logo
Leaving Cert maths paper 2: Students seeking H1s or H2s find paper particularly challenging

Leaving Cert maths paper 2: Students seeking H1s or H2s find paper particularly challenging

Irish Times09-06-2025

Higher-level maths students who were anxious about their performance in paper one did not find comfort in paper two, but ordinary-level students will be pleased, teachers have said.
Aidan Roantree, a maths teacher at the Institute of Education, said that students looking for H1s and H2s will have found the paper particularly challenging, especially towards the end.
'The paper continued the same mixture of the familiar and the quirky, but on a larger scale with more of both,' he said.
'The question setter is consciously creating papers that are unlike previous years by adding novel questions that would have been hard to prepare for,' Mr Roantree said.
READ MORE
'Upon opening the paper, students will have felt an initial confidence boost to get them going. Section A's Q1, Q, 2, Q3 offered a reassuring and familiar start to the paper. This will have allowed students to accrue marks before venturing into the trickier sections.
'At Q4, the quirkier aspects of the paper emerged with questions that were evocative of pre-2015 statistics: interquartile ranges, averages, and later stratified sampling in Q10.
Section B followed a similar pattern with approachable opening questions followed by mounting difficulty.
In particular, Q9's part C was a very challenging probability question which would have tested the abilities of even the highest achievers.
'Indeed this paper contained some of the hardest questions on either paper, so students will leave the exam with a sense of having really pushed themselves,' Mr Roantree said.
Niall Duddy, ASTI subject representative for maths and a teacher at Presentation College Athenry in Co Galway, agreed that higher-level paper two was more testing than paper one.
'But students didn't say they couldn't do it, and paper two is traditionally the trickier of the two,' he said.
'On the plus side, it was user-friendly and contained hints here and there, such as where to use sine and cosine.
'The topics were quite focused, except for the trigonometry question which included some algebra; this is part of a recent trend of amalgamating the topics on the papers.
'Questions on statistics and probability would be familiar. Some students didn't like the look of question eight, which included a 3-D problem, but the question itself wasn't unusual.
'Overall, my students felt that while it was trickier, it was doable.'
Conversely, on the ordinary-level exam, Jean Kelly, a maths teacher at the Institute of Education, said that students who felt uncertain about their performance on paper one will have been relieved.
'Gone are the questions that jump around topics or hide aspects behind the language of the question,' she said.
'The paper was snappy, cutting right to the point and unified in the topics examined. Question one was focused on statistics, Q2 on trigonometry, Q3 on the circle. This helped students stay focused on the task and feel like they are being helpfully scaffolded as the questions got harder. This feeling of momentum will help them get through the paper and feel much more assured in their performance.'
The paper was heavy on statistics, probability and trigonometry, with area and volume having a lesser presence than in previous years, which was likely due to a surprise appearance on paper one, Ms Kelly said.
'While there were enough challenging pieces on the paper to distinguish those striving for the O1, even those who struggle to pass will find themselves in a good position,' she said.
'The paper was often helpful, either through tips or by combining topics into a useful grouping. For example, the appearance of constructions in section B was new, but the helpful pairing of dilations and area and volume helped ease students through the material.
'While paper one needed students to constantly, even anxiously reread the questions, there was a nice snappiness to this paper. Students who had the fundamentals were able to quickly get their marks without fuss and frustration,' said Ms Kelly.
Mr Duddy said the ordinary-level topics were laid out clearly and that the paper was user-friendly with lots of helpful hints.

Orange background

Try Our AI Features

Explore what Daily8 AI can do for you:

Comments

No comments yet...

Related Articles

Emergency services carry out multiple coastal rescues over past two days
Emergency services carry out multiple coastal rescues over past two days

Irish Times

time10 hours ago

  • Irish Times

Emergency services carry out multiple coastal rescues over past two days

A number of sea and cliff rescue operations have taken place over the last two days in Donegal , Clare and Dublin as emergency services warn the public to stay back from cliff edges. A multi-agency rescue operation was launched shortly after 7am on Saturday at the West End in Bundoran, Co Donegal, after a person fell from a cliff. The alarm was raised when a member of the public heard cries for help and contacted the emergency services. Malin Head Coast Guard co-ordinated the response, tasking Bundoran RNLI, Donegal Fire Service, the National Ambulance Service and Sligo-based Coast Guard helicopter Rescue 118. Bundoran RNLI volunteers were on scene within minutes. The casualty was located at the base of the cliff having landed on rocks. READ MORE The RNLI crew on scene worked to recover the person to the beach. The person was stabilised and airlifted by Rescue 118 before being transferred to Sligo General hospital for further treatment. A multi-agency search and rescue operation was also launched in Lahinch, Co Clare, on Friday night after a man sustained injuries to his legs after he fell from a cliff. The man, who is believed to be a tourist, fell from a 7m height cliff at the Miltown Malbay Road car park in the town. The alarm was raised at 10.15pm. The Shannon-based Rescue 115 attended the scene along with the Doolin Coast Guard unit. The Coast Guard said it was a difficult rescue as the man had fallen into an inaccessible area. It caused certain difficulties for the fire service in terms of reaching him. A winchman was lowered to the man's location. The man, who is in his 20s, is being treated at Galway University Hospital for non-life-threatening injuries. He arrived on site shortly after midnight. [ Teenager (15) who died while swimming in Laytown, Co Meath is named Opens in new window ] On Friday, a teenager was airlifted to hospital with suspected multiple fractures and lacerations after falling 6m on to rocks in Howth. The teenager had to be winched by helicopter from the White Water Brook, a remote beach below cliffs on the eastern side of the Howth peninsula. The Rescue 116 hospital winching a teenager off the rocks at the Howth peninsula on Friday afternoon Another teenager who went to help him suffered from hypothermia. That boy was transferred to the all-weather lifeboat and taken back to Howth lifeboat station, where he was transferred into the care of an ambulance crew. Both teenagers were taken to Beaumont Hospital in Dublin. In a separate incident, the volunteer crew of the Howth RNLI rescued three children who had been cut off by the tide near Lion's Head – a popular swimming spot on the south side of the Howth peninsula, close to the Bailey lighthouse. The RNLI has reminded anyone visiting the coast to stay well back from cliff edges, take extreme care near the water, and in an emergency dial 999 or 112 and ask for the Coast Guard.

Poppies symbolise the fleeting, bittersweet beauty of summer gardens
Poppies symbolise the fleeting, bittersweet beauty of summer gardens

Irish Times

time18 hours ago

  • Irish Times

Poppies symbolise the fleeting, bittersweet beauty of summer gardens

If ever there was a flower that symbolises the fleeting, bittersweet beauty of the garden in summer, then it's surely the poppy, with its gossamer-thin petals and delicate, slender stems. But do you know your short-lived, sun-loving annual poppy species, including many that are suitable for poorer, free-draining soils, from longer-lived biennial, perennial and shrubby kinds, including some that will only flourish in cool, damp, humus-rich, woodland conditions? If you're lucky, you may have come across the very rare, yellow-horned poppy, Glaucium flavum (a particular favourite of the late British artist and gardener Derek Jarman), a wild biennial or short-lived perennial species sometimes found growing in shingly beaches along sheltered Irish coastlines. Much more common is the annual wild field poppy or corn poppy, Papaver rhoeas, whose vermilion blooms light up road verges and waste ground at this time of year. Each ephemeral flower lasts just three to four days, but then another quickly takes its place, resulting in a long-lasting display over several months. READ MORE For those who dislike red, consider the cultivated forms of this sun-loving, hardy annual, commonly known as the Shirley poppy, which are also available to gardeners, with both double and single flowers in soft shades of pink, apricot, white, peach and sooty purple. An enduring favourite is Papaver rhoeas 'Amazing Grey', famed for its silver-purple blooms. To enjoy it as a cut-flower indoors, simply sear the end of each stem with a lighter or candle or plunge the tips into boiling water for 7-10 seconds before quickly placing them in cold water. [ Slow Flower power is all about the local and the seasonal Opens in new window ] Easily raised from seed in autumn or early spring, the conventional advice is to direct-sow these into the ground where you want the plants to flower. But I've had much greater success with module-raised seedlings transplanted into the garden in very late spring and early summer. Just make sure to do this while they're still small. The annual/short-lived perennial poppy species commonly known as the Californian poppy, Eschscholzia californica, similarly loves a warm, sunny spot. But it usefully combines this with a remarkable ability to thrive in the poorest and stoniest of soils, making it a great choice for drought-prone gardens where it will also often self-seed. Typically known for its flame-orange flowers which appear throughout summer, many new varieties with blooms in shades of peach, pink, coral, cream, buttercup and apricot have been introduced in recent years and are easily raised from seed. Examples include the 'Thai Silk' series, especially 'Thai Silk Apricot Chiffon' with its luminously beautiful, deep apricot flowers. The Californian poppy, Eschscholzia californica, loves a warm, sunny spot By comparison, growing the outlandishly beautiful but famously capricious Icelandic poppy is a challenge for even seasoned gardeners. Best known as Papaver nudicaule, but recently renamed as Oreomecon nudicaulis, this late spring/early summer-flowering species loathes intense heat, preferring cool, bright conditions. Technically a perennial, it's best treated as a biennial raised from seed sowed in late spring and then planted out in autumn to flower the following year. Getting its tiny seeds to successfully germinate and then preventing them from damping-off can be fiendishly difficult, a challenge made more aggravating by the fact that seed of the most desirable strain – the Colibri poppy, originally bred for the cut-flower trade – is also mind-wateringly expensive. Icelandic poppy: Outlandishly beautiful but famously capricious But for those who succeed, the reward is giant poppy flowers in shades of peach, watermelon-pink, gold and brilliant orange, which emerge like tropical butterflies out of giant sculptural flower pods. Equally famous for its disdain of anything other than ideal growing conditions, the exquisite Himalayan poppy (Meconopsis baileyi; M 'Lingholm'; M 'Slieve Donard') is also that rarest of things in nature, which is blue-flowering. To grow it well – indeed, to grow it at all – you must give this summer-flowering perennial a cool, damp but free-draining, humus rich, neutral to slightly acid soil and edge-of-woodland growing conditions where its delicate blooms are protected from harsh winds and strong sunlight. For this reason, it's generally only found growing in parts of the country where rainfall levels are high and summers rarely get too hot. Himalayan blue poppy Only when it's entirely happy will it then self-seed, the caveat here being that you must grow a non-sterile variety for it to do so. Yet such is the glorious sight of it flowering en masse that many gardeners still go to extraordinary lengths to encourage this aristocratic poppy to establish. But nothing could be further from the case when it comes to the opium poppy, Papaver somniferum, a hardy, sun-loving annual species so promiscuous that once introduced, it's likely to self-seed itself about the place with happy abandon. It can even arrive unannounced, its tiny seeds hitching a lift in the soil of a potted plant or brought on the soles of muddy gardening boots. In my own garden, an unnamed variety with shocking-pink, double flowers did just this a few years ago, producing tall, large, violently colourful blooms so entirely out of place that it's as if a flock of noisy flamingos had descended without warning into the cool, damp green of an Irish landscape. Somehow, I just don't have the heart to pull the numerous seedlings out, excusing them on account of the large, long-lasting, ornamental seed-heads that eventually follow. But my favourite will always be the altogether subtler, plum-coloured Papaver 'Lauren's Grape'. Pink opium poppies Other abundantly self-seeding members of the poppy family eminently suitable for an Irish garden include the shade-loving Welsh poppy, Meconopsis cambricum, a late spring to early autumn flowering perennial species with an endearing way of insinuating itself into shady cracks in paving, steps and stone walls. A woodland plant at home in cool, damp, moderately rich but free-draining soils, the pretty flowers come in shades of orange, soft coral and bright yellow. Among the loveliest is the pale apricot-coloured Meconopsis cambricum var. aurantiacum. Also making the list is the oriental poppy, Papaver orientale, a herbaceous perennial species whose large, flouncy flowers are the stuff of cottage garden dreams. Its great failing, however, is the ugly gap left behind after this sun-loving border plant finishes flowering in early summer, a flaw best managed by cutting it back hard and then quickly following with a liquid feed. [ Natural liquid nettle feed is superb for keeping your plants healthy – it just smells terrible Opens in new window ] Last, but not least, is the Californian tree poppy, one of the few shrub-like members of the poppy family, with silver-grey foliage and giant, golden-eyed white flowers that appear on long, lax stems in late summer. This showstopper also has strong Irish connections, with its genus and species names celebrating two Irishmen, the botanist Thomas Coulter and the astronomer Thomas Romney Robinson. Flower of a California tree poppy, Romneya coulteri, whose genus and species names celebrate Irishmen Thomas Coulter and Thomas Romney Robinson Introduced into cultivation in the late 19th century, it first flowered in the National Botanic Gardens in Glasnevin in 1877. Typically requiring a sunny, sheltered spot and famously difficult to establish, it can unfortunately become too much of a good thing when it finally does, often sending out suckers that appear metres away from the parent plant. Still, such is its undeniable charm in full bloom that few gardeners can resist it. This week in the garden Deadhead, deadhead, deadhead … Heavy rain and hail showers in recent weeks have damaged the flowers of many plants. To encourage them to recover and start producing new blooms, use a sharp secateurs or snippers to cut them away, making sure not to accidentally remove any newly emerging flower buds. Mulch around the base of newly planted shrubs and trees to lock in moisture while soils are still wet after heavy rainfall. Suitable materials include fresh grass clippings, home-made compost, well-rotted garden manure and seaweed. Dates for dour diary Tullynally Castle & Gardens Plant Fair – Castlepollard, Co Westmeath. Saturday, June 21st. With stalls by many of the country's leading nurseries. Fruitlawn Garden Open Day – Abbeyleix, Co Laois. Sunday, June 22nd. With plant sales and refreshments. Delgany and District Horticultural Society Rose Show – St Patrick's National School, Greystones, Co Wicklow, Saturday, June 28th. All entries welcome, email by Thursday, June 25th.

How yellow rattle can inject new life into Ireland's green spaces
How yellow rattle can inject new life into Ireland's green spaces

Irish Times

time19 hours ago

  • Irish Times

How yellow rattle can inject new life into Ireland's green spaces

'Gliográn' means 'little rattler' – a clattery, tinkling thing – and it describes well the sound rippling across a field full of yellow rattle in late summer, around August, carried best on a dry day with a light breeze. The soft rattling noise comes from the dried seeds inside their papery bladder-like pods, which shake like tiny maracas. Years ago, a tinkling field told farmers it was time to make hay; they'd listen for the sound as their cue to take out the scythe and start cutting. Finding a large field full of yellow rattle isn't easy these days – it's often considered a weed , especially by farmers on high-yield grassland systems. But just last week I stood in a gently sloping Co Meath field filled with this yellow flower, with clover growing beneath, at the new 552-acre Brú na Bóinne National Park in Dowth, in the Boyne Valley. The park, which the State bought for €11 million in 2023, isn't yet open to the public (it will take a few more years). But the process of turning the high-nutrient grasslands into spaces for nature has already begun, led by the new park manager, Maurice Eakin. Dr Eakin has one goal: to bring life back to these lands. To begin the process, he sowed yellow rattle seeds in parts of the park last November. Often called 'the meadow maker' or 'nature's lawnmower', the yellow rattle is a handsome, striking plant with slender, toothed green leaves and sunlit yellow flowers shaped like snapdragon-style tubular bells clustered at the top of its stem. Above ground, the plant is all charm – a beautiful burst of yellow flowers swaying in the fields, as if butter wouldn't melt. Underground, though, it's quite the vampire and thief. As a seedling, yellow rattle sends out roots that latch on to those of neighbouring plants, especially grasses, and siphon off their water, minerals and nutrients. This parasitic habit weakens the grasses and slows their growth, and it's particularly effective against dominant grass species such as ryegrass. (This is why many farmers understandably dislike it since ryegrass is rich in energy and protein and is fed to livestock.) READ MORE By winning a war against dominant grasses, yellow rattle opens space for less competitive wildflowers to grow, such as oxeye daisy, buttercup, sweet vernal grass and common knapweed. The result is a diverse meadow with flowers that bloom at different times through the spring and summer, offering a steady supply of nectar and pollen for insects and somewhere to shelter and breed. As the wild plant conservation charity Plantlife says, yellow rattle is the 'single most important plant you need when creating a wildflower meadow'. Although it was cold and damp when I stood in the field with Dr Eakin, the hoverflies and bumblebees were out in numbers, landing on the yellow flowers in search of sweet nectar. As they moved from plant to plant, the bees brushed against the flowers' male parts and picked up dustings of fine, powdery pollen, each grain carrying the plant's sperm cells. When the bees visited the next flower, some of that pollen rubbed off on to the female part of the plant, fertilising it and allowing it to produce seeds. Just as the yellow rattle gets up to mischief beneath the soil, some bee species get up to tricks while feeding on its nectar. This sugar-rich liquid is buried deep inside the yellow flower, favouring long-tongued bees such as the garden bee, whose tongue can reach 20mm long. Shorter-tongued bees that arrive on the flower can't reach it, but that doesn't put them off. Instead of entering through the floral opening, they land on the side of the flower where the nectar collects, bite a small hole, and drink their fill. These 'nectar robbers' bypass the flower's reproductive parts, so while they get the sweet stuff, the plant gains nothing in return apart from a dose of its own medicine from one thief to another. [ Butterflies in free fall: 'It's really alarming because it shows that something significant is happening in the wider countryside' Opens in new window ] Dr Eakin says he is delighted with how the yellow rattle transforms the field from ryegrass-dominated grassland into a richer, more diverse meadow. His aim over the next few years is to restore life to this part of Meath, and his use of yellow rattle as a key tool in this process could inspire and guide urban park managers across Ireland. Injecting life into public green spaces – transitioning from mown grass to wildflower meadows – can help reverse insect decline and create healthier, more vibrant spaces for local communities. The impact of urban meadows can be significant. A study published last year by scientists at Warsaw University found that replacing regularly mowed lawns with wildflower meadows in cities leads to a high concentration of pollinating insects, making these urban meadows as valuable as natural meadows in rural areas. The outlook for pollinators in Ireland is bleak. Our butterflies are in free fall. Recent data from the National Biodiversity Data Centre reveals staggering, catastrophic declines in their populations between 2008 and 2021: the meadow brown down 86 per cent, the ringlet down 88 per cent, the green-veined white down 87.2 per cent. Like bumblebees, butterflies are homeless and starving, with little hope of recovery unless we urgently restore wildflowers to our landscape. [ Irish wildflowers: Growing your own mini-meadow isn't always easy but the results are magical Opens in new window ] In this battle, an gliográn – the yellow rattle – could be one of our most loyal and effective allies.

DOWNLOAD THE APP

Get Started Now: Download the App

Ready to dive into a world of global content with local flavor? Download Daily8 app today from your preferred app store and start exploring.
app-storeplay-store