PLC Papers - WordPress.com · 2016-10-21 · Adding and subtracting fractions 3 Grade 4 Objective: Add and subtract fractions including improper fractions and mixed numbers. Question

$Page 1: PLC Papers - WordPress.com · 2016-10-21 · Adding and subtracting fractions 3 Grade 4 Objective: Add and subtract fractions including improper fractions and mixed numbers. Question$
PLC Papers

Created For:

year 9 revision booklet_half term 1

Higher Number

PiXL PLC 2017 Certification

Decimals 3 Grade 3

Objective: Understand adding subtracting multiplying and dividing decimals.

Question 1 7 cans of a drink cost £5.11. How much does one drink cost? (2)

Question 2 Work out 10.7865 ÷ 0.5

(2)

Question 3 (a) Sunny, Pat and Tom went out one evening and it cost them altogether £87.60. How much does each

one of them have to pay?

(2)


(b) 6 people each weigh 75.9 kg. Find their total weight? (2)

Question 4

1 bottle of milk = £1.29

Kurt bought five bottles of milk how much will it cost altogether? (2)

Total /10


Multiplying integers 3 Grade 2 Objective: Multiplying integers using written methods.

Question 1

547 students in a school go on a school trip and each pay £9. Find the total amount of money paid by all of the students?

(2) Question 2

Which is larger 9 x 8 x 57 or 54 x 9 x 9 (2)

Question 3

Olivia sells blouses at £34 each. If she sold 43 blouses find out how much money she would receive in total?

(2)


Question 4

Can 35 2 be equal to 1250? Explain how you know your answer.

(2) Question 5

Work out: -5 x 579 x 0

(2)

Total /10


Adding and subtracting fractions 3 Grade 4 Objective: Add and subtract fractions including improper fractions and mixed numbers. Question 1 Work these out:

a) 47 +

35 + 27 =

(2)

b) 810 +

89 – 28 =

(2) Question 2 A tank contains 1

35 litres oil. Jan added 3 35 litres more oil into the tank.

a) Find the total amount of oil in the tank?

(2)


b) If 235 litres oil is now used, how much oil left in the tank?

(2) Question 3 72 +

(2)

Total /10

513 =


Estimation 3 Grade 4

Objective: Estimate answers

Question 1.

Apple juice costs 42p per carton.

(a) Estimate how many 58 cartons will cost

…………..(2) (b) How many can be bought with £2.50?

.

…………..(2)

(c) John says that he buys one a day for a week and it costs him £4.14. Can he be correct? Use an

estimate to prove your answer.

…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………..…………..(2)

(Total 6 marks)

Question 2

A length of rope measures 203cm.

Estimate how many 18 cm lengths can be cut from the rope

………..(2)

(Total 2 marks)


Question 3

Cupcakes cost 23p each. Michael has one cupcake per day. Estimate how much he spends in one month.

Circle the answer you think is best.

A: £7.00

B: £11.00

C: £3.00

………..(2)

(Total 2 marks)

Total /10


LCM and HCF 3 Grade 4 Objective: Understand and find LCM and HCF.

Question 1

Use factor tree diagrams or Venn diagrams to find LCM and HCF of

a) 136 and 420 (4)

b) 145 and 720 (4)


Question 2 Express 96 as a product of its prime factors using any method.

(2)

Total /10


Multiplying fractions 3 Grade 4 Objective: Multiply fractions including improper fractions and mixed numbers. Question 1

a) A photo frame measures 495 by 5

18 cm. Find the area of the photo frame.

(2)

b) A photo frame measures 595 by 5


(2) c)

(2)

235 x

358 + 3

35 =


Question 2 Which is smaller?

or

(2)

Which is bigger?

or

(2)

Total /10

45 of 514 35 of 7

12

27 of 425

35 of 237


Order of operations 3 Grade 4 Objective: Understand and use the order of operations. Question 1 Find the value of (a) 3 x 25 (b) -22 + 83

(2)

Question 2 The length of a rectangle is 12 cm more than the width. If the perimeter is 240cm find the length and width of the rectangle. (2)

Question 3 Which is larger:

13+8÷2 or (-15-3) ÷- 2 (2)


Question 4 John says (4+9)2 - 2+3 x 5=182 Jess says (4+9)2 - 2+3 x 5= 850 Who is correct? You must explain your answer clearly.

(2) Question 5 Insert brackets, if needed, to make the answer correct: (a) 4+52 x 10=810 (1) (b) 3+ 5– 17 x 2= -18 (1)

Total /10


Rounding 3 Grade 5

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

Question 1.

Bobby wins £12876998 on the National Lottery

(a) A local newspaper states that he has won £13 million pounds. To what degree of accuracy (in terms of place value) has the newspaper used when rounding his winnings?

…………..(2)

(b) A local newspaper states that he has won £13 million pounds. To what degree of accuracy (in terms of significant figures) has the newspaper used when rounding his winnings?

…………..(2)

(Total 4 marks)

Question 2 .

Hollie’s garden path is 1.2356 km long

(a) How long is Hollie’s garden path correct to 1 decimal place?

………..(2)

(b) How long is Hollie’s garden path correct to two significant figures?

………..(2)

(Total 4 marks)


Question 3

Daisy’s teacher tells her to round the number 2.009554 to one decimal place Hollie writes the answer 2.

Explain why her teacher tells her that this is incorrect.

…………………………………………………………………………………………………………………

…………………………………………………………………………………………………………………

…………………………………………………………………………………………………………………

……………………………………………………………………………………………………..………..(2)

(Total 2 marks)

Total /10


Calculating with fractions 3 Grade 5

Objective: Calculate exactly with fractions, including solving problems

Question 1

Rhiannon is checking her friend Kim’s work. Kim has worked out that

58 +

35 = 813

Without working it out, how can Rhiannon show Kim that her answer is incorrect. ………………………………………………………………………………………………… ………………………………………………………………………………………………… …………………………………………………………………………………………………

(1)

Question 2

a) The area of farmer Jackie’s field is 12m2. If the length of the field is 234m, calculate the width of the

field.

……………….m (3)

b) Calculate the perimeter of the field. Give your answer as a mixed number.

……………….m (3)


Question 3

PQRS is a square. This diagram is drawn accurately.

What fraction of the square is shaded?

………………. (3)

Total /10

P

R

Q

S


Dividing integers 3 Grade 2 Objective: Dividing integers using written methods. Question 1 A calculator costs £9.00. Ben’s math teacher has £250. How many calculators Ben’s teacher can buy at the most? (2) Question 2 Fill in the empty box to complete the following calculations: 512 ÷ (2) Question 3 A box can hold 12 bottles. How many boxes are needed to hold 156 bottles? (2)

= 64


Question 4 51 people can sit in a bus. How many buses are needed to carry 750 people? (2) Question 5 A stamp costs 26p. How many stamps can I buy if I have £5.00?

(2)

Total /10


Product of prime factors 3 Grade 6

Objective: Understand the unique factorisation theorem and perform prime factor decompositions

Question 1

Given

A = 22 x 35 x 53 and B = 24 x 33 x 52

Write down, as a product of its prime factors,

a) The highest common factor of A and B

…………………

(1)

b) The lowest common multiple of A and B

…………………

(1)

Question 2

a) Express 24 as a product of its prime factors

…………………

(2)

b) Use your answer to write 482 as a product of its prime factors in index form

…………………

(2)


Question 3

A number, n, in prime factor form is 32x3y, where x and y are odd prime numbers.

a) Circle the expressions which are factors of n

18 3xy x4y x2 9y

b) Circle the expressions which are multiples of n

18x3y 3xy 9x3y2 x3y 81x3y

(4)

Total /10


Product Rule 3 Grade 7

Objective: Use the product rule for counting

Question 1

Mr Green has blue, white, and pink shirts and grey and black ties. Does he have enough different coloured shirts and ties to wear and different combination of shirt and tie for every day of week? You must give a reason for your answer

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(2)

Question 2

New Jersey license plates now read, three letters-two digits -one letter. Not long ago, they had three letters followed by four digits. Under which system, old or new, are there more possibilities for a license plate? (All letters of the alphabet and all digits from 0 to 9 can be used but cannot be repeated)

……………………

(3)

Question 3

How many four digit numbers are there that only include the digits 3, 4 and 5?

……………………

(2)


Question 4

A café menu has 4 starters, 10 main meals and 5 desserts. A customer can choose the following meals

• Starter and main • Main and dessert • Starter, main and dessert.

How many ways are there of choosing a meal at this restaurant?

……………………

(3)

Total /10


Recurring Decimals 1 Grade 7

Objective: Change recurring decimals into fractions and vice versa.

Question1

a) Change 29 into a decimal.

(2)

b) Is the answer from part a recurring decimal or a terminating decimal? Explain your choice below. (2)

Question 2 . Change 0.37 into a fraction.

(2) Question 3 . . Change 0.47 into a fraction.

(2)


Question 4 . . . Convert the recurring decimal 0.178 in to a fraction.

(2)

Total /10

PLC Papers

Created For:

year 9 revision booklet_half term 1

Higher Number


Decimals 3 Grade 3 Solutions

Objective: Understand adding subtracting multiplying and dividing decimals.

Question 1 7 cans of a drink cost £5.11. How much does one drink cost? £5.12 / 7 (M1) £0.73 (A1) (2)

Question 2 Work out 10.7865 ÷ 0.5

107.865/5 (M1) =21.573 (A1) (2)

Question 3 (a) Sunny, Pat and Tom went out one evening and it cost them altogether £87.60. How much does each

one of them have to pay?

£87.60 / 3 (M1)

£29.20 (A1) (2)


(b) 6 people each weigh 75.9 kg. Find their total weight? 6 x 75.9 (M1) =455.4 kg (A1) (2)

Question 4

1 bottle of milk = £1.29

Kurt bought five bottles of milk how much will it cost altogether? 5 x £1.29 (M1) =£6.45 (A1) (2)

Total /10


Multiplying integers 3 Grade 2 Solutions Objective: Multiplying integers using written methods.

Question 1

547 students in a school go on a school trip and each pay £9. Find the total amount of money paid by all of the students?

(M1) = £4923 (A1)

(2) Question 2

Which is larger 9 x 8 x 57 or 54 x 9 x 9 = 4104 or 4374 (M1) =(54 x 9 x 9) is bigger (A1) (2)

Question 3

Olivia sells blouses at £34 each. If she sold 43 blouses find out how much money she would receive in total?

(M1) =£1462 (A1) (2)


Question 4

Can 35 2 be equal to 1250? Explain how you know your answer.

352 = 1225 (M1) 1225 ≠1250 (A1)

(2)


Question 5 Work out: -5 x 579 x 0

=0 (A2)

(2)

Total /10


Adding and subtracting fractions 3 Grade 4 Solutions Objective: Add and subtract fractions including improper fractions and mixed numbers. Question 1 Work these out:

a) 47 +

35 + 27 =

=(20+21+10)35 (M1)

= 5135 (A1)

(2)

b) 810 +

89 – 28 =

=(576+640−180)720 (M1)

=1036720

=259180 (A1)

(2) Question 2 A tank contains 1

35 litres oil. Jan added 3 35 litres more oil into the tank.

a) Find the total amount of oil in the tank?

8/5 + 18/5 (M1) = 26/5

=515 Litres (A1)

(2)


b) If 235 litres oil is now used, how much oil left in the tank?

(2)

26/5 – 13/5 (M1) = 13/5

=235 Litres

(A1) Question 3 72 +

7/2+16/3 (M1) = 53/6

=856 (A1)

(2)

Total /10

513 =


Estimation 3 Grade 4 Solutions

Objective: Estimate answers

Question 1.

Apple juice costs 42p per carton.

(a) Estimate how many 58 cartons will cost 60 x 40 = 2400 2400p = £24.00

…= £24.00………..(2)

(M1) (A1)

(b) How many can be bought with £2.50? £2.50=250p 250≈240 240÷40=6 .

…6………..(2) (M1) (A1)

(c) John says that he buys one a day for a week and it costs him £4.14. Can he be correct? Use an

estimate to prove your answer.

…40x7=280 or £2.80 so no he must be incorrect. (2)

(M1) (A1)

(Total 6 marks)

Question 2

A length of rope measures 203cm.


Estimate how many 18 cm lengths can be cut from the rope

200÷20 =10

10 ………..(2)

(M1) (A1)

(Total 2 marks)

Question 3

Cupcakes cost 23p each. Michael has one cupcake per day. Estimate how much he spends in one month.

Circle the answer you think is best.

A: £7.00

B: £11.00

C: £3.00

20 x 7 = 140p or £1.40= 1 week

1.40 x 4= £5.60 so A

………..(2)

(M1) (A1)

(Total 2 marks)

Total /10


LCM and HCF 3 Grade 4 Solutions Objective: Understand and find LCM and HCF.

Question 1

Use factor tree diagrams or Venn diagrams to find LCM and HCF of

a) 136 and 420

2 x 2 x 2 x 17 (M1)

2 x 2 x 3 x 5 x 7 (M1) (4) HCF: 4 (A1) LCM: 14280 (A1)

b) 145 and 720

5 x 29 (M1)


2 x 2 x 2 x 2 x 3 x 3 x 5 (M1) HCF: 5 (A1) LCM: 20880 (A1) (4)

Question 2 Express 96 as a product of its prime factors using any method.

(M1) 2 x 2 x 2 x 2 x 2 x 3 (A1)

(2)

Total /10


Multiplying fractions 3 Grade 4 Solutions Objective: Multiply fractions including improper fractions and mixed numbers. Question 1

a) A photo frame measures 495 by 5


29/5 x 41/8 (M1) =1189/40 cm2 or 29.725 cm2 (A1) (2)

b) A photo frame measures 595 by 5


34/5 x 36/7 (M1) 1224/35 cm2 or 34.97 cm2 (1 dp) to (A1) (2) c)

13/5 x 29/8 + 18/5 (M1) 377/40 + 144/40 521/40 (A1)

(2) -

235 x

358 + 3

35 =


Question 2 Which is smaller?

or

=21/5 or 9/2 =42/10 or 45/10 (M1) = (2)

Which is bigger?

or

=44/35 or 51/35 (M1) =

(A1)

(2)

Total /10

45 of 514 35 of 7

12

27 of 425

35 of 237

(A1)

35 of 237 is bigger

45 of 514 is smaller


Order of operations 3 Grade 4 Solutions Objective: Understand and use the order of operations. Question 1 Find the value of (a) 3 x 25 3 x 25= 96 (A1) (b) -22 + 83 -22 + 83=516 (A1)

(2)

Question 2 The length of a rectangle is 12 cm more than the width. If the perimeter is 240cm find the length and width of the rectangle. Let the width = X Length = X+12 2X + 2X +12 + 12 = 240 4X + 24 = 240 4X = 240-24 4X = 216 X=54 cm (M1) Width = 54cm Length = 66 cm (A1) (2)

Question 3 Which is larger:

13+8÷2 or (-15-3) ÷- 2 = 17 or 9 (M1) 13+8÷2 is bigger (A1) (2)


Question 4 John says (4+9)2 - 2+3 x 5=182 Jess says (4+9)2 - 2+3 x 5= 850 Who is correct? You must explain your answer clearly. (2) John, using BIDMAS, the sum becomes 169-2+15 = 182 (A2)

Question 5

Insert brackets, if needed, to make the answer correct: (a) (4+5)2 x 10=810 (A1) (1) (b) (3+ 5– 17) x 2= -18 (A1) (1)

Total /10


Rounding 3 Grade 5 Solutions

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

Question 1.

Bobby wins £12876998 on the National Lottery

(a) A local newspaper states that he has won £13 million pounds. To what degree of accuracy (in terms of place value) has the newspaper used when rounding his winnings?

Nearest million…………..(2)

(B2)

(b) A local newspaper states that he has won £13 million pounds. To what degree of accuracy (in terms

of significant figures) has the newspaper used when rounding his winnings?

Two significant figures…………..(2) (B2)

(Total 4 marks)

Question 2 .

Hollie’s garden path is 1.2356 km long

(a) How long is Hollie’s garden path correct to 1 decimal place?

…1.2km……..(2)

(B2)

(b) How long is Hollie’s garden path correct to two significant figures?

…1.2km……..(2)

(B2)


(Total 4 marks)

Question 3

Daisy’s teacher tells her to round the number 2.009554 to one decimal place Hollie writes the answer 2.

Explain why her teacher tells her that this is incorrect.

……this is to the nearest whole number and so she should have written the number 2.0 which has one

decimal place

.(2)

(B2)

(Total 2 marks)

Total /10


Calculating with fractions 3 Grade 5 Solutions

Objective: Calculate exactly with fractions, including solving problems

Question 1

Rhiannon is checking her friend Kim’s work. Kim has worked out that

58 +

35 = 813

Without working it out, how can Rhiannon show Kim that her answer is incorrect. C1 for one of the following: Both fractions are greater than a half so the answer should be a mixed number or you need common denominator or you can’t just add numerators and denomiators

(1) Question 2

a) The area of farmer Jackie’s field is 12m2. If the length of the field is 234m, calculate the width of the

field.

=12 ÷ 114

=12 x 411 (M1)

= 4811 (M1)

= 4411 (A1)

……………….m

(3) b) Calculate the perimeter of the field. Give your answer as a mixed number.

=4411 + 4

411 + 234 +2

34

= 12 + 1644 +1644+33 44 +3344 (M1)

= 129844 (M1)

= 14522 (A1)

……………….m (3)


Question 3

PQRS is a square. This diagram is drawn accurately.

What fraction of the square is shaded?

= 14 +

116 + 164 (M1)

= 1664 +

464 + 164 (M1)

= 2164 (A1)

………………. (3)

Total /10

P

R

Q

S


Dividing integers 3 Grade 2 Solutions Objective: Dividing integers using written methods. Question 1 A calculator costs £9.00. Ben’s math teacher has £250. How many calculators Ben’s teacher can buy at the most? £250/ £9.00 (M1) = 27.777777 =27 (A1) (2) Question 2 Fill in the empty boxes to complete the following calculations: 512 ÷ 512/64 = 8 (A2) (2) Question 3 A box can hold 12 bottles. How many boxes are needed to hold 156 bottles? 156/12 (M1) =13 boxes (A1) (2)

= 64


Question 4 51 people can sit in a bus. How many buses are needed to carry 750 people? 750/51 (M1) =14.705… =15 (A1) (2) Question 5 A stamp costs 26p. How many stamps can I buy if I have £5.00? £5.00 / £0.26 (M1) = 19.230… = 19 (A1)

(2)

Total /10


Product of prime factors 3 Grade 6 Solutions

Objective: Understand the unique factorisation theorem and perform prime factor decompositions

Question 1

Given

A = 22 x 35 x 53 and B = 24 x 33 x 52

Write down, as a product of its prime factors,

a) The highest common factor of A and B

……22 x 33 x 52 (A1)……………

(1)

b) The lowest common multiple of A and B

……24 x 35 x 53 (A1)……………

(1)

Question 2

a) Express 24 as a product of its prime factors

M1 for full systematic method of divisions by prime numbers oe factor trees; condone 1

calculation error

A1 for 2 x 2 x 2 x 3

…………………

(2)

b) Use your answer to write 482 as a product of its prime factors in index form

((2 x 2 x 2 x 3) x2 )2 (M1- allow ft marks)

28 x 32 (A1)

…………………

(2)


Question 3

A number, n, in prime factor form is 32x3y, where x and y are odd prime numbers.

a) Circle the expressions which are factors of n

18 3xy x4y x2 9y

A2 for all three correct, no errors

(M1 for any two correct, allow one error)

b) Circle the expressions which are multiples of n

18x3y 3xy 9x3y2 x3y 81x3y

A2 for all three correct, no errors

(M1 for any two correct, allow one error)

(4)

Total /10


Product Rule 3 Grade 7 Solutions

Objective: Use the product rule for counting

Question 1

Mr Green has blue, white, and pink shirts and grey and black ties. Does he have enough different coloured shirts and ties to wear and different combination of shirt and tie for every day of week? You must give a reason for your answer.

3 x 2 = 6 possible combinations (M1)

No, he does not have enough different coloured shirts and ties, only has enough for 6 rather than 7 days. (C1 dep on M1)

(2)

Question 2

New Jersey license plates now read, three letters-two digits -one letter. Not long ago, they had three letters followed by four digits. Under which system, old or new, are there more possibilities for a license plate? (All letters of the alphabet and all digits from 0 to 9 can be used but cannot be repeated)

26 x 25 x 24 x 10 x 9 x 8 x 7 or 26 x 25 x 24 x 10 x 9 x 23 (M1)

78, 624, 000 or 32, 292, 000 (M1)

More possibilities under the old system (C1 dependant on M2)

……………………

(3)

Question 3

How many four digit numbers are there that only include the digits 3, 4 and 5?

3 x 3 x 3 x 3 or starting to list combinations (M1)

81 (A1)

……………………

(2)


Question 4

A café menu has 4 starters, 10 main meals and 5 desserts. A customer can choose the following meals

• Starter and main • Main and dessert • Starter, main and dessert.

How many ways are there of choosing a meal at this restaurant?

Starter and main 4 x 10 = 40 (M1 for any correct product)

Main and desert 10 x 5 = 50

Starter, main and desert 4 x 10 x 5 = 200

40 + 50 + 200 (M1 for summing their correct products)

290 (A1)

……………………

(3)

Total /10


Recurring Decimals 1 Grade 7 Solutions

Objective: Change recurring decimals into fractions and vice versa.

Question1

a) Change 29 into a decimal.

0.222222222…… (2)

b) Is the answer from part a recurring decimal or a terminating decimal? Explain your choice below. Reocurring- the decimal goes on infinitely. (A2) (2)

Question 2 . Change 0.37 into a fraction.

X = 0. 37 37 37 - (1) 100 x = 37.37 37 - (2) (M1) (2) –(1) = 37/99 (A1)

(2)


Question 3 . . Change 0.47 into a fraction.

X = 0.47 47 47 -(1) 100X = 47. 47 47 47 -(2) (M1) (2) – (1) = 47/99 (A1) (2)

Question 4

. . . Convert the recurring decimal 0.178 in to a fraction.

X= 0.178 178 178 -(1) 1000 X= 178. 178 178 178 -(2) (2) – (1) = 178/999 (M1) (A1) (2)

Total /10

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PLC Papers - WordPress.com · 2016-10-21 · Adding and subtracting fractions 3 Grade 4 Objective: Add and subtract fractions including improper fractions and mixed numbers. Question