its prime factors. (2)

Total /10


Rounding 2 Grade 5

Objective: Round to an appropriate degree of accuracy (e.g. to decimal places or significant figures)

Question 1.

Round the following to the given degree of accuracy

(a) 2100.0012 to 1 decimal place

…………………….. (1)

(b) 0.009 to 2 decimal places

…………………….. (1)

(Total 2 marks)

Question 2

Round the following numbers to the degree of accuracy given

(a) 23.987 to 1 significant figure

…………………….. (1)

(b) 0.009876 to 2 significant figures

…………………….. (1)

(Total 2 marks)


Question 3.

Round these numbers to the nearest integer

(a) 0.0765

……………. (1)

(b) 1200987.0998

…………………….. (1)

(Total 2 marks)

4. Round these numbers to an appropriate degree of accuracy

(a) £67.098876

…………………….. (1)

(b) 16 mins 345654 seconds

…………………….. (1)

(Total 2 marks)


5. Round the following numbers to the degree of accuracy given

(a) 5.8764 to 3.d.p

……………. (1)

(b) 0.099780 to 4.d.p

…………….. (1)

(Total 2 marks)

Total /10


Standard form 2 Grade 4 Objective: Understand and use standard form for very large and very small numbers. Question 1 Write as ordinary numbers

a) 2.7654 x 10 5

b) 7.867899 x 10 −3

(2) Question 2 Write 867200009 in standard form. (1) Question 3 Write in standard form: a) 797.4

b) 0.0465

(2)


Question 4 Write these numbers in ascending order:

14 4798 1.76 x 10 4 1.45 x 10 3 (2) Question 5 Write three quarter of a million in standard form. (2) Question 6 Write 132344 in standard form:

(1)

Total /10


Terminating decimals and fractions 2 Grade 4 Objective: Convert between and work with terminating decimals and their equivalent fractions (including ordering).

Question 1

48, 1218, 350 , 37, 910, 16

a) Write each fraction as a decimal. (2) b) Which fractions are terminating? (2) Question 2 Order these fractions; starting with smallest first: 12, 37, 18 (2) Question 3 . . Change 0.14 into a fraction. (2)


Question 4 Convert these fractions into decimals: 2011, 8013 (2)

Total /10


Using standard Units 2 Grade 3

Objective: Use standard units of mass, length, time money and other measures

Question 1. Choose the most appropriate units for the following

(a) The weight of an orange Grams Kilograms Kilometres

(1)

(b) The perimeter of a playground Milli litres

Metres

Centimetres

(1)

(Total 2 marks)

Question 2

(a) Estimate the length of a finger nail

(i) 2.5cm (ii) 25cm (iii) 5m (1)

(b) Estimate the height of a child

(i) 100cm (ii) 100m (iii) 20mm (1)

(c) Estimate the weight of a man

(i) 5kg (ii) 75kg (iii) 200kg (1)

(d) Estimate the amount of water in a bath


(i) 200mls (ii) 200litres (iii) 2000cm (1)

(Total 4 mark)

Question 3.

State the metric unit that you would use to measure the following

(a) A bottle of water .................................... (1)

(b) The length of a classroom ................................... (1)

(c) The weight of a person ................................... (1)

(d) The height of a door .................................... (1)

(Total 4 marks)

Total /10

PLC Papers

Created For:


Adding and subtracting fractions 2 Grade 4 Solutions Objective: Add and subtract fractions including improper fractions and mixed numbers. Question 1 Work these out:

+

= (M1)

= (A1)

(2)

3 − 1 = (M1)

= (A1)

(2) Question 2

In a race, Matt took of a 50 seconds and Dom took of a minute to complete.

a) Who won the race?

(2)

(1/4 x 50) = 12.5 seconds (1/5 x 60)= 12 seconds (M1) Dom was quicker. (A1) b) What was the difference in time between the two reaching the finish line?

(2) 12.5 – 12 (M1) = 0.5 seconds (A1)


Question 3

Work out:

732 − 3

= 5

16

3

23− (M1)

=15

67

(A1)

(2)

Total /10


Checking Calculations 2 SOLUTIONS Grade 4

Objective: Check calculations using approximation and estimation (including using technology)

Question 1.

For each calculation write down the solution you consider to be the best estimate.

(a) 56.987 ÷ 7.876 (i) 6 (ii) 7 (iii) 9

……7 (B1)…………….. (1)

(b) 1.11 x 27.8 (i) 20 (ii) 30 (iii) 40

30 (B1..……………….. (1)

(c) 82.1 ÷ 0.99

(i) 8 (ii) 80 (iii) 800

…… 80 (B1…………(1)

(d) 9.992

(i) 20 (ii) 100 (iii) 1000

100 (B1………………….. (1)

(Total 4 marks)


Question 2 Use an estimate to show if these answers are correct and explain your answer

(a) 48% of £3244.45 = £1557.34

……50% of 3200=1600 so correct

(M1)…………………………………………………………………………

(A1)………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

.…………………... (2)

(b) 11% of £49.76 = £9.87

10% of 50= 5 so incorrect ………………………………………………………………………………

(M1)…………………………………………………………………………

(A1)………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

……………………. (2)

(c) 23% of £103.87 = £ 50.67

25% of 100 = 25 so incorrect………………………………………………………………………………

(M1)…………………………………………………………………………

(A1)………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………


………………………………………………………………………………

………………………………………………………………………………

……………………. (2)

(Total 6 marks)

Total /10


Compound Measures 2 SOLUTIONS Grade 4

Objective: Use Compound Measures

Question 1.


(a) 2.5 hrs to mins (B1)

…150MINS………….. (1)

(b) 252 mins to hours (B1)

..4 HRS 12 MINS /4.2HRS…….. (1)

(c) 0.25 hours to mins (B1)

.…15MINS……………….. (1)

(d) 48480 minutes to hours (B1)

……………808…….. (1)

(Total 4 marks)


Question 2

(a) A car travels 75mph for 90minutes. Calculate the distance travelled.

75 = 1 hour

37.5 in 30 mins

1.5 x 75 (M1)

………112.5 miles……(A1)……….. (2)

(b) It takes a bus 30 minutes to travel 15 miles. Calculate the average speed.

30 mins = 15 miles (x2) (M1)

1 hour = 30 miles (A1)

…………30mph………….. (2)

(Total 4 marks)

Question 3.

Eleanor leaves for work at 8.45am. She lives 15 miles from work and travels at a speed of 30mph. At what

time does she arrive for work?

Time = distance ÷ speed

Time = 15 ÷ 30 = 0.5 hour = 30 mins (M1)

8.45+ 30 mins = 9.15 am (A1)

……9:15am………. (2)


(Total 2 mark)

Total /10


Converting Metric Units 2 SOLUTIONS Grade 4

Objective: Know and use metric conversions of length, area, volume and capacity

Question 1.


(a) A triangle has a base of 2m and a height of 2m. Calculate the area of the rectangle in centimetres. 0.5(2X2)= 2METRES2 (M1)

20000CM2=2M2 (A1)

……20000……………��.. (2)

(b) A square has an area of 100c�2. What is the area in metres?

..0.01………(B2)……… ��.. (2)

(c) A square has an area of 4900��2. Find the length of one side in metres. √��=70

70/100 = 0.7 (M1)

.…0.7…(A1)……………m.. (2)

(d) A cube has a volume has a 300��3. Find the volume in �3

..……0.0003…(B2)…………�3.. (2)

(Total 8 marks)


Question 2

(a) The perimeter of an octagon is 40 metres. Find the length of one side in cm.

40/8= 5METRES (M1)

500CM=5M (A1)

……500………………cm.. (2)

(Total 2 marks)

Total /10


Decimals 2 Grade 3 Solutions

Objective: Understand adding, subtracting multiplying and dividing decimals.

Question 1

Work out a) 0.3 × 0.2

= 0.06 (A1)

b) 0.03 × 0.12 =0.0036 (A1)

(2)

Question 2 Work out 0.8965 ÷ 0.05

=89.65/5 (M1) =17.93 (A1) (2)

Question 3

Electricity is 41p per unit.

Helen’s household uses 250 units.

Work out the total cost of the electricity. 41p x 250 (M1) = 10250p or £102.50 (A1) (2)


(b) Gas is 31p per unit. Helen’s household uses 225 units. Work out the total cost of the gas.

31p x 225 = 6975p (M1) £69.75 (A1) (2)

Question 4 Evaluate:

= 1.35/ 0.5 (M1) =2.7 (A1)

(2)

Total /10


Estimation 2 SOLUTIONS Grade 4

Objective: Estimate answers

Question 1.

Use approximations to estimate the solution to the following

(a)

14.867

2.7

15÷3=5 (M1)

5 (A1)

…………5………….. (2)

(b)

989.087

99

1000÷100 (M1)

10 (A1)

……………10……….. (2)

(Total 4 marks)


Question 2

Estimate the solution to

0.09 x 41

0.1x40 (M1)

4 (A1)

………4…………….. (Total 2 marks)

3. Question 3.

Use approximations to find estimates to the following

(a)

1.24358 × 101

1x100 (M1)

100 (A1)

……100………. (2)

(b) √35.98 √�� = � (M1)

6 (A1)

……6………. (2)


(Total 4 marks)

Total /10


Fractions and percentages 2 Grade 4 Solutions

Objective: Interpret fractions and percentages as operators.

Question 1 Work out five eights of 512.

=5/8 x 512 (M1) = 320 (A1) (2)

Question 2 At ‘Amazing Maths Academy’ (AMA) there are 1500 students and 150 teachers.

25% of the students are left-handed.

18% of the teachers are left-handed.

How many left-handed students and teachers are there altogether? 25/100 x 1500 = 375 18/100 x 150 = 27 (M1) 375 +27 = 402 (A1) (2)

Question 3 a) Nisa scored 13 marks out of 40 in her Science test. What percentage is this?

13/40 x 100 = 32.5 % (A2)

(2) b) John buys a watch for £20.00 and sold it for £15.00. Find John’s percentage loss?

5/20 x 100 = 25% (A2)

(2) Question 4 Alex scored 18 out of 20 in a maths test. What percentage did she score?

18/20 x 100 = 90 % (A2) (2)


Total /10


Fractions and ratio problems 2 Grade 4 Solutions Objective: Identify and work with fractions in ratio problems. Question 1 Share £729 in the ratio 3:4:2. Find the value of largest share. £729 / 9 = 81 4 x 81= £324 (2) Question 2

In similar triangles PST and PQR side PS = 9 cm, side ST = 8cm, side PT = 7 cm and side SR=2 cm. Find a) Side RQ. Give your answer to 1 decimal place. SF = 11/9 11/9 x 8 (M1) = 9.8 cm (A1)

(2) b) Side TQ. Give your answer to 1 decimal place. 11/9 x 7 = 8.5….. (M1) 8.5…-7= 1.6…cm (A1)

(2)

P

R Q

8cm S T

9cm

NOT TO SCALE


Question 3 a) The ratio of boys to girls in a class is 3 : 17

What fractions of students are boys? 3/20 (A2) (2) b) The ratio of yellow balls to blue balls in a bag is 13 : 40 What fraction of the balls are yellow? 13/53 (A2) (2)

Total /10


Interpret calculator displays 2 Grade 4 Solutions Objective: Interpret calculator displays. Question 1 Find the value of: (2.8 x 10 9) ÷ (4 x 10 5). Give your answer in standard form. =7000 =7 x 103 (A2) (2) Question 2 Find the area of the circle with the radius of 7.2 cm. Give your answer correct to 1 d.p . A=πr2 A= π x 7.2 2 (M1) A= 162.9 cm2 (1.d.p) (A1) (2) Question 3 Find the circumference’ of the circle with a radius of 9.4 cm. Give your answer as a multiple of π. C=2πr C = 2 x π x 9.4 (M1) C= 18.8 π cm (A1) (2) Question 4 Find the value of: (2.8 x 10 9) x (4 x 10 5). Give your answer in standard form. = 1.12 X 1015 (A2) (2)


Question 5 Using a calculator work out the answers to these questions give your final answers correct to 2.d.ps

√(7.3 2 – 2.5 2)

√(17.3 2 – 6.3 2)

= 6.85857128/16.11210725 (M1) =0.43 (2.d.p.) (A1) (2)

Total /10


LCM and HCF 2 Grade 4 Solutions Objective: Understand and find LCM and HCF.

Question 1

Find the HCF of 36 and 42. Factors of 36: (18,2)(12,3)(9,4)(1,36) Factors of 42: (21,2)(14,3)(7,6)(1,42) (M1) HCF: 6 (A2) (2)

Question 2

Find the LCM of 52 and 78. Multiples of 52: 52, 104, 156, Multiples of 78: 78, 156, (M1) LCM: 156 (A1) (2)

Question 3 Express 60 as a product of its prime factors using any method.

(M1) 2 x 2 x 3 x 5 OR 22 x 31 x 51 (A2)


Question 4 (2) Which of the numbers 3, 6, 13, 12, 18, and 8 are factors of 48? To find out : 48/3, 48/6, 48/13, 48/12, 48/18, 48/8 (M1) 3, 6,12,8 (A1)

(2)


Question 5

Christmas cards are sold in packs of 30

Postage stamps are sold in packs of 12

John needs the same number of Christmas cards and Postage stamp.

What is the smallest number of each pack he can buy? Multiples of 30: 30, 60, 90, 120, Multiples of 12: 12, 24, 36, 48, 60, (M1) LCM: 60 (A1) (2)

Total /10


Listing Outcomes 2 Grade 3 Solutions Objective: Applying systematic listing strategies.

Question 1 How many numbers between 20 and 100 have at least one digit that is 6? 10 + 7 = 17 (M1 either 10 or 7 seen, A1 for 17) (NB 17 scores B2) (2) Question 2 At ‘The Amazing Maths Academy’, a fruit shop sells Apples (A), Pears (P) and Bananas (B).

Gaurav buys 3 fruits at random.

(a)

.

List all the possible pairs of fruits he could buy

AA

PP

AP

PA

(B2)

(2)

(b) Find the probability that two out of the fruits are the same.

1/2 (A2) (2)


Question 3

Luca flips two coins.

a) List all the possible outcomes?

(H,H),(T,T), (H,T), (T,H) (B2)

(2)

b) What’s the probability of getting two heads?

=1/4 (A2)

(2)

Total /10


Multiples and factors 2 Grade 4 Solutions Objective: Understand and find multiples and factors.

Question 1

a) Which of the numbers 3,15,18, 36, 72. 100 and 108 are multiples of 12.

36, 72, 108 (A2)

b) Which of the numbers 3,15, 6, 8, 3, 7, 2. 48 and 18 are factors of 42. (2) 3,6,7,2, (A2)

Question 2 Write 96 as the product of its prime factors.

Give your answer in index form.

(M1) 25 x 31 (A1)

(2)

Question 3 Find LCM of 16 and 24.

Multiple of 16: 16, 32, 48, 64, 80 Multiples of 24: 24, 48, 72, 96, 120, (M1) LCM: 48 (A1) (2)


Question 4 Find HCF of 32 and 48.

Factors of 32: (16,2)(8,4)(1,32) Factors of 48: (24,2)(16,3)(12,4)(8,6)(1,48) (M1) HCF: 16 (A1) (2)

Question 5

Is 51 a prime number? Explain your answer. 51 is a not a prime number as it has more than just factors 1 and itself. It is divisible by 3 (and 17).

(A2) (2)

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Multiplying fractions 2 Grade 4 Solutions Objective: Multiply fractions including improper fractions and mixed numbers. Question 1 Work out these questions always give your answer in the simplest form:

732 x 3

= 233 x

165 (M1)

=36815 (A1)

(2)

3 x 2

= 225 x

115 (M1)

= 24225 (A1)

(2)

x

= 2744 (A2)

(2)


Question 2 Which is smaller? You must show your working out.

3 x 8 or 5 x 2

= 29.3650 or 15.10714 (M1)

=3 x 8 > 5 x 2 (A1)

(2)

Which is bigger? You must show your working out.

4 x 5 or 3 x 6

=23.3 or 25.4571428 (M1)

= 4 x 5 < 3 x 6 (A1)

(2)

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Operations 2 Grade 4 Solutions Objective: Understand the relationships between operations e.g. Inverse operations.

Question 1

Work out the value of (152 −102)2 =(225-100)2 =1252 =125 x 125 (M1) =15625 (A1) (2)

Question 2 Emma says that

16 + 4 x 8 = 160

Jack says that

16 + 4 x 8 = 48

Who is correct? Explain your answer.

Jack- using BIDMAS, 16 +32= 48 (A2) (2)

Question 3 Find the missing number in the following

(64 ÷ 8) + (-3 + LET THE SQAURE = X

8 -3X = 24 -3X = 24-8 -3X= 16 (M1) X= -16/3 (A1)

) = 24 (2)


Question 4

Which is smaller : 15+ 4 x 3 or (15+4) x 3 = 27 or 57 = 15+ 4 x 3 < (15+4) x 3 (A2) (2)

Question 5

Ravi thinks of a number. He divides the number by 3 and takes away 2. His answer is 7. What number did he think of?

Let the number Ravi thinks of = X (X/3)-2= 7 (X/3)= 9 (M1) X=27 (A1) (2)

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Order of operations 2 Grade 4 Solutions Objective: Understand and use the order of operations. Question 1 A cup of coffee costs £1.50 . A cup of tea costs £1.30 .

I buy 2 cups of coffee and two cups of tea.

How much change should I get from a £20 note? = 20- ( (2 x £1.50) + (2 x £1.30) ) (M1) = £14.40 (A1)

(2) Question 2 Use all of the numbers 9, 5, 9 and 2 and any operations to write a numerical expression which is equal to 2.

9- (5+9)/2 = 2 (A2) (2)

Question 3 Which is larger

7+8÷2 or (-5+3) ÷ 2 = 11 or -1 (M1) =11 > -1 (A1) (2)

Question 4

Find the value of (44 −1)2 =(256-1)2 =2552 (M1) =65025 (A1)

(2)


Question 5 Insert brackets, if needed, to make the answer correct: 7+5 x (9-3)=37 (A1) (1) (9+ 5)2 – 7 x 2=182 (A1) (1)

Total /10


Powers 2 Grade 4 Solutions Objective: Understand and use powers, including square numbers up to 15 x 15.

Question 1

Solve 3x = 243 3 x = 35 (M1) X = 5 (A1) (2)

Question 2

Write down the value of 82, 53, 25 (2) 64, 125, 32 (A2) Question 3 Work out the value of 86 ÷ 85

=81 (M1) = 8 (A1) (2) Question 4 Estimate the value of (9.08) 2

= 9 2 (M1)

=81 (A1)

(2)

Question 5

Solve 2x = 1024 2 x = 2 10 (M1) x = 10 (A1) (2)

Total /10


Prime numbers 2 Grade 3 Solutions Objective: Understand prime numbers. Question 1 Write down all the prime numbers between 90 and 112. 97 101 103 107 109 (A1) (2) Question 2 Is 57 prime number?

Explain your answer:

No as 57 has more than 2 factors. It doesn’t have two factors only ( 1 and itself). For example it is divisible by 3. Prime numbers are numbers that only have factors 1 and itself. (A2)

(2)

Question 3 a) 17,13,111, 14, 16, 57, 91, 15 and 1

Which two numbers when added together equals a prime number?

16+57 = 73 (A1) (1)

NO YES


b) Write down all the prime numbers: 13, 17 (B2) (2)

Question 4

Give an example of prime number whose digit sum is 2 less than than a square number. 11 (B1) (1)

Question 5

Write 111 as a product of its prime factors.

(M1) 31 x 371 (A2) (2)

Total /10


Rounding 2 SOLUTIONS Grade 5

Objective: Round to an appropriate degree of accuracy (e.g. to decimal places or significant figures)

Question 1.

Round the following to the given degree of accuracy

(a) 2100.0012 to 1 decimal place

……2100.0……………(A1)….. (1)

(b) 0.009 to 2 decimal places

……0.01………… A1)…….. (1)

(Total 2 marks)

Question 2

Round the following numbers to the degree of accuracy given

(a) 23.987 to 1 significant figure

……20………… A1)…….. (1)

(b) 0.009876 to 2 significant figures

……0.0099………… A1)…….. (1)

(Total 2 marks)


Question 3.

Round these numbers to the nearest integer

(a) 0.0765

……0… A1)……. (1)

(b) 1200987.0998

……………1200987… A1)…….. (1)

(Total 2 marks)

4. Round these numbers to an appropriate degree of accuracy

(a) £67.098876

……………£67.10… A1)…….. (1)

(b) 16 mins 345654 seconds

……16mins 35 seconds………… A1)…….. (1)

(Total 2 marks)


5. Round the following numbers to the degree of accuracy given

(a) 5.8764 to 3.d.p

5.876……… A1)……. (1)

(b) 0.099780 to 4.d.p

0.0998……… A1)…….. (1)

(Total 2 marks)

Total /10


Standard form 2 Grade 4 Solutions Objective: Understand and use standard form for very large and very small numbers. Question 1 Write as ordinary numbers

a) 2.7654 x 10 5

b) 7.867899 x 10 −3

a) 276540 b) 0.007867899 (A2)

(2) Question 2 Write 867200009 in standard form. 8.67200009 x 10 8

(A2) (1) Question 3 Write in standard form: a) 797.4

b) 0.0465

7.974 x 102 (A1) 4.65 x 10-2 (A1) (2)


Question 4 Write these numbers in ascending order:

14 4798 1.76 x 10 4 1.45 x 10 3 144798, 17600, 1450 (M1) 1)1.45 x 10 3 2)1.76 x 10 4 (A1) 3)14 4798 (2) Question 5 Write three quarter of a million in standard form. ¾ x 1000000 = 750000 (M1) 7.5 x 105 (A1) (2) Question 6 Write 132344 in standard form: 1.32344 x 10 5 (A1)

(1)

Total /10


Terminating decimals and fractions 2 Grade 4 Solutions Objective: Convert between and work with terminating decimals and their equivalent fractions (including ordering).

Question 1

48, 1218, 350 , 37, 910, 16

a) Write each fraction as a decimal. 0.5,0.666.,0.06,0.428571….,0.9,0.16… (A2) (2) b) Which fractions are terminating? 48, 350 , 910, (A2)

(2) Question 2 Order these fractions; starting with smallest first: 12, 37, 18 0.5, 0.43 (2 sig fig), 0.125 (2) Question 3 . . Change 0.14 into a fraction. X= 0.14 14 14 -(1) 100X= 14.1414 14 -(2) 99X = 14 (M1) X= 14/99 (A1)


(2) Question 4

Convert these fractions into decimals: 2011, 8013

(M1) 1.818 (A1)

(M1) 6.153 (A1) (2)

Total /10


Using Standard Units 2 SOLUTIONS Grade 3

Objective: Use standard units of mass, length, time money and other measures

Question 1. Choose the most appropriate units for the following

(a) The weight of an orange Grams (B1) Kilograms Kilometres

(1)

(b) The perimeter of a playground Milli litres

Metres(B1)

Centimetres

(1)

(Total 2 marks)

Question 2

(a) Estimate the length of a finger nail (B1)

(i) 2.5cm (ii) 25cm (iii) 5m (1)

(b) (b)Estimate the height of a child (B1)

(i) 100cm (ii) 100m (iii) 20mm (1)

(c) (c )Estimate the weight of a man (B1)

(i) 5kg (ii ) 75kg (iii) 200kg (1)


(d) Estimate the amount of water in a bath (B1)

(i) 200mls (ii) 200litres (iii) 2000cm (1)

(Total 4 mark)

Question 3.

State the metric unit that you would use to measure the following

(a) (a) A bottle of water (B1)

...mls................................. (1)

(a) (b) The length of a classroom (B1)

.......metres............................ (1)

(a) (c) The weight of a person (B1)

......kg............................. (1)

(a) (d) The height of a door (B1)

........m............................ (1)

(Total 4 marks)

Total /10

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