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PLC Papers
Created For:
Year 11
Plotting Linear Graphs 1
Objective:
Question 1
Grade D
Plot the graphs of linear functions
Question 2
(1)
(Total: 3 marks)
Question 3
(1)
(Total: 3 marks)
Total Mark /10
Plotting Linear Graphs 2
Objective:
Grade D
Plot the graphs of linear functions
Question 1
(a) Complete the table of values for y = 2x + 5
(2)
(b) On the grid, draw the graph of y = 2x + 5 for values of x from x = -2 to x = 2
(2)
(Total: 4 marks)
Question 2
On the grid, draw the graph of y = 3x – 2 for values of x from –1 to 3
(3 marks)
Question 3
On the grid,
(a) draw the line x = 3
(b) draw the line y = −1
(c) draw the line y = x
(3 marks)
Total Mark /10
Sequences 1
Objective:
Grade C
Find the nth term of an arithmetic sequence, and generate terms using it.
Question 1
The first even number is 2
(a) Write down the 3rd even number
………………………………..(1)
Here are some patterns made from sticks.
(b) Draw pattern number 4 in the space below.
Pattern 4
………………………………..(1)
(c) Complete the table.
Pattern number
1
2
3
Number of sticks
3
6
9
4
5
………………………………..(2)
Jenny wants to find the number of sticks in pattern number 100
(d) Write down a method she could use.
……………………………………………………………………………………………………………………………………………………….
………………………………………………………………………………………………………………………………………………………(1)
(Total 5 marks)
Question 2
(a) The first odd number I s 1.
(i)
Find the 12th odd number.
……………………………………………..(1)
(ii)
Write down a method you could use to find the 100th odd number.
……………………………………………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………………………………(1)
Here are some patterns with dots.
(b) (i) In the space below, complete pattern number 4
(1)
(iii)
Work out the number of dots used to make pattern number 20.
(2)
(Total 5 marks)
Total marks / 10
Sequences 2
Objective:
Grade C
Find the nth term of an arithmetic sequence, and generate terms using it.
Question 1
Here are the first four terms of a number sequence.
3
7
11
15
(a) (i) Write down the next term in the sequence.
……………………………….
(ii) Explain how you got your answer.
………………………………………………………………………………………………………………………………………………………………………(2)
(b) Work out the 11th term in the sequence.
………………………….(1)
(c) Is 79 a term in this sequence?
Explain how you got your answer.
……………………………………………………………………………………………………………………………………………………..(1)
(Total 4 marks)
Question 2
Here is a number sequence.
7, 13, 19, 25 …………………….
(a) Explain why 286 cannot be in this sequence.
……………………………………………………………………………………………………………………………………………………….(1)
(b) Write an expression for the nth term of this sequence.
………………………………………………………………………………………………………………………………………………..…………………(2)
(Total 3 marks)
Question 3
The numbers in this sequence increase by the same amount each time.
11
What are the missing numbers?
…….
…….
35
You must explain clearly how you know.
……………………………………………………………………………………………………………………………………………………………………………………
Answers……………………………………………………….and ………………………………….
(Total 3 marks)
(Total marks / 10)
Solving Equations 1
Objective:
Grade D
Solve Linear Equations
Question 1
(a) Solve x + 4 = 7
x = ………………………………………
(1)
(b) Solve 3y = 15
y = ………………………………………
(1)
(Total: 2 marks)
Question 2
(a) Solve
=
y = ………………………………
(1)
(b) Solve 4x + 2 = 2x + 8
x = ……………………………
(2)
(Total: 3 marks)
Question 3
(a) Solve 4w + 3 = 2(w + 5)
w = …………………………………………
(3)
(b) Solve 5x – 7 = 3x – 3
x = ……………………………………………
(2)
(Total: 5 marks)
Total Mark /10
Solving Equations 2
Objective:
Grade D
Solve Linear Equations
Question 1
Solve 2x – 2 = 11
x = ………………………………………
(Total: 2 marks)
Question 2
(a) Solve
=
w = ………………………………
(1)
(b) Solve 3m + 7 = 34
m = ……………………………
(2)
(Total: 3 marks)
Question 3
(a) Solve 4(x + 7) = 44
x = …………………………………………
(3)
(b) Solve 2q – 4 = 5q + 5
q = ……………………………………………
(2)
(Total: 5 marks)
Total Mark /10
Trial and Improvement 1
Objective:
Grade C
Use trial and improvement to find approximate solutions to equations.
Question 1
The equation
+
= 37
has a solution between 3 and 4
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working.
= ………………………………...............
(3)
(Total 3 marks)
Question 2
The equation
+4
= 100
has a solution between 3 and 4
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working.
= ………………………………...............
(3)
(Total 3 marks)
Question 3
The equation
2
−
= 200
has a solution between 4 and 5.
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working.
= ………………………………...............
(4)
(Total 4 marks)
(Total
marks /10)
Trial and Improvement 2
Objective:
Grade C
Use trial and improvement to find approximate solutions to equations.
Question 1
The equation
− 3 = 23
has a solution between 3 and 4
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working.
= ………………………………...............
(3)
(Total 3 marks)
Question 2
The equation
− 5 = 60
has a solution between 4 and 5
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working.
= ………………………………...............
(3)
(Total 3 marks)
Question 3
Kim thinks of a number.
He adds 5, he then multiplies the result by his original number.
The answer is 456.
Find the number that Kim is thinking using a trial and improvement method.
You must show ALL your working.
= ………………………………...............
(4)
(Total 4 marks)
Total /10
Mean from a frequency table 1
Objective:
Grade C
Calculate the mean from a frequency distribution
Question 1
Zach has 20 CD’s
The table gives some information about the number of tracks on each CD.
a)
Number of tracks
Frequency
10
6
11
3
12
1
13
5
14
5
Zach estimates the mean, he thinks it will be approximately 6
Explain why Zach’s estimate is not correct
(1)
b) Work out the mean number of tracks on the CD’s
(3)
Question 2
A manufacturer states that the average number of sweets in each bag they sell is 15.
A sample of bags are tested and the results are shown in the table below
a)
Number of sweets
Number of bags
12
2
13
5
14
8
15
20
16
12
17
9
18
4
Find the range for the number of sweets in the bags
(1)
b) Is the manufacturer’s statement correct?
Calculate the mean number of sweets to explain your answer.
(5)
Total
/ 10
Mean from a frequency table 2
Objective:
Grade C
Calculate the mean from a frequency distribution
Question 1
Rosie had 25 boxes of matchsticks
The table gives some information about the number of matchsticks in each box.
a)
Number of matchsticks
Number of boxes
29
1
30
3
31
4
32
8
33
5
34
4
Find the mode
(1)
b) Work out the mean number of matchsticks in the boxes
(3)
Question 2
Allan measured the heights of some plants he had grown.
The measurements, in centimetres, are shown in the table.
a)
Height (cm)
Number of plants
18
7
19
9
20
18
21
12
22
9
Find the mean height for these plants.
Give your answer in centimetres, correct to 1 decimal place.
(5)
b) The mean for a the plants he grew last year was 23.7cm.
Which plants are taller? Give a reason for your answer.
(1)
Total
/ 10
Mean from grouped data 1
Objective:
Grade C
Estimate the mean of grouped data
Question 1
The table shows some information about the lengths, in minutes, of 50 films.
a)
Time, T, in minutes
Number of films
60 ≤ T < 80
9
80 ≤ T < 100
18
100 ≤ T < 120
8
120 ≤ T < 140
15
The lengths of 9 films were from 60 to 80 minutes
630 minutes is a sensible estimate for the total length of these 9 films
Explain why.
(1)
b) Calculate an estimate of the mean length of a film
(3)
Question 2
The heights of some students were measured and the results can be seen in the table below.
a)
Height (h cm)
Frequency
140 ≤ h < 150
12
150 ≤ h < 160
16
160 ≤ h < 170
25
170 ≤ h < 180
10
180 ≤ h < 190
7
Write down the modal class
(1)
b) Find the mean height for these students.
Give your answer in centimetres, correct to 1 decimal place.
(5)
Total
/ 10
Mean from grouped data 2
Objective:
Grade C
Estimate the mean of grouped data
Question 1
The grouped frequency table shows the weights of 60 babies born in Handlaw Hospital one week in May.
a)
Weight (w kg)
Frequency
1.5 ≤ w < 2.0
3
2.0 ≤ w < 2.5
9
2.5 ≤ w < 3.0
15
3.0 ≤ w < 3.5
16
3.5 ≤ w < 4.0
11
4.0 ≤ w < 4.5
6
Write down the class in which the median lies
(1)
b) Calculate an estimate of the mean weight of the babies
Round your answer to a sensible degree of accuracy
(4)
Question 2
Senthina recorded the times, in minutes, taken to repair 90 car tyres taken to a garage in June.
Information about these times is shown in the table.
a)
Time taken (t minutes)
Frequency
0≤ t < 6
16
6 ≤ t < 12
29
12 ≤ t < 18
19
18 ≤ t < 24
14
24 ≤ t < 30
12
Find the mean height for these students.
Give your answer in centimetres, correct to 1 decimal place.
(4)
b) Explain why the mean is an estimate rather than an exact value
(1)
Total
/ 10
HCF – LCM – Reciprocals 1
Objective:
Grade C
Use and understand the term reciprocal, HCF, LCM and prime numbers.
Question 1
a)
Find the LCM of 15 and 35
b) Find the HCF of 27 and 36
(2)
Question 2
a)
Find the reciprocal of 8
b) Find the reciprocal of 0.5
(2)
Question 3
The Highest common factor of two numbers is 7.
The lowest common multiple of the two numbers is 140.
Find the two numbers.
(3)
Question 4
Crackers are sold in boxes of 18.
Cheese slices are sold in packs of 14.
Sam wishes to buy the same number of crackers and cheese slices. What is the minimum number of boxes of crackers and packs
of cheese slices Sam should buy?
(3)
Total
/10
HCF-LCM-Reciprocals 2
Objective:
Grade C
Use and understand the term reciprocal, HCF, LCM and prime numbers.
Question 1
Find the sum of 20 and its reciprocal. Write your answer as a decimal.
(2)
Question 2
Find the HCF of 525 and 360
(3)
Question 3
The Highest common factor of two numbers is 5.
The lowest common multiple of the two numbers is 150.
Find the two numbers.
(2)
Question 4
Maddy is planning a party for children at a local nursery.
She wants all children to have a party hat and a whistle. She wishes to order the same number of party hats and whistles.
Party hats are sold in boxes of 12.
Whistles are sold in Boxes of 20.
a)
How many boxes of party hats should she order?
b) How many boxes of whistles should she order?
(3)
Total
/10
Percentage Change 1
Objective:
Grade C
Use and calculate percentage change.
Question 1
A new car is on sale for £9,200. The value of the car will decrease by 24% after one year.
What will be the value of the car after one year?
(2)
Question 2
Arif bought shares in a company worth £800 at the start of 2013.
By the end of 2013 the value of the shares had increased by 10%.
By the end of 2014 the value of the shares decreased by 10%.
Calculate the value of the shares at the end of 2014.
(4)
Question 3
Amber bought 12 crates of oranges for £6 each. There are 50 oranges in each crate.
She sells the oranges on her market stall in packs of 5. Each pack costs £1.20.
She sells all the packs of oranges but she reduces the price of 10% of the packs to 60p at the end of the day.
Calculate her profit on the sale of oranges.
(4)
Total
/10
Percentage Change 2
Objective:
Grade C
Use and calculate percentage change.
Question 1
A jeweller decides to increase prices by 5% or £10, whichever is greater.
a)
Find the new price of a watch which did cost £400.
b)
A necklace would be increased by the same amount using either 5% or £10. Find the original cost of the necklace.
(4)
Question 2
In an office block a lift has a notice that states “The maximum capacity is 12 people”.
a)
If 15 people use the lift at the same time, by what percentage is the maximum capacity of the lift being exceeded?
Another lift in the office block has a different maximum capacity.
When this lift leaves floor 4 it is carrying 60% of its maximum capacity. At floor 5, 3 people join the lift and this represents 80%
of maximum capacity.
b)
What is the maximum capacity of this lift?
c)
How many people were in the lift between floors 4 and 5?
(6)
Total
/10
Percentage & proportion 1
Objective:
Grade C
SOLUTIONS
Use percentages to compare proportions
Question 1
In a class 9K, 40% of the class are girls.
of the girls are left handed and
of the boys are left handed.
(4)
Question 2
Andrew scored 33 out of 60 in his Geography test.
Andrew scored 62% in his History test.
Which subject did he get a better mark in?
(3)
Question 3
Zeenat scored 53 out of 60 in her English test.
She scored 177 out of 200 in her Maths test.
Which subject did she get a better mark in?
(3)
Total
/10
Percentages & Proportion 2
Objective:
Grade C
Use percentages to compare proportions
Question 1
Two buses transport some pupils to school. On Monday:
Bus A has 28 pupils on it and the ratio of girls to boys is 2:5.
Bus B has 30 pupils and the ratio of girls to boys is 3:2.
On Monday, is the percentage of girls travelling to school by bus more than 50%?
Clearly show your method.
(4)
Question 2
Pupils took a test in Chemistry. The maximum mark possible is 40.
Mr Rogers, the Chemistry teacher, decides to give an A grade to any pupil able to score at least 84% on the test.
What is the lowest mark it is possible to score on the test and achieve an A grade?
(3)
Question 3
A library has some computers people can use.
At 10am there are 13 people using computers.
At 10.30am people arrive at the library and use the spare computers. All the computers are now being used.
At 11am 20% of the people using computers, leave the library. There are now 16 computers being used.
a)
How many computers are there in the library?
(2)
b) What percentage of the computers in the library was being used at 10am?
(1)
Total
/10
Product of prime factors 1
Objective:
Grade C
Be able to write a number as the product of its prime factors.
Question 1
Express 126 as the product of prime factors
(2)
Question 2
The number 48 can be written as 2n × 3.
Find the value of n.
(2)
Question 3
A number q is expressed as the product of its prime factors.
If q = 24 × 3, express 10q as the product of prime factors. Write your answer as simply as possible.
(3)
Question 4
50 is expressed as the product of its prime factors.
If 50 = an × b find the values of a, b and n.
(3)
Total
/10
Product of prime factors 2
Objective:
Grade C
Be able to write a number as the product of its prime factors.
Question 1
A number r is expressed as the product of its prime factors.
If r = 24 × 3 × 5, find the value of r.
(2)
Question 2
555 can be expressed as 3 × 5 × 37, when writing as the product of prime factors.
Explain how the product of prime factors of 5550 can be produced from 555 = 3 × 5 × 37.
(4)
Question 3
Express 675 as the product of prime factors
(2)
Question 4
Given 275 can be written as 25 × 11. Express 2752 as the product of prime factors.
(2)
Total
/10
Upper and Lower Bounds 1
Objective:
Grade C
Understand and use limits of measurement
Question 1
A whole number when rounded to 2 significant figures is 150. When the number is rounded to 1 significant figure
the answer it is 100.
a) Give two examples that the number could be.
b) What range of values could the number be?
(2)
Question 2
Mark buys four sandwiches, each with a weight given as 250g. Weights are given to the nearest 10g.
What is the maximum possible weight of the four sandwiches? Give your answer in kilograms.
(3)
Question 3
A rectangular garden has sides of 9m and 12m measured to the nearest metre.
Calculate
a) The maximum possible perimeter
(3)
b) The minimum possible area
(2)
Total
/10
Upper and Lower Bounds 2
Objective:
Grade C
Understand and use limits of measurement
Question 1
Jim the gardener wishes to put weed killer over a customer’s garden. The dimensions of the garden, measured to the
nearest metre are 9m and 12 m.
Each box of weed killer will treat 10m2 of grass.
How many boxes of week killer would you recommend Jim buys? You must show our working.
(4)
Question 2
A whole number when rounded to 2 significant figures is 150. When the number is rounded to 1 significant figure
the answer it is 100.
a) Give two examples that the number could be.
b) What range of values could the number be?
(2)
Question 3
Mark buys four sandwiches, each with a weight given as 250g. Weights are given to the nearest 10g.
What is the maximum possible weight of the four sandwiches? Give your answer in kilograms.
(4)
Total
/10
Constructions 1
Objective:
Grade C
Produce standard constructions including bisecting angles and lines
Question 1.
Bisect this angle
(Total 3 marks)
Question 2.
Construct an isosceles triangle with side length 4cm, 6cm, 6cm.
(Total 4 marks)
Question 3.
Construct a perpendicular bisector on the line AB below
B
A
(Total 3 marks)
Total /10
Constructions 2
Objective:
Grade C
Produce standard constructions including bisecting angles and lines
Question 1.
Bisect this angle
(Total 3 marks)
Question 2.
Construct an isosceles triangle with side length 5cm, 4cm, 4cm.
(Total 4 marks)
Q3.
Construct a perpendicular bisector on the line AB below
A
B
(Total for question – 3 marks)
END OF TEST
Total for test
/10
Loci 1
Grade C
Objective:
Construct loci to show paths and shapes
Question 1.
Here is a map.
The map shows two towns, Burford and Hightown.
Scale: 1 cm represents 10 km
A company is going to build a warehouse.
The warehouse will be less than 30 km from Burford and less than 50 km from Hightown.
Shade the region on the map where the company can build the warehouse.
(Total 3 marks)
Question 2.
Draw a circle of radius 5cm.
Use the cross (×) as the centre of your circle.
(Total 1 mark)
Question 3.
Here is a scale drawing of a rectangular garden ABCD.
Jane wants to plant a tree in the garden
at least 5m from point C,
nearer to AB than to AD
and less than 3m from DC.
On the diagram, shade the region where Jane can plant the tree.
(Total 4 marks)
Question 4.
Here is a scale drawing of Gilda's garden. Scale: 1 cm represents 1 m
Gilda is going to plant an elm tree in the garden. She must plant the elm tree at least 4
metres from the oak tree.
On the diagram, show by shading the region where Gilda can plant the elm tree.
(Total for 2 marks)
Total /10
Loci 2
Grade C
Objective:
Construct loci to show paths and shapes
Question 1.
Draw the locus of the points 30km from the line AB
B
A
Scale: 1 cm represents 10 km
(Total 2 marks)
Question 2.
On the diagram, draw the locus of the points, outside the rectangle, that are 3cm from the
edges of this rectangle.
(Total 3 marks)
Question 3.
There is a lighthouse at A and B. To avoid the rocks, a ship must sail equidistant to both A
and B.
Draw a line that is equidistant to A and B on the diagram.
A
B
(Total 2 marks)
Question 4.
The diagram represents a triangular garden ABC
The scale of the diagram is 1 cm represents 1 m.
A tree is to be planted in the garden so that it is
Nearer to AB than to AC,
Within 5m of point A.
On the diagram, shade the region where the tree may be planted.
(Total 3 marks)
Total /10
Surface Area of prisms & cylinders 1
Objective:
Grade D
Find the surface area of simple 3D shapes
Question 1
Diagram not accurately drawn
Answer _________
(2 marks)
Question 2
A solid cube has sides of length 5cm
5 cm
5 cm
5 cm
Work out the total surface area of the cube.
State the units of your answer.
Answer _________
(1 mark)
Question 3
Work out the surface area of the triangular prism.
………………… cm2
(Total 4 marks)
Question 4
Calculate the surface area of this cylinder to 2 decimal places.
Diagram not accurately drawn
Answer :
………………….cm2
(Total 3 marks)
Total / 10
Surface Area of prisms and cylinders 2
Grade D
Objective: work out the surface area of cuboids and cylinders
Question 1
Answer _________
(2 marks)
Question 2
A solid cube has sides of length 4cm
4 cm
4 cm
4 cm
Work out the total surface area of the cube.
State the units of your answer.
Answer _________
(1 mark)
Question 3
Work out the surface area of the triangular prism.
………………… cm2
(Total 4 marks)
Question 4
Calculate the surface area of this cylinder
Answer :
Total / 10
………………….cm2
(Total 3 marks)
PLC Papers
Created For:
Year 11
Plotting Linear Graphs 1
Objective:
Grade D
SOLUTIONS
Plot the graphs of linear functions
Question 1
-4
-2
8
B2 for all 3 values correct in table
B1 for 2 values correct
M1 ft for plotting at least 2
correct points
A1 for correct line from x = -2 to
x=2
Question 2
-5
3
7
B2 for all 3 values correct in table
B1 for 2 values correct
A1 for correct line from x = -2 to
x=2
(1)
(Total: 3 marks)
Question 3
-4
6
11
B2 for all 3 values correct in table
B1 for 2 values correct
A1 for correct line from x = -1 to
x=3
(1)
(Total: 3 marks)
Total Mark /10
Plotting Linear Graphs 2
Objective:
Grade D
SOLUTIONS
Plot the graphs of linear functions
Question 1
(a) Complete the table of values for y = 2x + 5
3
7
9
(2)
(b) On the grid, draw the graph of y = 2x + 5 for values of x from x = -2 to x = 2
B2 for all 3 values correct in table
B1 for 2 values correct
M1 ft for plotting at least 2
correct points
A1 for correct line from x = -2 to
x=2
(2)
(Total: 4 marks)
Question 2
On the grid, draw the graph of y = 3x – 2 for values of x from –1 to 3
M1 for at least 2 correct attempts to find
points
M1 ft for plotting at least 2 correct points
A1 for correct line from x = -1 to x = 3
OR
M2 for at least 2 correct points and no
incorrect points plotted
A1 for correct line from x=-1 to x=3
(3 marks)
Question 3
On the grid,
(a) draw the line x = 3
(b) draw the line y = −1
(c) draw the line y = x
x=3
A1
y=x
A1
y = -1
A1
(3 marks)
Total Mark /10
Sequences 1
Objective:
Grade C
SOLUTIONS
Find the nth term of an arithmetic sequence, and generate terms using it.
Question 1
The first even number is 2
(a) Write down the 3rd even number
6 (A1)
Here are some patterns made from sticks.
(b) Draw pattern number 4 in the space below.
correct picture (A1)
(c) Complete the table.
Pattern number
1
2
3
4
5
Number of sticks
3
6
9
12
(A1)
15
(A1)
Jenny wants to find the number of sticks in pattern number 100
(d) Write down a method she could use.
3n so 3 x 100 = 300 (A1)
Accept any correct method that gives 300
(total 5 marks)
Question 2
(a) The first odd number I s 1.
(i)
Find the 12th odd number.
(ii)
Write down a method you could use to find the 100th odd number.
2n -1 so 2 x 100 -1 = 199
(A1)
23 (A1)
(1)
(1)
Here are some patterns with dots.
(b) (i) In the space below, complete pattern number 4
(A1)
(1)
(iii)
Work out the number of dots used to make pattern number 20.
(2)
n 0 1 2 3
4
t 2 5 8 11 14
nth term is 3n + 2 accept any method that is correct (M1)
3(20) + 2
60 + 2
62
(A1)
(total 5 marks)
Total marks / 10
Sequences 2
Objective:
Grade C
SOLUTIONS
Find the nth term of an arithmetic sequence, and generate terms using it.
Question 1
Here are the first four terms of a number sequence.
3
7
11
15
19 (A1)
(a) (i) Write down the next term in the sequence.
(ii) Explain how you got your answer. The rule is ADD 4 each time (A1)
(2)
(b) Work out the 11th term in the sequence.
4n -1
4(11) - 1
44 -1
43
(A1)
(1)
(c) Is 79 a term in this sequence?
Explain how you got your answer.
(1)
4n -1 = 79
4n = 80
n = 20 YES 79 is the 20th term in this sequence
(A1)
(Total 4 marks)
Question 2
Here is a number sequence.
7, 13, 19, 25 …………………….
(a) Explain why 286 cannot be in this sequence.
All the terms in this sequence are odd numbers, and 286 is even
(1)
(A1)
(b) Write an expression for the nth term of this sequence.
6n + 1
(A1) for 6n, (A1) for +1
(2)
(Total 3 marks)
Question 3
The numbers in this sequence increase by the same amount each time.
11
What are the missing numbers?
19
27
35
(A2)
You must explain clearly how you know.
(3)
The rule is ADD 8 each time (A1)
(Total 3 marks)
Total marks / 10
Solving Equations 1
Objective:
Grade D
SOLUTIONS
Solve Linear Equations
Question 1
(a) Solve x + 4 = 7
x=3
B1
x = ……………
3…………………………
(1)
(b) Solve 3y = 15
y=5
B1
y = ………………………5………………
(1)
(Total: 2 marks)
Question 2
(a) Solve
=
y = 27
y = ……………27…………………
(1)
(b) Solve 4x + 2 = 2x + 8
2x = 6
M1
method mark for correct method to isolate x terms or number terms on opposite sides of the equation
x=3
x = ………3……………………
(2)
(Total: 4 marks)
Question 3
(a) Solve 4w + 3 = 2(w + 5)
4w + 3 = 2w + 10
M1
2w = 7
M1
w = 3.5
A1 oe
w = …………………3.5………………………
(3)
(b) Solve 5x – 7 = 3x – 3
2x = 4
M1
x=2
A1
method mark for correct method to isolate x terms or number terms on opposite sides of the equation
x = …………2…………………………………
(2)
(Total: 4 marks)
Total Mark /10
Solving Equations 2
Objective:
Grade D
SOLUTIONS
Solve Linear Equations
Question 1
Solve 2x – 2 = 11
2x = 13
M1
x = 6.5
A1
x = ………………………………………
(Total: 2 marks)
Question 2
(a) Solve
w = 15
=
A1
w = ………………………………
(1)
(b) Solve 3m + 7 = 34
3m = 27
M1
m=9
A1
m = ……………………………
(2)
(Total: 3 marks)
Question 3
(a) Solve 4(x + 7) = 44
x + 7 = 11
M1 or 4x + 28 = 44, 4x = 16 seen
x=4
A1
x = …………………………………………
(2)
(b) Solve 2q – 4 = 5q + 5
-3q = 9
M1 method mark for correct method to isolate q terms or number terms on opposite sides of the equation
q = -3
A1
q = ……………………………………………
(2)
(Total: 5 marks)
Total Mark /10
Trial and Improvement 1
Objective:
Grade C
SOLUTIONS
Use trial and improvement to find approximate solutions to equations.
Question 1
The equation
+
= 37
has a solution between 3 and 4
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working.
x
x3 + x
comment
3
30
Low
3.5
46.4
High
3.4
42.7
High
3.3
39.2
High
3.2
36.0
Low
3.25
37.6
high
One correct substitution (M1)
Two further correct substitutions getting closer to the answer (M1)
x = 3.2 (A1)
(Total 3 marks)
Question 2
The equation
+4
= 100
has a solution between 3 and 4
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working.
x
x3 + 4
comment
3
63
low
3.5
76
low
3.6
98.5
low
3.7
105.4
high
3.65
101.9
high
One correct substitution (M1)
Two further correct substitutions getting closer to the answer (M1)
x = 3.6 (A1)
(Total 3 marks)
Question 3
The equation
2
−
= 200
has a solution between 4 and 5.
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working.
x
2x3 - x
comment
4
124
low
4.5
177.8
low
4.6
190.1
low
4.7
202.9
high
4.65
196.4
low
One correct substitution (M1)
Three further correct substitutions (M2)
x = 4.7 (A1)
(Total 4 marks)
Total /10
Trial and Improvement 2
Objective:
Grade C
Use trial and improvement to find approximate solutions to equations.
Question 1
The equation
− 3 = 23
has a solution between 3 and 4
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working.
x
x3 – 3x
comment
3
18
Low
3.5
32.8
High
3.4
29.1
High
3.3
26.0
High
3.2
23.2
High
3.1
20.5
Low
3.15
21.8
Low
One correct substitution (M1)
Two further correct substitutions getting closer to the answer (M1)
x = 3.2 (A1)
(Total 3 marks)
Question 2
The equation
− 5 = 60
has a solution between 4 and 5
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show ALL your working.
x
x3 – 5x
comment
4
18
Low
4.5
32.8
High
4.4
29.1
High
4.3
26.0
Low
4.35
23.2
High
One correct substitution (M1)
Two further correct substitutions getting closer to the answer (M1)
x = 4.3 (A1)
(Total 3 marks)
Question 3
Kim thinks of a number.
He adds 5, he then multiplies the result by his original number.
The answer is 456.
Find the number that Kim is thinking using a trial and improvement method.
You must show ALL your working.
n(n + 5) = 456
n
n(n + 5)
comment
10
10 x 15 = 150
Low
20
20 x 25 = 500
High
15
15 x 20 = 300
Low
17
17 x 22 = 374
Low
18
18 x 23 = 414
Low
19
19 x 24 = 456
Exact
Form a correct equation or state the correct calculation to be made (M1)
One correct substitution (M1)
Two further correct substitutions getting closer to the answer (M1)
Answer 345 (A1)
(Total 4 marks)
Total /10
Mean from a frequency table 1
Objective:
Grade C
Calculate the mean from a frequency distribution
Question 1
Zach has 20 CD’s
The table gives some information about the number of tracks on each CD.
a)
Number of tracks
Frequency
N×F
10
6
60
11
3
33
12
1
12
13
5
65
14
5
70
Total
20
240
Zach estimates the mean, he thinks it will be approximately 6
Explain why Zach’s estimate is not correct
The lowest number of tracks on the CD’s is 10 so the mean must be at least 10
1M
(1)
b) Work out the mean number of tracks on the CD’s
Total number of tracks = 240
(award 1M if an attempt to add at least 3 subtotals is seen)
2M
240 ÷ 20 = 12
(allow FT from their total divided by 20)
1M
(3)
Question 2
A manufacturer states that the average number of sweets in each bag they sell is 15.
A sample of bags are tested and the results are shown in the table below
a)
Number of sweets
Number of bags
N×F
12
2
24
13
5
65
14
8
112
15
20
300
16
12
192
17
9
153
18
4
72
Total
60
918
Find the range for the number of sweets in the bags
18 – 12 = 6
The range is 6
1A
(1)
b) Is the manufacturer’s statement correct?
Calculate the mean number of sweets to explain your answer.
Number in sample = 60
Total number of sweets = 918
(award 1M if an attempt to add at least 3 subtotals is seen)
1M
2M
918 ÷ 60 = 15.3
(allow FT from their total number of sweets divided by their total number of bags)
1M
Yes the manufacturer is correct the average is 15 if you round to the nearest whole number
1M
(5)
Total
/ 10
Mean from a frequency table 2
Objective:
Grade C
Calculate the mean from a frequency distribution
Question 1
Rosie had 25 boxes of matchsticks
The table gives some information about the number of matchsticks in each box.
a)
Number of matchsticks
Number of boxes
N×F
29
1
29
30
3
90
31
4
124
32
8
256
33
5
165
34
4
136
Total
25
800
Find the mode
32 matchsticks
1M
(1)
b) Work out the mean number of matchsticks in the boxes
Total number of matches = 800
(award 1M if an attempt to add at least 3 subtotals is seen)
2M
800 ÷ 25 = 32
(allow FT from their total divided by 25)
1M
(3)
Question 2
Allan measured the heights of some plants he had grown.
The measurements, in centimetres, are shown in the table.
a)
Height (cm)
Number of plants
N×F
18
7
126
19
9
171
20
18
340
21
12
273
22
9
198
Total
55
1108
Find the mean height for these plants.
Give your answer in centimetres, correct to 1 decimal place.
Number in sample = 55
Total = 1108
(award 1M if an attempt to add at least 3 subtotals is seen)
1M
2M
1108 ÷ 55 = 20.1454545
(allow FT from their total number of sweets divided by their total)
1M
mean = 20.1 (1dp)
correct rounding
1M
(5)
b) The mean for a the plants he grew last year was 23.7cm.
Which plants are taller? Give a reason for your answer.
The plants he grew last year were taller because the mean was higher
1M
(1)
Total
/ 10
Mean from grouped data 1
Objective:
Grade C
Estimate the mean of grouped data
Question 1
The table shows some information about the lengths, in minutes, of 50 films.
a)
Time, T, in minutes
Number of films
midpoint
60 ≤ T < 80
9
70
630
80 ≤ T < 100
18
90
1620
100 ≤ T < 120
8
110
880
120 ≤ T < 140
15
130
1950
Total
50
5080
The lengths of 9 films were from 60 to 80 minutes
630 minutes is a sensible estimate for the total length of these 9 films
Explain why.
70 is half way between 60 and 80
70 × 9 = 630
so 630 is a sensible estimate
1M
(1)
b) Calculate an estimate of the mean length of a film
Attempt to multiply mid points by frequencies
1M
Attempt to add their subtotals
(630, 1620, 880 and 1950)
1M
5080 ÷ 50 = 101.6
(allow FT from their total divided by 50)
1M
(3)
Question 2
The heights of some students were measured and the results can be seen in the table below.
a)
Height (h cm)
Frequency
midpoint
M×f
140 ≤ h < 150
12
145
1740
150 ≤ h < 160
16
155
2480
160 ≤ h < 170
25
165
4125
170 ≤ h < 180
10
175
1750
180 ≤ h < 190
Total
7
185
70
1295
11390
Write down the modal class
The modal group is 160 ≤ h < 170
1M
(1)
b) Find the mean height for these students.
Give your answer in centimetres, correct to 1 decimal place.
Correct total frequency = 70
Attempt to multiply mid points by frequencies
1M
1M
Attempt to add their subtotals
(1740, 2480, 4125, 1750, 1295)
1M
11390 ÷ 70 = 162.714286
(allow FT from their total divided by 70)
1M
mean = 162.7cm (1dp)
correct rounding
1M
(5)
Total
/ 10
Mean from grouped data 2
Objective:
Grade C
Estimate the mean of grouped data
Question 1
The grouped frequency table shows the weights of 60 babies born in Handlaw Hospital one week in May.
a)
Weight (w kg)
Frequency
midpoint
1.5 ≤ w < 2.0
3
1.75
5.25
2.0 ≤ w < 2.5
9
2.25
20.25
2.5 ≤ w < 3.0
15
2.75
41.25
3.0 ≤ w < 3.5
16
3.25
52
3.5 ≤ w < 4.0
11
3.75
41.25
4.0 ≤ w < 4.5
6
4.25
25.5
Total
60
185.5
Write down the class in which the median lies
3.0 ≤ w < 3.5
1M
(1)
b) Calculate an estimate of the mean weight of the babies
Round your answer to a sensible degree of accuracy
Attempt to multiply mid points by frequencies
1M
Attempt to add their subtotals
(20.25, 41.25, 52, 41.25, 25.5)
1M
185.5 ÷ 60 = 3.09166667
(allow FT from their total divided by 60)
1M
mean weight = 3.1 kg
( Allow 1dp or nearest whole number)
1M
(4)
Question 2
Senthina recorded the times, in minutes, taken to repair 90 car tyres taken to a garage in June.
Information about these times is shown in the table.
a)
Time taken (t minutes)
Frequency
midpoint
M×f
0≤ t < 6
16
3
48
6 ≤ t < 12
29
9
261
12 ≤ t < 18
19
15
285
18 ≤ t < 24
14
21
294
24 ≤ t < 30
Total
12
27
324
90
1212
Find the mean height for these students.
Give your answer in centimetres, correct to 1 decimal place.
Attempt to multiply mid points by frequencies
1M
Attempt to add their subtotals
(48, 261, 285, 294, 324)
1M
1212 ÷ 90 = 13.4666666
(allow FT from their total divided by 90)
1M
mean = 162.7cm (1dp)
correct rounding
1M
(4)
b) Explain why the mean is an estimate rather than an exact value
The data is grouped so you don’t know the exact values
1M
(1)
Total
/ 10
HCF – LCM – Reciprocals 1
Objective:
Grade C
SOLUTIONS
Use and understand the term reciprocal, HCF, LCM and prime numbers.
Question 1
a)
Find the LCM of 15 and 35
105
B1
9
B1
b) Find the HCF of 27 and 36
(2)
Question 2
a)
Find the reciprocal of 8
1/8
B1
2
B1
b) Find the reciprocal of 0.5
(2)
Question 3
The Highest common factor of two numbers is 7.
The lowest common multiple of the two numbers is 140.
Find the two numbers.
Find 2 numbers with LCM 20 (other methods acceptable)
Multiply by 7
28, 35
M1
M1
A1
(3)
Question 4
Crackers are sold in boxes of 18.
Cheese slices are sold in packs of 14.
Sam wishes to buy the same number of crackers and cheese slices. What is the minimum number of boxes of crackers and packs
of cheese slices Sam should buy?
18 = 2 x 3 x 3
14 = 2 x 7
M1
LCM = 2 x 3 x 3 x 7 = 126
M1 A1
(3)
Total
/10
HCF-LCM-Reciprocals 2
Objective:
Grade C
SOLUTIONS
Use and understand the term reciprocal, HCF, LCM and prime numbers.
Question 1
Find the sum of 20 and its reciprocal. Write your answer as a decimal
M1: 20 +
A1: 20.05
(2)
Question 2
Find the HCF of 525 and 360
M1: Clear method to find prime factors of 525 as 3 × 52 × 7 allow one error
M1: Clear method to find prime factors of 360 as 23 × 32 × 5 allow one error
A1: cao 15
(3)
Question 3
The Highest common factor of two numbers is 5.
The lowest common multiple of the two numbers is 150.
Find the two numbers.
M1: 5 × 30 seen or use of Venn diagram with 15,2,5 shown
A1: 10 and 75
(2)
Question 4
Maddy is planning a party for children at a local nursery.
She wants all children to have a party hat and a whistle. She wishes to order the same number of party hats and whistles.
Party hats are sold in boxes of 12.
Whistles are sold in Boxes of 20.
a)
How many boxes of party hats should she order?
M1: Use of prime factors or listing multiples of 12 and 20
A1: 5
b) How many boxes of whistles should she order?
A1: 3
(3)
Total
/10
Percentage Change 1
Objective:
Grade C
SOLUTIONS
Use and calculate percentage change.
Question 1
A new car is on sale for £9,200. The value of the car will decrease by 24% after one year.
What will be the value of the car after one year?
M1 uses a suitable method to find 24% of 9,200 eg 0.24 × 9200
A1 £6992
(2)
Question 2
Arif bought shares in a company worth £800 at the start of 2013.
By the end of 2013 the value of the shares had increased by 10%.
By the end of 2014 the value of the shares decreased by 10%.
Calculate the value of the shares at the end of 2014.
M1 800×1.1 or equivalent
A1 880
M1 0.9×800
A1 £792
(4)
Question 3
Amber bought 12 crates of oranges for £6 each. There are 50 oranges in each crate.
She sells the oranges on her market stall in packs of 5. Each pack costs £1.20.
She sells all the packs of oranges but she reduces the price of 10% of the packs to 60p at the end of the day.
Calculate her profit on the sale of oranges.
M1
Calculate the total number oranges 12 × 50 = 600 and cost of oranges 12 × 6 = 72
A1
Calculate number of packs 600 ÷5 = 120 and Finds 10% of “120” = 12
M1 Calculate revenue from the oranges “108”× 1.20 + “12” × 0.60 = 136.80
A1 cao £64.80
(4)
Total
/10
Percentage Change 2
Objective:
Grade C
SOLUTIONS
Use and calculate percentage change.
Question 1
A jeweller decides to increase prices by 5% or £10, whichever is greater.
a)
Find the new price of a watch which did cost £400.
b)
M1: 400 × 1.05 or equivalent method
A1: £420
A necklace would be increased by the same amount using either 5% or £10. Find the original cost of the necklace.
M1: 0.05p = 10
A1: £200
(4)
Question 2
In an office block a lift has a notice that states “The maximum capacity is 12 people”.
a)
If 15 people use the lift at the same time, by what percentage is the maximum capacity of the lift being exceeded?
M1:
×100 or
seen
A1: 25%
Another lift in the office block has a different maximum capacity.
When this lift leaves floor 4 it is carrying 60% of its maximum capacity. At floor 5, 3 people join the lift and this represents 80%
of maximum capacity.
b)
What is the maximum capacity of this lift?
M1: 3 people = 20% or equivalent statement
M1: Clear attempt to find 100%
A1: 15 people
c)
How many people were in the lift between floors 4 and 5?
A1: 9 people
(6)
Total
/10
Percentage & proportion 1
Objective:
Grade C
SOLUTIONS
Use percentages to compare proportions
Question 1
In a class 9K, 40% of the class are girls.
of the girls are left handed and
of the boys are left handed.
What percentage of the class 9K is left handed?
A1
60% of class is girls
M1 Suitable method to find 1/5 of 40% and 1/10 of 60%
A1 at least one of 8% and 6%
A1 14%
(4)
Question 2
Andrew scored 33 out of 60 in his Geography test.
Andrew scored 62% in his History test.
Which subject did he get a better mark in?
M1
attempt to convert 34/60 to a percentage eg 33/60 = 11/20 = 55%
A1
Geography = 55%
C1
History
(3)
Question 3
Zeenat scored 53 out of 60 in her English test.
She scored 177 out of 200 in her Maths test.
Which subject did she get a better mark in?
M1
M1
attempt to convert 53/60 to a percentage = (88.3%)
attempt to convert 177/200 to a percentage = (88.5%)
C1
Maths
(3)
Total
/10
Percentages & Proportion 2
Objective:
Grade C
SOLUTIONS
Use percentages to compare proportions
Question 1
Two buses transport some pupils to school. On Monday:
Bus A has 28 pupils on it and the ratio of girls to boys is 2:5.
Bus B has 30 pupils and the ratio of girls to boys is 3:2.
On Monday, is the percentage of girls travelling to school by bus more than 50%?
Clearly show your method.
M1: No of girls on Bus A 28÷7 × 2 on Bus B 30÷5×3 oe
A1: 26
M1 Either
or 29 calculated
A1: cao No with working above
(4)
Question 2
Pupils took a test in Chemistry. The maximum mark possible is 40.
Mr Rogers, the Chemistry teacher, decides to give an A grade to any pupil able to score at least 84% on the test.
What is the lowest mark it is possible to score on the test and achieve an A grade?
M1: 0.84 × 40
A1: 33.6
A1 34 marks
(3)
Question 3
A library has some computers people can use.
At 10am there are 13 people using computers.
At 10.30am people arrive at the library and use the spare computers. All the computers are now being used.
At 11am 20% of the people using computers, leave the library. There are now 16 computers being used.
a)
How many computers are there in the library?
M1: 80% = 16 computers and other % calculated which is a factor of 100 eg 20% = 4 or × 1.25 seen
A1: 20 computers
(2)
b) What percentage of the computers in the library was being used at 10am?
A1: 65%
(1)
Total
/10
Product of prime factors 1
Objective:
Grade C
SOLUTIONS
Be able to write a number as the product of its prime factors.
Question 1
Express 126 as the product of prime factors
M1 Find at least one of the pairs 2, 63 or 3, 42
A1 2 × 32× 7
(2)
Question 2
The number 48 can be written as 2n × 3.
Find the value of n.
M1 Isolate 2n = 16
A1 n = 4
(2)
Question 3
A number q is expressed as the product of its prime factors.
If q = 24 × 3, express 10q as the product of prime factors. Write your answer as simply as possible.
M1 10q = 10 × 24 × 3
A1
5 × 2 × 24 × 3
A1 25 × 3 × 5
(3)
Question 4
50 is expressed as the product of its prime factors.
If 50 = an × b find the values of a, b and n.
A1 a = 5
A1 b = 2
A1 n = 2
(3)
Total
/10
Product of prime factors 2
Objective:
Grade C
SOLUTIONS
Be able to write a number as the product of its prime factors.
Question 1
A number r is expressed as the product of its prime factors.
If r = 24 × 3 × 5, find the value of r.
M1: 24 shown to be 16 or 8 × 3 × 10 shown
A1: 240
(2)
Question 2
555 can be expressed as 3 × 5 × 37, when writing as the product of prime factors.
Explain how the product of prime factors of 5550 can be produced from 555 = 3 × 5 × 37.
M1: Shows or implies 5550 ÷ 555 = 10
M1: 3 × 5 × 37 × 10
A1: 2× 3 × 52 × 37
(3)
Question 3
Express 675 as the product of prime factors
M1: 5 × 135 or other product with one prime factor
A1: 33 × 52
(2)
Question 4
Given 275 can be written as 25 × 11. Express 2752 as the product of prime factors. Write your answer using index notation
M1: 275 = 5 × 5 × 11
M1: 2752 = 5 × 5 × 5 ×5 × 11 × 11
A1: 54 × 112
(3)
Total
/10
Upper and Lower Bounds 1
Objective:
Grade C
Understand and use limits of measurement
Question 1
A whole number when rounded to 2 significant figures is 150. When the number is rounded to 1 significant figure
the answer it is 100.
a) Give two examples that the number could be.
A1
Any of 145,146,147,148,149
b) What range of values could the number be?
A1
list of above integers or 145≤x<150
(2)
Question 2
Mark buys four sandwiches, each with a weight given as 250g. Weights are given to the nearest 10g.
What is the maximum possible weight of the four sandwiches? Give your answer in kilograms.
A1
identifies the upper bound as 255g
M1
Multiplies their “255” by 4, allow ft
A1 1.02kg
(3)
Question 3
A rectangular garden has sides of 9m and 12m measured to the nearest metre.
Calculate
a) The maximum possible perimeter
A1:
Limits stated as 9.5 and 12.5
M1: 2×”9.5” + 2×”12.5”
A1 cao 44m
(3)
b) The minimum possible area
A1 limits stated as 8.5 and 11.5
A1 cao 97.75m2
(2)
Total
/10
Upper and Lower Bounds 2
Objective:
Grade C
SOLUTIONS
Understand and use limits of measurement
Question 1
Jim the gardener wishes to put weed killer over a customer’s garden. The dimensions of the garden, measured to the
nearest metre are 9m and 12 m.
Each box of weed killer will treat 10m2 of grass.
a) How many boxes of week killer would you recommend Jim buys. You must show our working.
A1 States that the upper bound should be used
A1 Area calculated as 118.75m2
M1 Their “118.75”÷ 10 = 11.875
A1 cao 12 boxes needed
(4)
Question 2
A whole number when rounded to 2 significant figures is 150. When the number is rounded to 1 significant figure
the answer it is 100.
a) Give two examples that the number could be.
A1 Any of 145,146,147,148,149
b) What range of values could the number be?
A1 list of above integers or 145≤x<150
(2)
Question 3
Mark buys four sandwiches, each with a weight given as 250g. Weights are given to the nearest 10g.
What is the maximum possible weight of the four sandwiches? Give your answer in kilograms.
A1 identifies the upper bound as 255g
M1 Multiplies their “255” by 4, allow ft
A1 cao 1020g
A1 1.02kg ft from previous answer
(4)
(4)
Total
/10
Constructions 1
Objective:
Grade C
SOLUTIONS
Produce standard constructions including bisecting angles and lines
Question 1.
Bisect this angle
(Total 3 marks)
Question 2.
Construct an isosceles triangle with side length 4cm, 6cm, 6cm.
M1 for 4 cm line
B1B1 for each 6cm arc
A1 for correct triangle
(Total 4 marks)
Question 3.
Construct a perpendicular bisector on the line AB below
(Total 3 marks)
Total /10
Constructions 2
Objective:
Grade C
SOLUTIONS
Produce standard constructions including bisecting angles and lines
Question 1.
Bisect this angle
(Total 3 marks)
Question 2.
Construct an isosceles triangle with side length 5cm, 4cm, 4cm.
M1 for 5cm line drawn
B1 B1 for construction arcs drawn from each end
A1 for correct triangle
(Total 4 marks)
Question 3.
Construct a perpendicular bisector on the line AB below
(Total 3 marks)
Total /10
Loci 1
Grade C
SOLUTIONS
Objective:
Construct loci to show paths and shapes
Question 1.
Here is a map.
The map shows two towns, Burford and Hightown.
Scale: 1 cm represents 10 km
A company is going to build a warehouse.
The warehouse will be less than 30 km from Burford and less than 50 km from Hightown.
Shade the region on the map where the company can build the warehouse.
(Total 3 marks)
Question 2.
(Total 1 mark)
Question 3.
Here is a scale drawing of a rectangular garden ABCD.
(Total 4marks)
Question 4.
Here is a scale drawing of Gilda's garden. Scale: 1 cm represents 1 m
Gilda is going to plant an elm tree in the garden. She must plant the elm tree at least 4
metres from the oak tree.
On the diagram, show by shading the region where Gilda can plant the elm tree.
(Total 2 marks)
Total /10
Loci 2
Grade C
SOLUTIONS
Objective:
Construct loci to show paths and shapes
Question 1.
(Total 2 marks)
Question 2.
(Total 3 marks)
Question 3.
(Total 2 marks)
Question 4.
(Total 3 marks)
END OF TEST
Total for test
/10
Surface Area of prisms & cylinders 1
Objective:
Grade D
SOLUTIONS
Find the surface area of simple 3D shapes
Question 1
2 x 5 = 10 cm2
2cm
5cm
2 x 3 = 6 cm2
2cm
3cm
5 x 3 = 15 cm2
3cm
5cm
Surface area of 3 seperate rectangles = 31 cm2 M1
Surface area of cuboid with 6 faces = 31 x 2 = 62 cm2 A1
2
62 cm M1 A1
Answer__________________
(2 marks)
Question 2
A solid cube has sides of length 5cm
5 cm
5 x 5 = 25cm2
5cm
5cm
5 cm
5 cm
Work out the total surface area of the cube.
State the units of your answer.
Answer
= 25 cm2 x 6 squares
= 150cm2 A1
_________
(1 mark)
Question 3
Work out the surface area of the triangular prism.
Area of 2 triangles = (
10cm
×
) x 2 = 48 cm2
10 x 9 = 90 cm2
9cm
8 x 9 = 72 cm2
8cm
9cm
6 x 9 = 54 cm2
6cm
9cm
Minimum of 2shapes areas worked out correctly
216+ 48 cm2 M1
= 264 cm2 A1
Total 3 rectangles area
= 90 + 72 + 54 = 216cm2 M1
Question 4
Calculate the surface area of this cylinder
………………… cm2
(Total 4 marks)
S.area = 2 circles + curved area
S.area = 2
+ ℎ
= 2 × 1.5 + × 3 × 4
M1 if areas of 2 circles is seen
= 14.13716.. + 37.6991 ..
M1 if rectangular area is seen
= 51.83626.. cm2
A1 for the total surface area
Answer :
51.84 cm2 M1 M1 A1
(Total 3 marks)
M1
Total / 10
Surface Area of prisms and cylinders 2
SOLUTIONS
Grade D
Objective: work out the surface area of cuboids and cylinders
Question 1
8 x 4 = 32 cm2
8cm
4cm
4 x 3 = 12 cm2
4cm
3cm
8 x 3 = 24 cm2
3cm
8cm
Surface area of 3 separate rectangles = 68 cm2 M1
Surface area of cuboid with 6 faces = 68 x 2 = 136 cm2 A1
136cm2 M1 A1
Answer__________________
(2 marks)
Question 2
A solid cube has sides of length 4cm
4 cm
4 x 4 = 16cm2
4cm
4cm
4 cm
4 cm
Work out the total surface area of the cube.
State the units of your answer.
Answer
= 16 cm2 x 6 squares
= 96 cm2 A1 (1 mark)
_________
Question 3
Work out the surface area of the triangular prism.
Area of 2 triangles = (
11cm
7cm
×
) x 2 = 20 cm2
11 x 7 = 77 cm2
7x 4 = 28 cm2
7cm
4cm
5cm
5 x 7 = 35 cm2
7cm
Total 3 rectangles area
= 77+28+35 = 140 cm2 M1
Minimum of 2shapes areas worked out correctly
140 +20cm2 M1
M1
= 160
cm2 A1 cm2
…………………
(Total 4 marks)
Question 4
Calculate the surface area of this cylinder
S.area = 2 circles + curved area
2
+ ℎ
= 2 × 2.5 +
S.area = 2
× 5 × 10
M1 if areas of 2 circles is seen
= 39.2699.. + 157.079 ..
M1 if rectangular area is seen
= 196.34953.. cm2
A1 for the total surface area
Answer :
196.35 cm2 M1 M1 A1
(Total 3 marks)
Total / 10