Download grade-4-number - King`s Lynn Academy

PLC Papers
Created For:
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)
PiXL PLC 2017 Certification
Question 3
Work out:
72 −3
3
(2)
Total /10
PiXL PLC 2017 Certification
Checking Calculations 2
Objective:
Grade 4
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)
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
Total /10
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
Converting Metric Units 2
Objective:
Grade 4
Know and use metric conversions of length, area, volume and capacity
Question 1.
Convert the following units
(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?
(c) A square has an area of 4900��2 . Find the length of one side in metres.
..……………… �� .. (2)
.…………………m.. (2)
(d) A cube has a volume has a 300��3 . Find the volume in �3
..…………………�3 .. (2)
(Total 8 marks)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
(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
PiXL PLC 2017 Certification
Estimation 2
Objective:
Grade 4
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)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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
P
NOT TO SCALE
9cm
S
8cm
R
T
Q
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)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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
Which of the numbers 3, 6, 13, 12, 18, and 8 are factors of 48?
(2)
(2)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
Question 5
Is 51 a prime number? Explain your answer.
(2)
Total /10
PiXL PLC 2017 Certification
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:
72 x3
3
(2)
3
x2
(2)
x
(2)
PiXL PLC 2017 Certification
Question 2
Which is smaller? You must show your working out.
3
x8
or
5
x2
(2)
Which is bigger? You must show your working out.
4
x5
or
3
x6
(2)
Total /10
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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?
NO
YES
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)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
Rounding 2
Objective:
figures)
Grade 5
Round to an appropriate degree of accuracy (e.g. to decimal places or significant
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)
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
Terminating decimals and fractions 2
Grade 4
Objective: Convert between and work with terminating decimals and their equivalent fractions
(including ordering).
Question 1
4
,
8
12
,
18
3
50
3
, ,
7
9
,
10
1
6
a) Write each fraction as a decimal.
(2)
b) Which fractions are terminating?
(2)
Question 2
Order these fractions; starting with smallest first:
1
,
2
3
,
7
1
8
(2)
Question 3
..
Change 0.14 into a fraction.
(2)
PiXL PLC 2017 Certification
Question 4
Convert these fractions into decimals:
20 80
,
11 13
(2)
Total /10
PiXL PLC 2017 Certification
Using standard Units 2
Objective:
Grade 3
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
Millilitres
Metres
Centimetres
(1)
(Total 2 marks)
Question 2
(a) Estimate the length of a finger nail
(i)
2.5cm
(ii) 25cm
(iii) 5m
(1)
(iii) 20mm
(1)
(iii) 200kg
(1)
(b) Estimate the height of a child
(i)
100cm
(ii) 100m
(c) Estimate the weight of a man
(i)
5kg
(ii) 75kg
(d) Estimate the amount of water in a bath
PiXL PLC 2017 Certification
(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
PiXL PLC 2017 Certification
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
of a 50 seconds and Dom took
In a race, Matt 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
Dom was quicker.
(M1)
(A1)
b) What was the difference in time between the two reaching the finish line?
(2)
12.5 – 12
(M1)
= 0.5 seconds (A1)
PiXL PLC 2017 Certification
Question 3
Work out:
72 −3
3
23 16
−
3 5
67
=
15 (A1)
=
(M1)
(2)
Total /10
PiXL PLC 2017 Certification
Checking Calculations 2
Objective:
SOLUTIONS
Grade 4
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)
PiXL PLC 2017 Certification
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)………………………………………………………………………………
………………………………………………………………………………
………………………………………………………………………………
PiXL PLC 2017 Certification
………………………………………………………………………………
………………………………………………………………………………
……………………. (2)
(Total 6 marks)
Total /10
PiXL PLC 2017 Certification
Compound Measures 2
Objective:
SOLUTIONS
Grade 4
Use Compound Measures
Question 1.
Convert the following units
(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)
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
(Total 2 mark)
Total /10
PiXL PLC 2017 Certification
Converting Metric Units 2
Objective:
SOLUTIONS
Grade 4
Know and use metric conversions of length, area, volume and capacity
Question 1.
Convert the following units
(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)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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
=17.93
(A1)
(M1)
(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)
PiXL PLC 2017 Certification
(b) Gas is 31p per unit.
Helen’s household uses 225 units. Work out the total cost of the gas.
31p x 225 = 6975p
£69.75
(M1)
(A1)
(2)
Question 4
Evaluate:
= 1.35/ 0.5
=2.7
(M1)
(A1)
(2)
Total /10
PiXL PLC 2017 Certification
Estimation 2
Objective:
SOLUTIONS
Grade 4
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)
PiXL PLC 2017 Certification
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)
√�� = � (M1)
√35.98
6 (A1)
……6………. (2)
PiXL PLC 2017 Certification
(Total 4 marks)
Total /10
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
Total /10
PiXL PLC 2017 Certification
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
P
NOT TO SCALE
9cm
S
8cm
T
Q
R
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…..
8.5…-7= 1.6…cm
(M1)
(A1)
(2)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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
C= 18.8 π cm
(M1)
(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)
PiXL PLC 2017 Certification
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
=0.43 (2.d.p.)
(A1)
(M1)
(2)
Total /10
PiXL PLC 2017 Certification
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)
HCF: 6
(M1)
(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 2 x 3 x 51
2
PiXL PLC 2017 Certification
1
(A2)
Question 4
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)
(2)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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)
1/2
Find the probability that two out of the fruits are the same.
(A2)
(2)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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)
5
1
2 x3
(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)
PiXL PLC 2017 Certification
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)
HCF: 16
(M1)
(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)
Total /10
PiXL PLC 2017 Certification
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:
72 x3
3
=
=
23
3
368
x
16
5
(M1)
(A1)
15
(2)
3
x2
=
22 11
=
x
5 5
242
25
(M1)
(A1)
(2)
x
=
27
44
(A2)
(2)
PiXL PLC 2017 Certification
Question 2
Which is smaller? You must show your working out.
3
x8
or
5
x2
= 29.3650 or 15.10714
=3
x8
>
(M1)
5
x2
(A1)
(2)
Which is bigger? You must show your working out.
4
x5
or
3
x6
=23.3 or 25.4571428
=4
x5
<
3
x6
(M1)
(A1)
(2)
Total /10
PiXL PLC 2017 Certification
Operations 2
Grade 4
Solutions
Objective: Understand the relationships between operations e.g. Inverse operations.
Question 1
(152 −102)2
Work out the value of
=(225-100)2
=1252
=125 x 125
=15625
(M1)
(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 +
) = 24
(2)
LET THE SQAURE = X
8 -3X = 24
-3X = 24-8
-3X= 16
(M1)
X= -16/3
(A1)
PiXL PLC 2017 Certification
Question 4
Which is smaller :
15+ 4 x 3
= 27 or 57
= 15+ 4 x 3 < (15+4) x 3
or
(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)
Total /10
PiXL PLC 2017 Certification
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) )
= £14.40
(A1)
(M1)
(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
=(256-1)2
=2552
=65025
(44 −1)2
(M1)
(A1)
(2)
PiXL PLC 2017 Certification
Question 5
Insert brackets, if needed, to make the answer correct:
7+5 x (9-3)=37
(A1)
(9+ 5)2 – 7 x 2=182
(A1)
(1)
(1)
Total /10
PiXL PLC 2017 Certification
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
x = 10 (A1)
(M1)
(2)
Total /10
PiXL PLC 2017 Certification
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?
YES
NO
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)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
Rounding 2
Objective:
figures)
SOLUTIONS
Grade 5
Round to an appropriate degree of accuracy (e.g. to decimal places or significant
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)
PiXL PLC 2017 Certification
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)
PiXL PLC 2017 Certification
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
PiXL PLC 2017 Certification
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
4.65 x 10-2
(A1)
(A1)
(2)
PiXL PLC 2017 Certification
Question 4
Write these numbers in ascending order:
1.76 x 10 4
14 4798
144798, 17600, 1450
1)1.45 x 10 3
2)1.76 x 10 4
3)14 4798
1.45 x 10 3
(M1)
(A1)
(2)
Question 5
Write three quarter of a million in standard form.
¾ x 1000000 = 750000
7.5 x 105
(M1)
(A1)
(2)
Question 6
Write 132344 in standard form:
1.32344 x 10 5
(A1)
(1)
Total /10
PiXL PLC 2017 Certification
Terminating decimals and fractions 2
Grade 4
Solutions
Objective: Convert between and work with terminating decimals and their equivalent fractions
(including ordering).
Question 1
4
,
8
12
,
18
3
50
3
, ,
7
9
,
10
1
6
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?
4 3
,
,
8 50
9
, (A2)
10
(2)
Question 2
Order these fractions; starting with smallest first:
1
,
2
3
,
7
1
8
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
99X = 14
-(2)
(M1)
X= 14/99
(A1)
PiXL PLC 2017 Certification
(2)
Question 4
Convert these fractions into decimals:
20 80
,
11 13
(M1)
1.818 (A1)
(M1)
6.153 (A1)
(2)
Total /10
PiXL PLC 2017 Certification
Using Standard Units 2
Objective:
SOLUTIONS
Grade 3
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
Millilitres
Metres(B1)
Centimetres
(1)
(Total 2 marks)
Question 2
(a) Estimate the length of a finger nail (B1)
(i)
2.5cm
(b)
(i)
(iii) 5m
(1)
(iii) 20mm
(1)
(iii) 200kg
(1)
(b)Estimate the height of a child (B1)
100cm
(c)
(i)
(ii) 25cm
(ii) 100m
(c )Estimate the weight of a man (B1)
5kg
PiXL PLC 2017 Certification
(ii) 75kg
(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
PiXL PLC 2017 Certification