Question 1 · Maths (arithmetic)

What is 32% of 75?

• A24✓ Correct
• B25
• C43
• D107
• E240

Solution

32% of 75 is the same as 75% of 32, because percentages are reversible (both mean 32 × 75 ÷ 100). 75% = ¾, and ¾ of 32 = 24.

Question 2 · Maths (word problem)

Tap A can fill a tank in 20 minutes, and Tap B can fill the same tank in 30 minutes. A drain can empty a full tank in 60 minutes. The tank is initially half full. Both taps and the drain are then opened together. How long will it take to fill the tank completely?

• A6 minutes
• B7 minutes 30 seconds✓ Correct
• C10 minutes
• D12 minutes 30 seconds
• E15 minutes

Solution

Look at all the rates in terms of 60 minutes:

• Tap A: 1 tank in 20 minutes, so 3 tanks in 60 minutes
• Tap B: 1 tank in 30 minutes, so 2 tanks in 60 minutes
• Drain: empties 1 tank in 60 minutes

Altogether, A + B – Drain = 3 + 2 – 1 = 4 tanks in 1 hour. So 1 tank takes ¼ hour (15 minutes), and ½ a tank takes ⅛ hour (7.5 minutes). One tankful takes 15 minutes, so half a tank takes 7 minutes 30 seconds.

Question 3 · English (spelling)

Which word is spelt incorrectly?

• AEmbarrass
• BOccurence✓ Correct
• CConscientious
• DAccommodate
• ERhythm

Solution

The correct spelling is occurrence, with a double c and a double r.

Question 4 · English (vocabulary)

Meticulous is closest in meaning to:

• AForgetful
• BClever
• CFussy
• DCareful and precise✓ Correct
• ESlow

Solution

Meticulous means showing great attention to detail. Fussy is close, but suggests being hard to please, which isn't quite the same thing.

Question 5 · Reasoning (find the link)

Which word has a similar meaning to BOTH sets of words? (hide, conceal) (unclear, dubious)

• AObscure✓ Correct
• BUnusual
• CArcane
• DCover
• EWeird

Solution

As a verb, obscure means “to hide or cover”. As an adjective, it means “confusing or rare”.

Question 1 · Maths (fractions)

Which fraction is closest to 1?

• A31/32
• B42/41
• C49/50
• D61/60
• E73/74✓ Correct

Solution

Each fraction is exactly one piece away from 1: 31/32 is 1/32 below 1, 42/41 is 1/41 above 1, and so on. The bigger the denominator, the smaller the piece, so 73/74, only 1/74 away, is closest. Being above 1 doesn’t matter; only the size of the gap does.

Question 2 · Maths (word problem)

A floor has 6 rows and 5 columns of square tiles. A rectangular mat covers exactly 2 rows by 3 columns of tiles, and it may be turned by 90°. In how many different positions can the mat be placed so that it exactly covers whole tiles?

• A15
• B17
• C30
• D31✓ Correct
• E32

Solution

Unturned (2 rows tall, 3 columns wide), its top edge can be on rows 1 to 5 and its left edge on columns 1 to 3, so there are 5 × 3 = 15 places it can be on the floor.

When turned 90°, the mat is 3 rows tall and 2 columns wide. Its top edge can be on rows 1 to 4 and its left edge can be on columns 1 to 4, so there are 4 × 4 = 16 places it can be on the floor.

In total, there are 15 + 16 = 31 ways to position the mat on the floor.

Question 3 · English (sentence structure)

Which sentence makes it clear that Jacob was crossing the street?

• ACrossing the street, the cat looked back at Jacob.
• BJacob watched from the pavement as the cat crossed the street.
• CThe cat watched Jacob as it crossed the street.
• DJacob watched the cat crossing the street.
• EWhile crossing the street, Jacob watched the cat.✓ Correct

Solution

Only this sentence clearly makes Jacob the person crossing. In the others, the cat is crossing or Jacob is on the pavement; “Jacob watched the cat crossing the street” most naturally means the cat is crossing.

Question 4 · English (comprehension)

The old clock had not chimed for years, yet every night Grandpa still wound it. Why does Grandpa continue winding the clock?

• AOut of habit or attachment✓ Correct
• BBecause he cannot sleep
• CTo make it chime
• DBecause someone has asked him to
• EBecause it keeps perfect time

Solution

The clock hasn’t chimed for years, yet Grandpa still winds it. The word yet suggests he does it out of habit or fondness rather than to hear it chime.

Question 5 · Reasoning (missing letter)

One letter completes the first word and begins the second word. ABSOR (?) OUGH

• AT
• BB✓ Correct
• CR
• DC
• ED

Solution

The letter B completes ABSORB and begins BOUGH.

Question 1 · Maths (arithmetic)

What is the ones digit of 7 × 17 × 27 × 37 × 47 × 57?

• A1
• B3
• C5
• D7
• E9✓ Correct

Solution

Only the ones digits matter, and every number ends in 7, so keep multiplying ones digits by 7. 7 × 7 = 49, which ends in 9. Then 9 × 7 = 63 ends in 3, 3 × 7 = 21 ends in 1, 1 × 7 = 7 ends in 7, and 7 × 7 = 49 ends in 9 again. That is six 7s multiplied together, so the answer ends in 9.

Question 2 · Maths (word problem)

A pupil starts a quiz with 0 points. Each correct answer earns 9 points, and each incorrect answer loses 6 points. After answering eight questions, the pupil has 42 points. How many questions did the pupil answer correctly?

• A3
• B4
• C5
• D6✓ Correct
• E7

Solution

If all eight answers were correct, the score would be 72. Changing a correct answer into an incorrect one decreases the score by 15 points. 72 – 42 = 30 points, so 30 ÷ 15 = 2 answers were incorrect. Therefore, 6 answers were correct.

Question 3 · English (sentence rearrangement)

Rearrange the words below to make a meaningful sentence. One word will not fit. carefully · praised · worked · the · for · artist · working · was. Which word does not fit?

• Aworked✓ Correct
• Bworking
• Ccarefully
• Dfor
• Ewas

Solution

The sentence is “The artist was praised for working carefully.” The word worked does not fit.

Question 4 · English (vocabulary in context)

Despite the warm welcome, the ambassador’s remarks were ______, avoiding any definite promises. Which word best completes the sentence?

• Aunequivocal
• Bjubilant
• Cguarded✓ Correct
• Dcandid
• Eemphatic

Solution

Guarded means cautious or deliberately restrained. The ambassador avoided definite promises rather than speaking openly, forcefully or joyfully.

Question 5 · English (word meaning)

The kumquats were abundant this year, so Gus could make pies for his community. What does abundant mean?

• AExpensive
• BScarce
• CAbdicate
• DAbstract
• EPlentiful✓ Correct

Solution

Abundant means plentiful.

Question 1 · Maths (factors)

How many whole numbers from 1 to 100 inclusive have exactly three different positive whole-number factors?

• A3
• B4✓ Correct
• C5
• D6
• E10

Solution

Only squares of prime numbers have exactly three factors. For example, 25 has factors 1, 5 and 25: the 5 pairs with itself, and because 5 is prime, there are no others. (36 has many more because 6 is not prime.) Since the question asks for numbers from 1 to 100 inclusive, we need the squares of prime numbers that are less than 10, i.e. 2, 3, 5, 7. Their squares are 4, 9, 25 and 49, so there are 4.

Question 2 · Maths (word problem)

The table below shows how many pupils chose four activities. Eight pupils change their choice from Archery to Climbing. After this change, exactly one-third of all pupils have chosen Climbing. How many pupils originally chose Climbing?

• A18✓ Correct
• B20
• C26
• D30
• E34

Solution

After the change, Archery has 24 − 8 = 16, Bowling still has 16 and Dance still has 20. Together that is 52 pupils, which is two-thirds of everyone.

So, one-third is 52 ÷ 2 = 26, so Climbing now has 26 pupils. Before the 8 moved across, Climbing had 26 − 8 = 18.

Question 3 · English (punctuation)

Which sentence is punctuated correctly?

• A“Hurry up” shouted Dad, “we’ll be late!”
• B“Hurry up!” shouted Dad, “We’ll be late!”
• CHurry up! shouted Dad “We’ll be late!”
• D“Hurry up!” shouted Dad. “We’ll be late!”✓ Correct
• E“Hurry up!” Shouted Dad, “we’ll be late.”

Solution

The exclamation mark goes inside the speech marks, and shouted stays lower case because the sentence continues. “We’ll be late!” is a new sentence, so it follows a full stop and begins with a capital letter.

Question 4 · English (comprehension: inference)

At the end of the exhibition, Isla paused at the noticeboard to read every prize winner’s name. When her friend asked whether she was disappointed, she replied, “Not particularly,” then quietly began packing away her brushes. What is most strongly suggested about Isla?

• AShe has forgotten to check the competition results.
• BShe is angry with her friend for asking.
• CShe has decided to stop painting.
• DShe is pleased that her friends have won prizes.
• EShe is disappointed but reluctant to admit it.✓ Correct

Solution

Reading every winner’s name shows the results matter to her, despite her claim. Quietly packing away suggests she doesn’t want to talk about how she feels.

Question 5 · Reasoning (missing letter strings)

Choose the pair of letter strings that completes BOTH words. ru___e    trou___

• Aonn & ser
• Bstl & ten
• Cbbl & ghs✓ Correct
• Dtll & ble
• Embl & tts

Solution

BBL completes RUBBLE and GHS completes TROUGHS.

Question 1 · Maths (percentages)

A number is increased by 20%. The result is then decreased by 20%. What fraction of the original number remains?

• A23/25
• B24/25✓ Correct
• C1
• D26/25
• E6/5

Solution

Start with 100: increasing by 20% gives 120, then reducing 120 by 20% takes off 24, giving 96. The fraction remaining is 96/100 = 24/25. It isn’t 1, because the 20% taken off is 20% of a bigger number.

Question 2 · Maths (angles on a clock)

At 2:50, what is the smaller angle between the hour hand and the minute hand of a clock?

• A120°
• B125°
• C145°✓ Correct
• D150°
• E215°

Solution

Each hour on a clock is 360° ÷ 12 = 30°. From the 10 (where the minute hand points) to the 2 is four hour-gaps of 30°, which is 120°.

But the hour hand has also moved 50/60 of the way from 2 to 3, which is 5/6 of 30° = 25°. So, the angle is 120° + 25° = 145°.

Question 3 · English (punctuation: capital letters)

How many words in the sentence below should begin with a capital letter? last tuesday, my cousin and i visited the natural history museum in london.

• A5
• B6
• C7✓ Correct
• D8
• E9

Solution

The seven words are Last (start of the sentence), Tuesday, I, Natural, History, Museum and London. Days of the week, the word I, and every word in a proper name take capitals.

Question 4 · English (comprehension: sibilance)

The snake slid silently through the silver grass, its scales softly brushing the stones. Which of the following is NOT an effect of the repeated ‘s’ sounds?

• AThey help the reader imagine the snake’s quiet approach.
• BThey make the snake’s movements seem abrupt and forceful.✓ Correct
• CThey emphasise the snake’s smooth, quiet movement.
• DThey echo the hissing sound associated with snakes.
• EThey create a soft, whispering quality.

Solution

The repeated ‘s’ sounds create sibilance, suggesting hissing and smooth, quiet movement rather than abrupt force.

Question 5 · Reasoning (letter code)

If the code for STEEP is TUFFQ, what does DBMMT mean?

• ATOUGH
• BCELLS
• CDUMMY
• DSTEAL
• ECALLS✓ Correct

Solution

Each letter of the word moves forward one place in the alphabet to make the code (S→T, T→U, E→F, E→F, P→Q). To decode, move each letter back one place: D→C, B→A, M→L, M→L, T→S, which gives CALLS.

Question 1 · Maths (negative numbers)

All the integers from −15 to 20 inclusive are added together, but one number is accidentally left out. The total is 98. Which number was left out?

• A-12
• B-8✓ Correct
• C-6
• D8
• E12

Solution

The integers from −15 to 15 cancel in positive-negative pairs, leaving 16 + 17 + 18 + 19 + 20 = 90. But the total is 98, which is 8 greater. Therefore, −8 must have been left out.

(8 cannot be the number that is left out, because then −8 would be left, so the total would be 82.)

Question 2 · Maths (area and perimeter)

A square courtyard is surrounded by a path exactly 2 m wide on every side. The path covers an area of 80 m². What is the perimeter of the courtyard itself?

• A32 m✓ Correct
• B40 m
• C48 m
• D64 m
• E80 m

Solution

Split the path into four 2 m × 2 m corner squares (16 m² altogether) and four strips, each 2 m wide and as long as one side of the courtyard.

The strips make 80 − 16 = 64 m², so each strip is 16 m², and the courtyard side is 16 ÷ 2 = 8 m. Perimeter: 4 × 8 = 32 m.

Question 3 · Grammatical terminology

What type of phrase is “The unusually quiet crowd outside the theatre” in the sentence below? The unusually quiet crowd outside the theatre stood still.

• AAdverbial phrase
• BAdjective phrase
• CPrepositional phrase
• DSubordinate clause
• ENoun phrase✓ Correct

Solution

The whole group of words is a noun phrase, with crowd as its main noun. The other words tell us more about the crowd.

Question 4 · Vocabulary

Despite the glowing reviews, Theo remained sceptical about the new invention. Which action would best demonstrate his scepticism?

• AAsking for evidence that it worked✓ Correct
• BRefusing to discuss it
• CPraising it to his friends
• DOrdering one immediately
• EClaiming that it was certainly a failure

Solution

Being sceptical means doubting something until there is convincing evidence. Asking for proof shows scepticism without assuming the invention is a failure.

Question 5 · Ordering units of length

Arrange these lengths from longest to shortest. Which unit is THIRD?

• ACentimetre
• BMillimetre
• CDecimetre✓ Correct
• DMetre
• EKilometre

Solution

From longest to shortest: kilometre, metre, decimetre, centimetre, millimetre. A decimetre is 0.1 of a metre and a centimetre is 0.01 of a metre, so the decimetre comes third.

Question 1 · Maths (units of area)

An area of 0.08 m² is compared with an area of 750 cm². By how many square centimetres is the first area larger?

• A50 cm²✓ Correct
• B500 cm²
• C670 cm²
• D742 cm²
• E750 cm²

Solution

1 m = 100 cm, so 1 m² = 100 cm × 100 cm = 10,000 cm², not 100 cm². So, 0.08 m² = 0.08 × 10,000 = 800 cm², and 800 − 750 = 50 cm².

Question 2 · Maths (money problem)

Pens cost 35p each and pencils cost 20p each. Sam spends exactly £2 and buys at least one of each. How many pencils does he buy?

• A3✓ Correct
• B4
• C5
• D7
• E10

Solution

Pencils always cost a multiple of 20p, so the pens must cost a multiple of 20p too. 1, 2 or 3 pens cost 35p, 70p or 105p, none of which is a multiple of 20p, but 4 pens cost 140p. That leaves 200p − 140p = 60p, which buys 3 pencils.

(4 is the number of pens and 7 is the total number of items.)

Question 3 · Punctuation (dashes)

Which sentence uses dashes correctly to mark extra information?

• AThe rescue team exhausted – after the climb – reached the village.
• BThe rescue team – exhausted after the climb – reached the village.✓ Correct
• CThe rescue team – exhausted after the climb reached – the village.
• DThe rescue team exhausted after the – climb reached – the village.
• EThe rescue team – exhausted after the climb reached the village.

Solution

The dashes surround “exhausted after the climb”, which adds extra information. Removing this phrase leaves a complete sentence.

Question 4 · Vocabulary

Ominous is closest in meaning to:

• Amysterious
• Benormous
• Cancient
• Dthreatening✓ Correct
• Enoisy

Solution

Ominous suggests that something bad or threatening may happen. Mysterious is close, but does not necessarily suggest danger.

Question 5 · Synonyms

Which pair of words is closest in meaning?

• Apossible, feasible✓ Correct
• Battentively, focus
• Cdisaster, tragic
• Dabundant, rare
• Eunbeaten, uncommon

Question 1 · Maths (fractions)

What is -1/4 - 2/6 + 3/8 + 4/12 + 5/10 - 6/16 + 7/8 - 8/16?

• A1/4
• B3/8
• C5/8✓ Correct
• D3/4
• E7/8

Solution

Recognise the equivalent fractions: 2/6 and 4/12 are equivalent, so -2/6 + 4/12 = 0. Similarly, 3/8 - 6/16 = 0 and 5/10 - 8/16 = 0, leaving 7/8 - 1/4 = 5/8.

Question 2 · Maths (area)

A rectangular garden is divided into four smaller rectangular beds by one horizontal line and one vertical line, as shown. The diagram is not drawn to scale. What is the area of the fourth bed?

• A24 m²
• B26 m²
• C28 m²
• D30 m²✓ Correct
• E32 m²

Solution

The top two beds have the same height, and 18 m² is 1½ times 12 m², so the right-hand beds are 1½ times as wide as the left-hand ones. The bottom two beds also share a height, so the missing area is 1½ times 20 m² = 30 m².

Question 3 · Spelling

Which sentence is spelt correctly?

• AThe independent committee reached a consensus.✓ Correct
• BThe independant committee reached a consensus.
• CThe independant committee reached a concensus.
• DThe independent committee reached a concensus.
• EThe independent comittee reached a consensus.

Solution

Independent ends in -ent, not -ant. Committee has a double m and a double t, and consensus is spelt with an s after con, not a c.

Question 4 · Comprehension (summarising)

Every autumn, thousands of salmon leave the sea and swim upstream towards the rivers where they hatched. Strong currents, waterfalls and predators make the journey dangerous. Those that reach their destination lay their eggs, beginning the next generation.

Which is the best summary?

• ASalmon prefer swimming in strong currents.
• BSalmon are unable to reproduce until they have escaped waterfalls.
• CSalmon spend most of their lives living in rivers.
• DSalmon migrate mainly to escape predators in the sea.
• ESalmon return to their original rivers to reproduce, despite the dangers of the journey.✓ Correct

Solution

This summarises both the purpose of the journey and its dangers, without adding anything that isn’t in the passage.

Question 5 · Statement logic

Read the statements and choose the option that MUST be true. There are 10 girls in Class A.

Jade wears her hair in plaits to school every day except Thursdays, when she only ever wears it in pigtails.

Sophie wears her hair in a bun three days a week, but on a Wednesday and at weekends she always wears it in a ponytail.

Millie will only ever wear her hair in plaits, regardless of what day it is.

Andrea doesn’t like having her hair up, so she always wears it down when she’s at school.

• AOn a Monday, Jade has her hair in pigtails, Sophie has her hair in a ponytail and Millie has her hair in plaits.
• BOn a Tuesday, Andrea has her hair down, Millie has her hair in plaits and Sophie has her hair in a ponytail.
• COn a Monday, Jade and Millie have their hair in plaits and Sophie has her hair in a ponytail.✓ Correct
• DOn a Friday, Andrea, Sophie and Jade all have their hair in pigtails.
• EOn a Thursday, Jade has her hair in pigtails and Andrea and Sophie have their hair in a bun.

Solution

Note: the question should have said Sophie wears a ponytail on Mondays and Wednesdays, so C is the intended answer.

Question 1 · Maths (mental calculation)

What is 88 × 112 + 12 × 12?

• A9,712
• B9,856
• C9,988
• D10,000✓ Correct
• E10,144

Solution

Split 112 into 100 + 12.

Then 88 × 112 = (88 × 100) + (88 × 12)

Notice that (88 × 12) + (12 × 12) = 100 × 12

So, 88 × 112 + 12 × 12 = (88 × 100) + (100 × 12) = 8800 + 1200 = 10,000

Question 2 · Maths (word problem)

When a jar is one-third full of rice, it weighs 1.5 kg. When the same jar is five-sixths full, it weighs 2.7 kg. How much does the empty jar weigh?

• A0.3 kg
• B0.7 kg✓ Correct
• C0.8 kg
• D0.9 kg
• E1.2 kg

Solution

Draw a bar model, including the jar. Split the first into thirds and the second into sixths. Then split each of the thirds into two, making the first bar also into sixths.

The difference between the two values is 3 equal parts of the bar, representing 1.2 kg.

Then one equal part = 1.2 kg ÷ 3 = 0.4 kg

Two equal parts plus the jar are 1.5 kg, so the jar is 1.5 – (2 × 0.4) = 0.7 kg

Question 3 · Punctuation (apostrophes)

How many words in the sentence below need an apostrophe?

The girls coats were hanging in the schools cloakroom, but Ellas wasnt there.

• A1
• B2
• C3
• D4✓ Correct
• E5

Solution

The four words are girls’ (or girl’s), school’s, Ella’s and wasn’t. Three show possession and one is a contraction.

Question 4 · Vocabulary

Which word means to make something less severe?

• Aalienate
• Balleviate✓ Correct
• Cabbreviate
• Daggravate
• Eelevate

Solution

Alleviate means to ease or lessen something unpleasant. Aggravate means the opposite: to make it worse.

Question 5 · Non-verbal reasoning (odd one out)

Identify the odd one out by looking at what the images below have in common.

• APicture A
• BPicture B
• CPicture C
• DPicture D
• EPicture E✓ Correct

Solution

Note: picture E should have shown two triangles and one square.

Question 1 · Maths (multiples)

The digits 0, 2, 4 and 6 are each used exactly once to form a four-digit number. How many different multiples of 4 can be made?

• A6
• B10✓ Correct
• C12
• D18
• E24

Solution

A number is a multiple of 4 if its last two digits make a multiple of 4. So, the possible endings that are multiples of 4 are 04, 20, 24, 40, 60 and 64. For each ending, the other two digits can go either way round, except 0 cannot be first (otherwise it wouldn’t be a 4-digit number).

Four of these endings contain 0. For each of these, the remaining two digits can go either way round, giving 2 possibilities. For example, ending in 04 gives 2604 and 6204. So there are 4 × 2 = 8 possibilities.

If the last two digits do not contain zero and the first digit cannot be zero, the remaining possibilities are 24 and 64, each give just one possibility because 0 cannot be the first digit.

In total, there are 8 + 2 = 10 possibilities.

Question 2 · Maths (word problem)

One-third of the pupils in a school club cycle to school. Twelve of the cyclists leave the club. No other pupils leave or join. Now exactly one-quarter of the club cycles to school. How many pupils were in the club originally?

• A36
• B48
• C72
• D96
• E108✓ Correct

Solution

Use the block method. In this case, we have a constant part – the number of pupils in the club who do not cycle to school.

We need the same number of blocks before and after for the pupils who do not cycle to school, so multiply the ‘before’ ratio by 3 and the ‘after’ ratio by 2.

Then the number who cycle before and after differs by 1 block, representing 12 pupils, so [] = 12.

There were 9 blocks in total in the scaled ‘before’ ratio, so there were 9 × 12 = 108 pupils in the club before.

Question 3 · Spelling and word choice

The new curtains ______ the pale green walls perfectly.

Which word correctly completes the sentence?

• Acompelled
• Bcomplimented
• Ccomplemented✓ Correct
• Dcomplimentted
• Ecomplementted

Solution

Complement means to go well with something, while compliment means to praise. A useful reminder is that a complement completes.

Question 4 · Vocabulary (ambiguous)

A notice at a school event read:

“Parents should collect children wearing green badges at the main entrance.”

Which word best describes the instruction?

• APersuasive
• BExaggerated
• CAmbiguous✓ Correct
• DContradictory
• EPrecise

Solution

Ambiguous means open to more than one interpretation. The notice could mean that the parents should wear green badges, or that they should collect the children who are wearing them.

Question 5 · Non-verbal reasoning (transformation)

The first image has been transformed to make the second image.

Which of the images below follows the same transformation of the third image?

• APicture A
• BPicture B
• CPicture C
• DPicture D
• EPicture E✓ Correct

Solution

The number of rings around the black dots gives the number of dotted lines. In the first image the black dots have 3 + 2 + 1 = 6 rings, making 6 lines. In the third image they have 3 + 3 + 2 = 8 rings, so the answer has 8 lines.

Question 1 · Maths (arithmetic)

What is 6.25 x 48 + 6.25 x 32 -1.25 x 80?

• A300
• B325
• C350
• D375
• E400✓ Correct

Solution

The first two products both have 6.25, so combine them: 6.25 × (48 + 32) = 6.25 × 80. Now both remaining terms have 80: (6.25 × 80) – (1.25 × 80) = (6.25 – 1.25) × 80 = 5 × 80 = 400.

Question 2 · Maths (cubes)

A large cube is made from 64 identical small cubes, arranged in a 4 × 4 × 4 cube.

The top and four side faces of the large cube are painted, but the bottom face is not.

The large cube is then separated into its individual small cubes.

How many small cubes have paint on exactly two faces?

• A12
• B16
• C20✓ Correct
• D24
• E28

Solution

8 cubes along the top edges have exactly two faces painted. The top corners have three painted faces, so they don't count.

12 cubes along the vertical edges, below the top layer, have exactly two faces painted. (Three of these cubes are hidden from view in the diagram.)

Total: 8 + 12 = 20 cubes.

Question 3 · Grammar (relative pronouns)

The explorer, ______ account of the journey was published later, travelled alone.

Which word correctly completes the sentence?

• Awhom
• Bwhich
• Cwho
• Dthat
• Ewhose✓ Correct

Solution

Whose shows possession: the account belongs to the explorer.

Question 4 · Comprehension (comparing attitudes)

The path curved out of sight.

“I wonder what we’ll find,” said Luca, quickening his pace.

“I wonder how we’ll get back,” replied Saira, studying the map.

How do the characters’ attitudes differ?

• ABoth characters are equally excited about what lies ahead.
• BBoth characters trust the map more than each other.
• CLuca has travelled this route before, but Saira has not.
• DLuca sees uncertainty as an opportunity, while Saira sees it as a risk.✓ Correct
• ESaira is eager to explore, while Luca wants to return.

Solution

Luca quickens his pace, suggesting excitement about the unknown. Saira checks the map and worries about getting back, suggesting caution.

Question 5 · Non-verbal reasoning (paper folding)

This piece of paper has been folded and then had shapes cut out of it. Which of the images below shows how the paper will look once it has been unfolded?

• APicture A
• BPicture B
• CPicture C✓ Correct
• DPicture D
• EPicture E

Solution

The number of layers of paper gives the number of holes. Once folded, the paper has 8 layers, so there are 8 triangles when it is unfolded.

Each fold line acts like a mirror line: each triangle is a reflection of the triangle on the other side of the fold. Picture C is the only one that shows this.

Question 1 · Maths (counting digits)

The pages of a book are numbered from 1 to 120. How many times does the digit 1 appear in all the page numbers?

• A32
• B40
• C51
• D52
• E53✓ Correct

Solution

From pages 1–99, the digit 1 occurs 10 times in the ones position and 10 times in the tens position: 20 times. From 100–120, it occurs 21 times in the hundreds position, 10 times in the tens position and twice in the ones position. Total: 20 + 21 + 10 + 2 = 53.

Question 2 · Maths (percentages)

Two groups of pupils answer the same survey. The percentage answering Yes is shown in the table. Exactly the same number answered Yes in both groups. Group B has 20 more pupils than Group A. How many pupils are in Group A?

• A60
• B64
• C72
• D80✓ Correct
• E100

Solution

The same number of pupils who answered Yes is ¾ of Group A and ⅗ of Group B. Since the number of pupils answering Yes is 3 parts in Group A, Group A is 4 parts. Similarly, Group B is 5 parts. B has 1 part more, which is 20 pupils, so A has 4 × 20 = 80.

Question 3 · Punctuation (commas)

A writer has only one uncle.

Which sentence is correctly punctuated?

• AMy uncle, who lives in Bristol, is a pilot.✓ Correct
• BMy uncle who lives in Bristol, is a pilot.
• CMy uncle, who lives in Bristol is a pilot.
• DMy uncle who lives in Bristol is a pilot.
• EMy uncle, who, lives in Bristol is a pilot.

Solution

The writer has only one uncle, so “who lives in Bristol” is extra information and needs commas on both sides. Without commas, it could suggest the writer has other uncles.

Question 4 · Vocabulary

The discovery of an earlier map undermined the explorer’s claim that he had been the first to reach the island.

What effect did the discovery have on his claim?

• AIt proved the claim beyond doubt.
• BIt made the claim more widely known.
• CIt made the claim easier to understand.
• DIt caused the claim to be published.
• EIt made the claim less convincing.✓ Correct

Solution

To undermine something is to weaken it. The earlier map makes the explorer’s claim less believable.

Question 5 · Non-verbal reasoning (cube nets)

Which cube can be made from this net?

• APicture A
• BPicture B
• CPicture C✓ Correct
• DPicture D
• EPicture E

Solution

A, D and E: the faces are shown in the wrong orientation.

B: it shows two faces next to each other that would be opposite each other on the cube.

C is the only cube that can be made from the net.

Question 1 · Maths (sequences)

The first five terms of a sequence are 3, 8, 15, 24, 35, … . What is the 20th term?

• A418
• B420
• C440✓ Correct
• D462
• E483

Solution

The terms follow 1 × 3, 2 × 4, 3 × 5, 4 × 6, 5 × 7, … . The 20th term is 20 × 22 = 440. Equivalently, each term is one less than a square: the 20th is 21² − 1.

Question 2 · Maths (time)

At exactly noon, Clock A shows 11:55 am and Clock B shows 12:09 pm. Clock A gains 2 minutes every 30 minutes, while Clock B loses 3 minutes every hour. At what actual time will both clocks next show the same time?

• A1:00 pm
• B1:30 pm
• C2:00 pm✓ Correct
• D2:30 pm
• E3:00 pm

Solution

Clock B starts 14 minutes ahead of Clock A. A gains 4 minutes every hour, while B loses 3, so the gap closes by 7 minutes every hour. It closes in 14 ÷ 7 = 2 hours, at 2:00 pm.

Check: At 1:00 pm, Clock A shows 12:59 and Clock B shows 1:06. At 2:00 pm, both clocks show 2:03.

Question 3 · Spelling (prefixes)

Which pair of prefixes correctly forms the opposites of legible and relevant, in that order?

• Aun-, in-
• Bin-, un-
• Cim-, dis-
• Dil-, ir-✓ Correct
• Eir-, il-

Solution

The prefix in- changes to il- before l (illegible) and to ir- before r (irrelevant). Watch the order: the question asks for legible first.

Question 4 · Vocabulary

The museum increased its admission prices, but an unexpected repercussion was a sharp fall in visitor numbers.

What does repercussion mean in this context?

• AAn indirect consequence✓ Correct
• BA deliberate improvement
• CA warning given beforehand
• DA sudden loud noise
• EA condition that must be met

Solution

A repercussion is a consequence, often an unwelcome one, that follows from an action. Here, the price rise led to fewer visitors. Despite the sound of the word, it has nothing to do with noise or percussion.

Question 5 · Non-verbal reasoning (combining shapes)

Which image is created by combining the two shapes below? The shapes may have been rotated.

• APicture A
• BPicture B✓ Correct
• CPicture C
• DPicture D
• EPicture E

Solution

In picture B, the diagonal line of the first shape runs from corner to corner across the L-shape (shown in red), and its other line sits along the top edge of the L-shape.

Question 1 · Maths (divisibility)

A four-digit number has the form 4□7□. What is the largest possible number of this form that is divisible by both 5 and 9?

• A4,275
• B4,770✓ Correct
• C4,875
• D4,970
• E4,975

Solution

Divisible by 5 means it ends in 0 or 5. Divisible by 9 means its digits add up to a multiple of 9. Ending in 0: 4 + □ + 7 + 0 must make 18, so □ is 7, giving 4,770. Ending in 5: 4 + □ + 7 + 5 must make 18, so □ is 2, giving 4,275. The larger is 4,770. (4,875 is divisible by 3, but not by 9.)

Alternatively, make use of the multiple-choice options. The question asks about the largest number, so start with the largest and work down to see if it is a multiple of both 5 and 9. All the options are multiples of 5. Then check which ones add up to a multiple of 9. 4770 is the largest one in the answer choices whose digits add up to a multiple of 9.

Question 2 · Maths (fractions and tables)

The table shows how pupils in Years 5 and 6 travel to school. What fraction of the Year 6 pupils who do not travel by bus come to school by car?

• A1/4
• B1/3
• C3/7✓ Correct
• D4/7
• E15/23

Solution

Year 6 has 32 − 12 = 20 walkers and 23 − 8 = 15 car travellers. Of the Year 6 pupils who do not use the bus, 20 + 15 = 35 pupils remain. The fraction who come by car is 15/35 = 3/7.

Question 3 · Grammar (subject–verb agreement)

Which sentence is grammatically correct?

• AThe keys to the cupboard is lost.
• BThe label on the boxes is missing.✓ Correct
• CThe results of the survey was unexpected.
• DThe colour of the walls have changed.
• EThe pattern on the curtains are difficult to see.

Solution

The verb agrees with the main noun, not the nearest noun. The correct forms are: label is, pattern is, results were, colour has and keys are.

Question 4 · Comprehension (evaluating evidence)

A collector claimed that a recently discovered painting must be a forgery because its signature looked different from the artist’s other works. A museum curator pointed out that the artist’s signature had changed considerably throughout his career.

Which conclusion is best supported by the information?

• AThe painting must be genuine because the artist changed his signature.
• BThe collector deliberately made a false accusation.
• CThe different signature raises questions, but is not enough to prove the painting is a forgery.✓ Correct
• DThe curator proved that the painting is genuine.
• EThe painting is definitely a forgery because the signatures differ.

Solution

The different signature might be suspicious, but there is another possible explanation. More evidence would be needed to decide whether the painting is genuine.

Question 5 · Non-verbal reasoning (codes)

Each letter represents a feature of the image. Which code applies to the final image?

• ASU
• BKH
• CUS
• DSK
• EUH✓ Correct

Solution

The first letter shows the direction of the two shapes. S: the shapes go from top left to bottom right. U: the shapes go from bottom left to top right.

The second letter shows the type of shape. I: triangles. H: arrows.

In the final image, the arrows go from bottom left to top right, so the code is UH.