Year 10 maths, English and science practice for NSW

What your child works on in Year 10

Maths

Negative indices, compound interest and depreciation, equations with algebraic fractions and from formulas, gradient-intercept form, parallel and perpendicular lines, parabolas and exponential curves, finding an angle with trigonometry, elevation and bearings, cylinders and composite solids, scale drawings, box plots, standard deviation, scatter plots and multistage probability. This is the Stage 5 core: path topics such as quadratic equations and surds are not in Learnest yet.

English

Technical and subject words, figurative language and naming the technique, concise noun and verb groups, punctuation for effect, cohesion, how characters and arguments are built, perspective, style, genre, connections between texts, and a thesis with topic sentences.

Science

Hypotheses, validity and reliability, trends and evaluating a conclusion, correlation and cause, energy efficiency, circuits and Ohm's law, homeostasis and disease, bonding and chemical formulas, balanced equations and rates of reaction, radioactivity, waves, sound and light, motion and Newton's laws, climate data and sustainability, and DNA, inheritance and evolution.

Years 9 and 10 share Stage 5 of the NSW syllabus, so Learnest works from one list of Stage 5 skills. The first day in each subject is a check, so a Year 10 child who is ready starts on the later skills.

Tests around Year 10

• AMC-style maths competition practice for Years 3 to 10AMC Intermediate is for Years 9 and 10. On maths days the stretch question is problem solving.

Sample questions

Questions from Learnest's own Stage 5 question bank. Try each one, then open the worked answer.

Or hand the device over: let your child try seven questions on the real screens, about five minutes, no sign-up.

Pick an answer to check it. Try a wrong one too: you see the mistake that usually leads to it.

1. Sample

   1Maths: compound interest

   $6000 is invested at 5% per year, compounded yearly. Working year by year, what is it worth after 3 years?

   Your child types the answer.

   See the worked answer

   Answer: $6945.75

   Each year adds 5% of the balance at the start of that year: $6300, then $6615, then the third year. Here $6615 × 0.05 = $330.75, and $6615 + $330.75 = $6945.75.

2. Sample

   2Maths: standard deviation

   Every player's score goes up by 4 points. The old mean was 61 and the old standard deviation was 7.5. What are the new mean and standard deviation?

   1. AOption A: Mean 61, standard deviation 7.5
   2. BOption B: Mean 65, standard deviation 7.5
   3. COption C: Mean 61, standard deviation 11.5
   4. DOption D: Mean 65, standard deviation 11.5
   See the worked answer

   Answer: B, Mean 65, standard deviation 7.5

   Adding 4 to every score moves the whole set up by 4, so the mean rises by 4. The scores stay the same distance apart, so the standard deviation does not change. Here the mean is 61 + 4 = 65, and the standard deviation stays 7.5.

3. Sample

   3English: semicolons

   Which version uses its semicolon correctly?

   1. AOption A: Although the trail was steep, we reached the lookout; the view was worth every step.
   2. BOption B: Although the trail was steep; we reached the lookout, the view was worth every step.
   3. COption C: Although the trail was steep, we reached the lookout, the view was worth every step.
   4. DOption D: Although the trail was steep, we reached the lookout; The view was worth every step.
   See the worked answer

   Answer: A, Although the trail was steep, we reached the lookout; the view was worth every step.

   A semicolon needs a complete sentence on each side; although the trail was steep cannot stand alone, so it takes a comma.

4. Sample

   4Science: Newton's second law

   A 1000 kg car has a driving force of 4000 N, while drag and friction add up to 1500 N. What is its acceleration, in metres per second squared?

   Your child types the answer.

   See the worked answer

   Answer: 2.5

   Net force = 4000 - 1500 = 2500 N. Then a = F / m = 2500 / 1000 = 2.5 metres per second squared.

Questions parents ask