Use a ruler to draw a straight line of length 4 cm
Worked Solution & Answer
4 cm B1
Answer: Line of length 4 cm
Reading scales — Notes & Worked Examples Show / Hide
Explanation:
To read any scale accurately, never guess what each small mark goes up in. First find the difference between two neighbouring numbered marks, then count the number of spaces (divisions) between them (count the gaps, not the tick lines).
Divide the difference by the number of gaps: 1 small division = Gap ÷ Number of spaces. Also check whether the question asks you to convert units (e.g. 1 kg = 1000 g, 1 litre = 1000 ml).
Example 1: Write down the reading shown by the arrow on this kitchen scale.
• Gap = 300 − 200 = 100 g split into 5 spaces
• Each division = 100 ÷ 5 = 20 g
• 3 divisions past 200 g = 200 + 60 = 260 g
Example 2: A jug has 10 divisions between 1.5 L and 2.0 L. Water is 7 divisions above 1.5 L. Find the volume in L and ml.
• 1 division = (2.0 − 1.5) ÷ 10 = 0.05 L (50 ml)
• Reading = 1.5 + 7 × 0.05 = 1.85 L (1850 ml)
Measure the length of this line in cm
cm
Worked Solution & Answer
Align the 0 mark of your ruler with one end of the line and read off the measurement carefully in the required units (1 cm = 10 mm).
3.5 cm
3.5 cm
Answer: 3.5 cm cm
The diagram shows a parallelogram, ABCD and the diagonal AC.
Tick (✓) the two correct statements.
Identify the two correct statements from the list:
1. ABĈ is not equal to CDÂ
2. AB = DC and AD = BC and AC is a side of both triangle ABC and triangle CDA
3. Triangle ABC is similar to triangle CDA with enlargement scale factor 0.5
4. Triangle ABC is not congruent to triangle CDA
5. Triangle ABC is congruent to triangle CDA
6. AB represents the shortest distance from B to AC
Identify the two correct statements from the list:
1. ABĈ is not equal to CDÂ
2. AB = DC and AD = BC and AC is a side of both triangle ABC and triangle CDA
3. Triangle ABC is similar to triangle CDA with enlargement scale factor 0.5
4. Triangle ABC is not congruent to triangle CDA
5. Triangle ABC is congruent to triangle CDA
6. AB represents the shortest distance from B to AC
Worked Solution & Answer
Opposite sides of a parallelogram are equal (AB = DC and AD = BC), and AC is common, so by SSS the triangles ABC and CDA are congruent. M1 A1
Answer: Statements 2 and 5 are correct.
Amir is going on holiday.
He weighs his suitcase on the weighing scales at the airport.
The reading on the scale gives the weight of Amir's suitcase.
He weighs his suitcase on the weighing scales at the airport.
The reading on the scale gives the weight of Amir's suitcase.
An excess luggage charge has to be paid when the weight of a suitcase is greater than 25 kg.
This charge is 7.45 euros for each kilogram over the 25 kg limit.
Work out the excess luggage charge that Amir has to pay.
This charge is 7.45 euros for each kilogram over the 25 kg limit.
Work out the excess luggage charge that Amir has to pay.
euros
Worked Solution & Answer
Reading on scale = 36 kg M1
Excess weight = 36 – 25 = 11 kg M1
Charge = 11 × 7.45 = 81.95 euros. A1
Excess weight = 36 – 25 = 11 kg M1
Charge = 11 × 7.45 = 81.95 euros. A1
Answer: 81.95 euros euros
The diagram shows a tree and a man.
The man is of average height.
The tree and the man are drawn to the same scale.
The tree and the man are drawn to the same scale.
(a) Write down an estimate for the real height, in metres, of the man. [1 mark]
metres
(b) Find an estimate for the real height, in metres, of the tree. [2 marks]
metres
Worked Solution & Answer
(a)
Average adult man height ≈ 1.75 m (or 1.5 to 2 m) B1
Answer (a): 1.5 to 2 metres
(b)
Tree is about 5.5 times as tall as the man → 5.5 × 1.75 ≈ 9.6 m (or 7.5 to 12 m) M1 A1
Answer (b): 7.5 to 12 metres
(a) The diagram shows a fair spinner for a simple game.
Rhian needs to score 7 or more with a single spin to win the game.
On the probability scale below, mark with an arrow the probability that Rhian wins the game.
(b) Tomas is playing a game with a different fair spinner.
Here is the shape of his spinner.
The arrow on the probability scale below shows the probability that Tomas scores less than 4 with one spin.
Write five numbers on Tomas' spinner so that the scale is correct.
(c) Simon is playing a game.
The probability that he wins the game is (0.7).
What is the probability that Simon does not win his game?
Rhian needs to score 7 or more with a single spin to win the game.
On the probability scale below, mark with an arrow the probability that Rhian wins the game.
(b) Tomas is playing a game with a different fair spinner.
Here is the shape of his spinner.
The arrow on the probability scale below shows the probability that Tomas scores less than 4 with one spin.
Write five numbers on Tomas' spinner so that the scale is correct.
(c) Simon is playing a game.
The probability that he wins the game is (0.7).
What is the probability that Simon does not win his game?
(a) The diagram shows a fair spinner for a simple game.
Rhian needs to score 7 or more with a single spin to win the game. [1 mark]
Rhian needs to score 7 or more with a single spin to win the game. [1 mark]
On the probability scale below, mark with an arrow the probability that Rhian wins the game.
(b) Tomas is playing a game with a different fair spinner.
Here is the shape of his spinner.
The arrow on the probability scale below shows the probability that Tomas scores less than 4 with one spin.
Write five numbers on Tomas' spinner so that the scale is correct. [1 mark]
Here is the shape of his spinner.
The arrow on the probability scale below shows the probability that Tomas scores less than 4 with one spin.
Write five numbers on Tomas' spinner so that the scale is correct. [1 mark]
(c) Simon is playing a game. The probability that he wins the game is (0.7).
What is the probability that Simon does not win his game? [1 mark]
What is the probability that Simon does not win his game? [1 mark]
Worked Solution & Answer
(a)
Scores 7 or more are 7 and 8 (2 outcomes out of 8).
Probability = 28 = 14. B1
Probability = 28 = 14. B1
Answer (a): Arrow marked at 2/8 (or 1/4)
(b)
The arrow on the scale indicates 25
Therefore, exactly 2 of the 5 numbers on the spinner must be less than 4. B1
Therefore, exactly 2 of the 5 numbers on the spinner must be less than 4. B1
Answer (b): Any five numbers where exactly 2 are less than 4 (e.g. 1, 2, 4, 5, 6)
(c)
(1 - 0.7 = 0.3) B1
Answer (c): 0.3
The picture below shows 3 identical apples on a set of scales.
(a) What is the mass of one apple? [1 mark]
g
(b) 5 identical pears have the same total mass as the 3 apples.
What is the total mass of two apples and two pears? [3 marks]
What is the total mass of two apples and two pears? [3 marks]
g
Worked Solution & Answer
(a)
Reading on scale = 450 g
Mass of 1 apple = 450 ÷ 3 = 150 g. B1
Mass of 1 apple = 450 ÷ 3 = 150 g. B1
Answer (a): 150 g g
(b)
Total mass of 5 pears = 450 g M1
Mass of 1 pear = 450 ÷ 5 = 90 g
Mass of 2 apples = 2 × 150 = 300 g M1
Mass of 2 pears = 2 × 90 = 180 g
Total mass = 300 + 180 = 480 g. A1
Mass of 1 pear = 450 ÷ 5 = 90 g
Mass of 2 apples = 2 × 150 = 300 g M1
Mass of 2 pears = 2 × 90 = 180 g
Total mass = 300 + 180 = 480 g. A1
Answer (b): 480 g g
Here is a solid shape.
(a) Write down the number of edges of this shape. [1 mark]
(b) On the grid below, draw a shape that is congruent to shape T [1 mark]
(c) Write down the order of rotational symmetry of the parallelogram. [1 mark]
(d) Write down the weight marked by the arrow. [1 mark]
kilograms
Worked Solution & Answer
(a)
4 base edges + 4 slant edges = 8 B1
Answer (a): 8
(b)
Congruent triangle drawn on grid
Answer (b): Congruent triangle drawn on grid
(c)
Order 2 B1
Answer (c): 2
(d)
Each division is 20 kg, 2 divisions past 200 = 240 kg B1
Answer (d): 240 kilograms
Here is a polygon.
(a) Write down the mathematical name of this polygon. [1 mark]
(b) On the scale, mark with an arrow (↑) the number 360 [1 mark]
(c) Write down the time shown on the clock face. [1 mark]
(d) Complete the following sentence by writing a suitable metric unit on the dotted line. [1 mark]
Worked Solution & Answer
(a)
5 sides = pentagon B1
Answer (a): Pentagon
(b)
Each division is 20, so 360 is 3 divisions past 300 B1
Answer (b): Arrow at 360 (3 divisions after 300)
(c)
1:45 B1
Answer (c): 1:45 (or quarter to 2)
(d)
centimetres B1
Answer (d): centimetres (or cm)
(a) (i) Circle the best expression for the chance that it will snow in the UK in July:
Impossible Unlikely Even chance Likely Certain
(a) (ii) A dish contains equal numbers of green grapes and black grapes.
Pedro takes one grape at random from the dish.
Circle the best expression for the chance that Pedro takes a green grape:
Impossible Unlikely Even chance Likely Certain
(b) (i) One letter is chosen at random from the 9-letter word AUSTRALIA.
On the probability scale below, mark with an arrow (\downarrow) the probability that the letter chosen from the word AUSTRALIA is T.
(b) (ii) A, E, I, O, U are vowels.
On the probability scale below, mark with an arrow (\downarrow) the probability that the letter chosen from the word AUSTRALIA is a vowel.
Impossible Unlikely Even chance Likely Certain
(a) (ii) A dish contains equal numbers of green grapes and black grapes.
Pedro takes one grape at random from the dish.
Circle the best expression for the chance that Pedro takes a green grape:
Impossible Unlikely Even chance Likely Certain
(b) (i) One letter is chosen at random from the 9-letter word AUSTRALIA.
On the probability scale below, mark with an arrow (\downarrow) the probability that the letter chosen from the word AUSTRALIA is T.
(b) (ii) A, E, I, O, U are vowels.
On the probability scale below, mark with an arrow (\downarrow) the probability that the letter chosen from the word AUSTRALIA is a vowel.
(a) Circle the best expression for the chance that it will snow in the UK in July:
Impossible Unlikely Even chance Likely Certain [1 mark]
Impossible Unlikely Even chance Likely Certain [1 mark]
(b) A dish contains equal numbers of green grapes and black grapes.
Pedro takes one grape at random from the dish.
Circle the best expression for the chance that Pedro takes a green grape:
Impossible Unlikely Even chance Likely Certain [1 mark]
Pedro takes one grape at random from the dish.
Circle the best expression for the chance that Pedro takes a green grape:
Impossible Unlikely Even chance Likely Certain [1 mark]
(b) One letter is chosen at random from the 9-letter word AUSTRALIA.
On the probability scale below, mark with an arrow (\downarrow) the probability that the letter chosen from the word AUSTRALIA is T. [1 mark]
On the probability scale below, mark with an arrow (\downarrow) the probability that the letter chosen from the word AUSTRALIA is T. [1 mark]
(d) A, E, I, O, U are vowels.
On the probability scale below, mark with an arrow (\downarrow) the probability that the letter chosen from the word AUSTRALIA is a vowel. [1 mark]
On the probability scale below, mark with an arrow (\downarrow) the probability that the letter chosen from the word AUSTRALIA is a vowel. [1 mark]
Worked Solution & Answer
(a)
Unlikely
Answer (a): Unlikely
(b)
Even chance
Answer (b): Even chance
(b)
There is 1 T in AUSTRALIA (9 letters), so probability is 19. B1
Answer (b): Arrow at 19 (the first mark after 0)
(d)
The vowels in AUSTRALIA are A, U, A, I, A (5 vowels out of 9 letters), so probability is 59. B1
Answer (d): Arrow at 59 (the fifth mark after 0)