PLC Papers - · PDF filePiXL PLC 2017 Certification Fractions and percentages 1 Grade 4...

$: PLC Papers - · PDF filePiXL PLC 2017 Certification Fractions and percentages 1 Grade 4 Objective: Interpret fractions and percentages as operators. Question 1 Work out 343 x 3$
PLC Papers

Created For:

year 10 test 2 revision

PiXL PLC 2017 Certification

Fractions and percentages 1 Grade 4

Objective: Interpret fractions and percentages as operators.

Question 1

Work out 343 x 37

(2)

Question 2 A sofa costs £925. During a sale its price has been reduced by a fifth. What is the sale price of this sofa?

(2)

Question 3 Megan surveyed 2200 dog owners. 7 out of 20 dog owners bought ‘Doggy Biscuits’ dog food. a) What percentage of the dog owners bought ‘Doggy Biscuits’ dog food?

(2) b) How many people bought ‘Doggy Biscuits’ dog food?

(2)

Question 4 Parveen scored 18 out of 25 in a maths test. What percentage did she score?

(2)

Total /10


Standard form 1 Grade 4 Objective: Understand and use standard form for very large and very small numbers. Question 1 Write 0.000256 in standard form. (1) Question 2 Write 5200009 in standard form. (1) Question 3 Order these smallest to largest: 4.75 X 10 4 45 X 10 3 45900 17 X 4.8 X 10 4

(2)


Question 4 The sun is 1.496 x 10 8 kilometres from Earth. Light travels at 2.9979 x 105 KM / second. How many seconds does it take for light to travel from the sun to the Earth? Give your answer to the nearest second. (3) Question 5 E = MC 2 If M= 4 x 10 -8

C= 3 x 10 8 Find the value of E? (2) Question 6 Write 5 in standard form:

(1)

Total /10


Division of a quantity as a ratio 1 Grade 4 Objective: Express the division of a quantity into two parts as a ratio

Question 1

Grace and Jack share £140 in the ratio 3 : 4

Work out the amount of money that Jack gets.

£ . . . . . . . . . . . . . . . . . . . . . .

(Total 2 marks)

Question 2

Keith and Graham share £105 in the ratio 4:3

Work out how much Keith gets.

£ . . . . . . . . . . . . . . . . . .

(Total 2 marks)

Question 3

Graham and Michael share £35 in the ratio 5 : 2

Work out the amount of money that Graham gets.

£ . . . . . . . . . . . . . . . . . .


(Total 2 marks)

Question 4

In the 2012 Paralympic Games, the total number of gold and silver medals won by Brazil was 35 The ratio of the number of gold medals that Brazil won to the number of silver medals that Brazil won was 3 : 2

How many silver medals were won by Brazil?

...........................................................

(Total 2 marks)

Question 5

Green paint can be made by mixing yellow paint and blue paint in the ratio 2 : 3 Wendy makes 15 litres of green paint. Work out how many litres of blue paint Wendy uses.

...............................litres (Total 2 marks)

Total /10


Non standard real life graphs 1 Grade 4

Objective: Plot and interpret non-standard real-life graphs to find approximate solutions to kinematics

problems involving distance, speed and acceleration

Question 1

Here is part of a travel graph of Jacob’s journey from his house to the library.

(a) How far is Jacob’s house from the library?

……………………………………….km (1)

(b) Work out Jacob’s speed for the first 20 minutes of his journey.

Give your answer in km/h.

…………………………………….km/h (2)

Jacob spends 30 minutes at the library.

He then travels back to his house at a steady speed of 64 km/h

(c) Complete the travel graph to show this. (2)

(Total 5 marks)


Question 2

Here is a conversion graph changing between kilograms and pounds.

(a) Use the graph to change 22 pounds to kilograms.

.………………………………….kg (1)

(b) Use the graph to change 2.5 kilograms to pounds.

…………………………………pounds (1)

Fabio weighs 110 pounds.

(c) Change 110 pounds to kilograms.

.………………………………….kg (1)

(Total 3 marks)


Question 3

Gary goes for a drive in his car.

Here is a distance-time graph for his journey.

(a) For which section of the journey is the car travelling fastest?

…………………..to………………… (1)

(b) State a section of the journey when the car is slowing down.

…………………..to………………… (1)

(Total 2 marks)

Total marks / 10


Area of Triangles, Trapezia and Parallelograms 1 Grade 4

Objective: Know and apply formulae to calculate areas of triangles, trapezia and parallelograms.

Question 1.

Find the areas of the following 2D shapes.

(a)

…………………………m2

(2)

(b)

……………………cm2

(2)

(c)

……………………m2

(2)


(d)

…………………… cm2

(2)

(e)

.

………………… cm2.

(2)

Total /10


Area of Composite Shapes 1 Grade 4

Objective: Calculate the area of composite shapes including circles.

Question 1.

Find the area of the following composite shapes:

(a)

……………………………

(2)

(b)

……………………………

(2)

(Total 4 marks)


Question 2.

Find the area of the shape.

……………………………m2

(3)

Question 3.

Find the area of the shaded region.

……………………………

(3)

Total /10


nth term of quadratic sequences 1 Grade 6

Objective: Write and expression for the nth term of a sequence, including quadratic sequences.

Question 1.

(a) Here are the first five terms of a sequence.

4, 7, 12, 19, 28, …

Find the next term two terms of the sequence.

………………… and ………………… (1)

(b) The nth term of a different sequence is 2n2 – 8.

Work out the third term of this sequence.

…………………………… (1)

(Total 2 marks)

Question 2.

Here are the first five terms of a quadratic sequence.

2, 5, 10, 17, 26, …

(a) Write down the next term of the sequence.

………………………… (1)

(b) Find an expression in terms of n, for the nth term of this quadratic sequence. .

……………………………………… (2)

(Total 3 marks)


Question 3.

Find an expression in terms of n, for the nth tem of this quadratic sequence.

3, 9, 19, 33, 51, …

………………………………………………………………………………………

(Total 2 marks)

Question 4.

Find the nth tem of this sequence.

4, 10, 18, 28, 40, …

………………………………………………………………………………………

(Total 3 marks)

Total /10


Arcs and Sectors 1 Grade 6

Objective: Calculate arc lengths and angles, and areas of sectors

Question 1.

PQ is an arc of a circle with radius 1.64m.

Angle POQ = 71o

(a) Calculate the perimeter of sector POQ.

Give your answer to three significant figures.

................................

(3)

(b) Calculate the area of sector POQ.


................................

(2)

(Total 5 marks)


Question 2.

PQ is an arc of a circle with radius xcm.

Angle POQ = 120o

(a) Write down in terms of x and π an expression for the perimeter of sector POQ. Simplify your answer fully.

................................

(3)

(b) Write down in terms of x and π an expression for the area of sector POQ. Simplify your answer fully.

................................

(2)

(Total 5 marks)

Total /10

PLC Papers

Created For:

year 10 test 2 revision


Fractions and percentages 1 Grade 4 Solutions

Objective: Interpret fractions and percentages as operators.

Question 1

Work out 343 x 37

= 343 x 37

= 10297 (M1)

=147 (A1) (2)

Question 2 A sofa costs £925. During a sale its price has been reduced by a fifth. What is the sale price of this sofa?

= 15 x 925

= £185 (M1) £925 - £185 = £740 (A1) (2)

Question 3 Megan surveyed 2200 dog owners. 7 out of 20 dog owners bought ‘Doggy Biscuits’ dog food. a) What percentage of the dog owners bought ‘Doggy Biscuits’ dog food?

720 x 100 (M1)

=35 % (A1) (2)

b) How many people bought ‘Doggy Biscuits’ dog food? 720 x 2200 (M1)

= 770 (A1) (2)


Question 4 Parveen scored 18 out of 25 in a maths test. What percentage did she score? 1825 x 100 (M1)

= 72 % (A1) (2)

Total /10


Standard form 1 Grade 4 Solutions Objective: Understand and use standard form for very large and very small numbers. Question 1 Write 0.000256 in standard form. =2.56 x 10-4 (A1) (1) Question 2 Write 5200009 in standard form. 5.200009 x 106 (A1) (1) Question 3 Order these smallest to largest: 4.75 X 10 4= 47500 45 X 10 3=45000 45900 17 X 4.8 X 10 4=816000 (M1) 45 X 10 3, 45900, 4.75 X 10 4, 17 X 4.8 X 10 4 (A1) (2)


Question 4 The sun is 1.496 x 10 8 kilometres from Earth. Light travels at 2.9979 x 105 KM / second. How many seconds does it take for light to travel from the sun to the Earth? Give your answer to the nearest second. Speed = Distance / Time 2.9979 105 = 1.496 x 10 8 / T (M2) T = 499.0159779 seconds (A1) = 499 seconds (3) Question 5 E = MC 2 If M= 4 x 10 -8

C= 3 x 10 8 Find the value of E? E = 4 x 10 -8 x 3 x 10 8 x 3 x 10 8 = 36 x 108 = 3.6 x109 (A2) (2) Question 6 Write 5 in standard form: 5.0 x 100 (A1)

(1)

Total /10


Division of a quantity as a ratio 1 Grade 4 Solutions Objective: Express the division of a quantity into two parts as a ratio

Question 1

Grace and Jack share £140 in the ratio 3 : 4

Work out the amount of money that Jack gets.

3 + 4 = 7 140 ÷ 7 = 20 M1 4 × 20 = £80 A1

£ . . . . . . . . . . . . . . . . . . . . . .

(Total 2 marks)

Question 2

Keith and Graham share £105 in the ratio 4:3

Work out how much Keith gets.

4 + 3 = 7 105 ÷ 7 = 15 M1 4 × 15 = £60 A1

£ . . . . . . . . . . . . . . . . . .

(Total 2 marks)


Question 3

Graham and Michael share £35 in the ratio 5 : 2

Work out the amount of money that Graham gets.

5 + 2 = 7 35 ÷ 7 = 5 M1 5 × 5 = £25 A1

£ . . . . . . . . . . . . . . . . . .

(Total 2 marks)

Question 4

In the 2012 Paralympic Games, the total number of gold and silver medals won by Brazil was 35 The ratio of the number of gold medals that Brazil won to the number of silver medals that Brazil won was 3 : 2

How many silver medals were won by Brazil?

3 + 2 = 5 35 ÷ 5 = 7 M1 2 × 7 = £14 A1

...........................................................

(Total 2 marks)

Question 5

Green paint can be made by mixing yellow paint and blue paint in the ratio 2 : 3 Wendy makes 15 litres of green paint. Work out how many litres of blue paint Wendy uses.

2 + 3 = 5 15 ÷5 = 3 M1 3 × 3 = £9 A1

...............................litres (Total 2 marks)

Total /10


Non standard real life graphs 1 Grade 4 SOLUTIONS

Objective: Plot and interpret non-standard real-life graphs to find approximate solutions to kinematics

problems involving distance, speed and acceleration

Question 1

Here is part of a travel graph of Jacob’s journey from his house to the library.

(a) How far is Jacob’s house from the library?

16 km (A1) (1)

(b) Work out Jacob’s speed for the first 20 minutes of his journey.

Give your answer in km/h.

16 km in 20 mins reads correctly from the graph (M1)

X3

48 km in 60 mins

48 km/h (A1) (2)

Jacob spends 30 minutes at the library.

He then travels back to his house at a steady speed of 64 km/h

(c) Complete the travel graph to show this. (2)

See red line on the graph above

Line that cuts the bottom axis from 60 to 70 (M1)

Line that cuts at exactly (65, 0) (A1)

(Total 5 marks)


Question 2

Here is a conversion graph changing between kilograms and pounds.

(a) Use the graph to change 22 pounds to kilograms. (1)

10 kg (A1)

(b) Use the graph to change 2.5 kilograms to pounds. (1)

5.5 pounds (A1)

Fabio weighs 110 pounds.

(c) Change pounds to kilograms. (1)

110 = 22 x 5

22 pounds = 10 kg

110 pounds = 50 kg

50kg (A1)

(Total 3 marks)


Question 3

Gary goes for a drive in his car.

Here is a distance-time graph for his journey.

(a) For which section of the journey is the car travelling fastest?

C to D (A1) (1)

(b) State a section of the journey when the car is slowing down.

D to E or H to I (A1) (1)

(Total 2 marks)

Total marks / 10


Area of Triangles, Trapezia and Parallelograms 1 Grade 4 Solutions

Objective: Know and apply formulae to calculate areas of triangles, trapezia and parallelograms.

Question 1.

Find the areas of the following 2D shapes.

(a)

Multiply perpendicular lengths

5.2x6=31.2cm2 (M1 A1)

………………………cm2

(2)

(b)

Multiply perpendicular lengths then half.

14x4/2=28 cm2 (M1 A1)

……………………… cm2

(2)

(c)

Triangle: 0.5x2x3=3

Parallogram: 2x3=6 (M1 for both)

3+6=9m2(A1)

……………………… m2

(2)


(d)

Add parallel sides, multiply by distance between and half.

0.5x5x(6+10) = 40cm2 (M1A1)

……………………… cm2

(2)

(e) Add parallel sides, multiply by distance between and half.

0.5x4x(9+6)=30cm2 (M1A1)

……………………… cm2

(2)

(Total 10 marks)

Total /10


Area of Composite Shapes 1 Grade 4 Solutions

Objective: Calculate the area of composite shapes including circles.

Question 1.

Find the area of the following composite shapes:

(a)

9x2=18

2x4x0.5=4 (M1)

18+4=22m2 (A1)

……………………………m2

(2)

(b)

14x12=168

9x6=54 (M1)

168-54=114m2 (A1)

……………………………

(2)

(Total 4 marks)


Question 2.

Find the area of the shape.

50x30=1500 (M1)

152 × � = 706.86 (�1)

706.86+1500=2206.86m2 (A1)

……………………………m2

(3)

Question 3.

Find the area of the shaded region.

40x30=1200 (M1)

152 × � = 706.86 (�1)

1200− 706.86 = 493.14�2 (A1)

……………………………

(3)

Total /10


nth term of quadratic sequences 1 Grade 6 Solutions

Objective: Write and expression for the nth term of a sequence, including quadratic sequences.

Question 1.

(a) Here are the first five terms of a sequence.

4, 7, 12, 19, 28, …

Find the next term two terms of the sequence.

Sequence is going up in 3, 5, 7, 9, so next two terms will be add 11 then add 13.

39 and 52 (A1)

………………… and ………………… (1)

(b) The nth term of a different sequence is 2n2 – 8.

Work out the third term of this sequence.

= 2(32) - 8

= 10 (A1)

…………………………… (1)

(Total 2 marks)

Question 2.

Here are the first five terms of a quadratic sequence.

2, 5, 10, 17, 26, …

(a) Write down the next term of the sequence.

Sequence is going up in 3, 5, 7, 9, so nest time will be add 11

37 (A1)

………………………… (1)

(b) Find an expression in terms of n, for the nth term of this quadratic sequence. .

first difference = 3, 5, 7, 9

Second difference = 2 so n2


Sequence = 2, 5, 10, 17, 26 n2 = 1, 4, 9, 16, 25, difference = 1, 1, 1, 1, 1, nth term is n2 + 1 (A1)

……………………………………… (2)

(Total 3 marks)

Question 3.

Find an expression in terms of n, for the nth tem of this quadratic sequence.

3, 9, 19, 33, 51, …

First difference = 6, 10, 14, 18 Second difference = 4, 4, 4, 4, so 2n2 Sequence = 3, 9, 19, 33, 51 2n2 = 2, 8, 18, 32, 50, Difference = 1, 1, 1, 1, 1 nth term is 2n2 + 1 (A1 for each term) ………………………………………………………………………………………

(Total 2 marks)

Question 4.

Find the nth tem of this sequence.

4, 10, 18, 28, 40, …

First difference = 6, 8, 10, 12 Second difference = 2, 2, 2, 2, so n2

Sequence = 4, 10, 18, 28, 40 n2 = 1, 4, 9, 16, 25 Difference = 3, 6, 9, 12, 15 so 3n

nth term is n2 + 3n


………………………………………………………………………………………

(Total 3 marks)

Total /10


Arcs and Sectors 1 Grade 6 Solutions

Objective: Calculate arc lengths and angles, and areas of sectors

Question 1.

PQ is an arc of a circle with radius 1.64m.

Angle POQ = 71o

(a) Calculate the perimeter of sector POQ.


Arc length = 71360 x π x 3.28 (=2.0322…) (M1)

Perimeter = Arc length + 1.64 x 2 (M1)

Perimeter = 5.31m (A1)

................................

(3)

(b) Calculate the area of sector POQ.


Area = 71360 x π x 1.642 (M1)

Area = 1.67m2 (A1)

................................

(2)

(Total 5 marks)


Question 2.

PQ is an arc of a circle with radius xcm.

Angle POQ = 120o

(a) Write down in terms of x and π an expression for the perimeter of sector POQ. Simplify your answer fully.

Arc length = 120360 x π x 2x (oe B1)

Perimeter = Arc length + 2x (B1)

Perimeter = 23 πx + 2x or

2��3 + 2x or 2x(�3 + 1) (A1)

................................

(3)

(b) Write down in terms of x and π an expression for the area of sector POQ. Simplify your answer fully.

Area = 120360 x π x x2 (oe B1)

Area = 13πx2 or

��23 (A1)

................................

(2)

(Total 5 marks)

Total /10

PLC Papers - · PDF filePiXL PLC 2017 Certification Fractions and percentages 1 Grade 4...

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