Chapters

Congratulations, you are about to sit one of your first NCEA Level 1 exams! Excited? Nervous? Wondering how to allocate your time effectively? Either way, we have got you sorted. You likely already know that your exam will be three hours long and that they start either at 9.30am or 2.00pm. But what do you do with all that time in between? Join us as we break down your externals bit by bit so you know what to expect and how to tackle them time-wise accordingly.

## AS91027 Apply algebraic procedures in solving problems

Your first standard involves **applying algebraic procedures**, using extended abstract thinking, in problem-solving. This may be done during class time rather than a separate end of year external, so be sure to check with your teacher regarding the official time duration of this bad boy to avoid any confusion. Got that sorted? Great. So, what else do we have to tackle here?

Markers are looking for** your ability** to handle operations with fractional numbers and integers, rational numbers including the properties of exponents, smash your way through forming and solving linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns. If you are gunning for those **excellence grades**, remember to show your work when developing a strategy to investigate or solve a problem, identify all relevant concepts in context, show your proof, and generalisation. Make sure these are all done by communicating mathematical insight! That’s well and good, but what do some of these terms actually mean?

Digging deeper, we know that **problems** are situations in which you can flex your knowledge and understanding of mathematical concepts and procedures. Basically, we want you to find a solution to the issue at hand, but mathematically. These will usually involve a combination of factorising, expanding, simplifying equations, substitution, simplifying expression, rearranging questions, solving linear and quadratic equations and finally, best for last – solving simple equations. The key to these is practice makes perfect, so be sure to get plenty of practice papers under your belt to really nail down that ability to finish these all comfortably within the given time allocation for your external!

## AS91028 Investigate relationships between tables, equations and graphs

Moving on, we are now looking at your ability to find **optimal solutions**, using numerical approaches. This involves solving linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns. You may have to relate graphs, tables, and equations to these linear, quadratic, and exponential relationships, as well as, of course, reflect any change in the gradient of the graph.

For our **excellence** seekers, make sure to show your strategy in formulating your solution to the problem, depict the relevant concepts in context, and like last time, show your proof. When we talk about relationships, we aren’t meaning that cute guy or girl in class. This time, we are focusing on the connections between tables, equations, graphs and variables.

## AS91031 Apply geometric reasoning in solving problems

Time to apply **geometric reasoning**, using extended abstract thinking, in solving problems! To show **extended abstract thinking**, like in the previous two externals, markers want to see your strategy, logic and proof behind your calculations. We already know by now that problems are situations in which you are able to flex your knowledge and application of mathematical concepts and methods. That’s right, they are your time to shine. For this particular external, be sure to brush up on your **revision** of Pythagoras’ theorem, trigonometric relationships in right-angled triangles, similar triangles, angle properties of intersecting and parallel lines, angle properties of polygons and angle properties of circles.

## AS91037 Demonstrate understanding of chance and data

Now this one relates to **statistical chance and data, **for all you statisticians out there. Here, we just turn our focus to investigating data collection methods, choice of measures and how these impact the validity of findings, which a lot of we can use our common sense to decipher. Regarding what we have to calculate, that relates to probabilities, using fractions, percentages, and ratios. We also have to evaluate statistical reports through analysis of their displays, statistics, processes, and probabilities backing their claims. That’s pretty relevant given the number of statistical reports we are presented with in these COVID days!

**Critical evaluation** and explanation of your reasoning start to display proof of that deeper level of thinking here. Key concepts for your revision include the statistical enquiry cycle, interpreting statistical tables, graphs and associated text, analysing statistical investigations, multivariate, bivariate and time-series data and finally, probability concepts.

Further details on your exams are found on the official NZQA website.

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