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Fundamentals of Modern Mathematics 1, 8th paper options

MATH130 practice questions

cutline’s math130 bank is being built lecture by lecture across the otago fundamentals of modern mathematics course. it covers calculus and linear algebra with the full worked method shown, matching the working-marked style math130 assesses, and you can start free without a card.

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1,690published MCQs
41worksheets and mock exams

As the catalogue lists them, checked 23 Oct 2026.

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  • Differentiation RulesSample 1 of 4
    Which of the following is equal to the derivative of f(x)=x1/7?f(x) = x^{1/7}?
    Answer choices
    Show answer

    Correct answer: A

    Worked solution

    ddxxn=nxn−1\frac{d}{dx}x^{n} = n x^{n-1} =17x17−1= \frac{1}{7}x^{\frac{1}{7}-1} =17x−6/7= \frac{1}{7}x^{-6/7}
  • Continuity and the Intermediate Value TheoremSample 2 of 4
    Which of the following is the correct definition of what it means for a function ff to be continuous at a point aa?
    Answer choices
    Show answer

    Correct answer: A

    Worked solution

    Continuity at a point ties together three requirements. The point must lie in the domain, so f(a)f(a) is defined, a∈dom⁡(f)a \in \operatorname{dom}(f) the limit must exist, lim⁡x→af(x) exists\lim_{x\to a} f(x) \text{ exists} and the limit must agree with the value, lim⁡x→af(x)=f(a)\lim_{x\to a} f(x) = f(a) A limit that merely exists, or a value that is merely defined, is not enough on its own.
  • The Definite Integral and AreaSample 3 of 4
    Interpreting the definite integral as the area under the graph, evaluate ∫043 dx.\int_{0}^{4} 3\,dx.
    Answer choices
    Show answer

    Correct answer: A

    Worked solution

    The graph of y=3y=3 is a horizontal line, so the region is a rectangle of height 33 over an interval of width 4−0=4.4-0=4. ∫abc dx=(b−a)c\int_a^b c\,dx = (b-a)c =(4−0)×3= (4-0)\times 3 =12= 12
  • The Dot ProductSample 4 of 4
    Compute the dot product u⋅vu \cdot v of the vectors u=[43],v=[25].u = \begin{bmatrix} 4 \\ 3 \end{bmatrix}, \qquad v = \begin{bmatrix} 2 \\ 5 \end{bmatrix}.
    Answer choices
    Show answer

    Correct answer: A

    Worked solution

    u⋅v=(4)(2)+(3)(5)u \cdot v = (4)(2) + (3)(5) =8+15=23= 8 + 15 = 23

Published MCQ practice

Teaching practice and mock exams currently listed for this paper.

Teaching practice

  • Functions

    Worksheets: 3

    MCQs: 131

    • Sets, Intervals and DomainsMCQs: 40
    • Catalogue of Functions and Piecewise FunctionsMCQs: 48
    • Combining and Inverse FunctionsMCQs: 43

  • Limits and Continuity

    Worksheets: 3

    MCQs: 126

    • Computing LimitsMCQs: 42
    • Limits at Infinity and Special LimitsMCQs: 42
    • Continuity and the Intermediate Value TheoremMCQs: 42

  • Differentiation

    Worksheets: 5

    MCQs: 216

    • The Derivative from First PrinciplesMCQs: 42
    • Differentiation RulesMCQs: 39
    • Derivatives of Standard FunctionsMCQs: 39
    • Stationary Points, Increasing and DecreasingMCQs: 46
    • Optimisation ProblemsMCQs: 50

  • Integration

    Worksheets: 5

    MCQs: 207

    • The Definite Integral as AreaMCQs: 44
    • Antiderivatives and the Fundamental TheoremMCQs: 43
    • Integration by SubstitutionMCQs: 40
    • Integration by PartsMCQs: 40
    • Integration and MotionMCQs: 40

  • Complex Numbers

    Worksheets: 2

    MCQs: 85

    • Complex Arithmetic, Conjugates and QuadraticsMCQs: 40
    • Polar Form, Modulus and ArgumentMCQs: 45

  • Vectors and Lines

    Worksheets: 2

    MCQs: 85

    • Vectors, Scaling and Parametric LinesMCQs: 42
    • Dot Product, Magnitude and OrthogonalityMCQs: 43

  • Linear Systems and Subspaces

    Worksheets: 2

    MCQs: 80

    • Solving Linear Systems and Triangular SystemsMCQs: 40
    • Lines, Planes, Hyperplanes and SubspacesMCQs: 40

  • Matrices and Transformations

    Worksheets: 3

    MCQs: 120

    • Matrix times Vector, Systems as Matrices, and LinearityMCQs: 40
    • Transformations of the Plane and Matrix MultiplicationMCQs: 40
    • Inverse MatricesMCQs: 40

  • Solving Matrix Equations

    Worksheets: 2

    MCQs: 80

    • Null Space and Column SpaceMCQs: 40
    • Row Echelon Form and Gaussian EliminationMCQs: 40

Mock exams

  • Final Exam Mocks

    Mock exams: 14

    MCQs: 560

    • Final Exam Mock 01MCQs: 40
    • Final Exam Mock 02MCQs: 40
    • Final Exam Mock 03MCQs: 40
    • Final Exam Mock 04MCQs: 40
    • Final Exam Mock 05MCQs: 40
    • Final Exam Mock 06MCQs: 40
    • Final Exam Mock 07MCQs: 40
    • Final Exam Mock 08MCQs: 40
    • Final Exam Mock 09MCQs: 40
    • Final Exam Mock 10MCQs: 40
    • Final Exam Mock 11MCQs: 40
    • Final Exam Mock 12MCQs: 40
    • Final Exam Mock 13MCQs: 40
    • Final Exam Mock 14MCQs: 40
Open MATH130 catalogue

What this list includes. Active products only. Published worksheets in visible groups, with unrestricted multiple-choice questions. Retired questions, module tests and written questions are excluded. This does not measure whole-course coverage or concept articles. This catalogue is cached. The app rechecks access before you start. .

What this paper covers

These are paper topics, not a list of published worksheets.

  • functions
  • limits and continuity
  • differentiation
  • integration
  • complex numbers
  • vectors and lines
  • linear systems and subspaces
  • matrices and transformations

How to approach MATH130

math130 is introductory and, like stat, a nice paper once you get going. the one difference is that it is not all multi-choice, some answers need working shown and that working gets marked, so practising the method matters as much as landing the final answer. the bank here is built around that, working through problems the way the exam wants them.

worth
18 points (0.15 EFTS)
taught
semester 1 or semester 2
format
calculus and linear algebra, and not all multi-choice, some working is marked

How to study MATH130 (science-based)

These are established findings, not fringe claims, and recent reviews keep confirming them (Carpenter et al., 2022; Weinstein et al., 2018). The emphasis here is on the higher-order skill of applying and transferring ideas to unseen questions, which is what separates the top HSFY grades and the study habits medicine selects for.

math130 is an approachable introductory paper covering calculus and linear algebra, with one important difference from a pure multiple-choice paper: it marks your working as well as the final answer. the methods below train both the selection skill and the disciplined method the exam rewards.

  1. interleave problem types (this paper is the case study)

    the classic interleaving experiment was run on mathematics problems: students who shuffled problem types learned to tell them apart and outperformed students who practised in blocks, despite the blocked group feeling more confident during study (Rohrer & Taylor, 2007). math130 is the exact setting that research describes.

    the paper deliberately weaves together calculus, linear algebra and geometry, so blocked practice lets you coast on knowing which technique the chapter wants. a mixed set forces you to look at a fresh problem and decide whether it needs differentiation, a matrix operation, or a geometric argument, which is the real exam skill and the one blocked practice hides. (Rohrer & Taylor, 2007; Brunmair & Richter, 2019)

    Try it: make a set that alternates a derivative, a matrix operation and a geometry question rather than a page of one kind.

  2. show working, then check the method

    because math130 marks method and not only the answer, the useful feedback is about where your reasoning breaks, not merely whether you were right. effective feedback identifies the gap and how to close it, which drives more improvement than a bare right-or-wrong (Hattie & Timperley, 2007).

    practise by writing out every step of a solution as if it were being marked, then compare against a worked solution to find the exact line where your logic slipped, a sign error, a skipped justification, a misapplied rule. fixing the specific step is far more valuable than noting that the final number was wrong, and it directly protects the method marks the exam awards. (Hattie & Timperley, 2007)

    Try it: write out every step, then compare against the worked solution to find the exact line where your reasoning slipped.

  3. attempt before the solution

    peeking at the solution early feels smooth and fast, but that fluency is misleading: struggling with a problem first is a desirable difficulty that makes the method stick better than reading someone else’s working (Bjork & Bjork, 2011).

    give each math130 problem a genuine attempt before opening the answer, and use the answer only to check and correct. the productive struggle is where the learning happens, and it also builds the independent problem-solving the paper is designed to develop. (Bjork & Bjork, 2011)

    Try it: give each problem a genuine attempt before opening the answer, then use the answer only to check.

  4. practise applying methods to new problems

    the difference between a good and a top math130 grade is usually the ability to apply a method to a problem you have not seen, and to combine ideas, rather than to reproduce a memorised solution. varied retrieval practice builds this transfer, the flexible application of a method to new situations (Pan & Rickard, 2018; Carpenter et al., 2022).

    deliberately work unfamiliar and combined problems, a question that needs both calculus and a matrix step, for instance, rather than repeating drills of the same form. because math130 marks method, practising how to apply and justify a technique on a novel problem is exactly what earns the higher marks. (Pan & Rickard, 2018; Carpenter et al., 2022)

    Try it: work a problem that combines two techniques or applies a method in an unfamiliar form, showing your full method.

Flashcards, spaced repetition and Anki

The spacing effect is why flashcards work: revisiting a fact just as you are about to forget it locks it in far better than cramming (Cepeda et al., 2006). Anki is the tool most health-science students reach for, and it is good. flashcards suit the definitions and rules; pair them with worked-problem practice, since math130 also marks method. Cutline pairs Anki-style flashcards for the raw facts with a qbank of exam-style MATH130 questions, so you can drill what needs memorising and then practise applying it.

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Questions about MATH130

is math130 fully published yet?

the bank is being built out lecture by lecture, so this page updates as more content is published.

does math130 show full worked solutions?

yes, every sample question includes a full worked solution as well as the final answer.

Keep reading

The evidence

The study methods above come from established research in cognitive and educational psychology.

  1. Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics problems improves learning. Instructional Science, 35(6), 481 to 498.
  2. Brunmair, M., & Richter, T. (2019). Similarity matters: A meta-analysis of interleaved learning and its moderators. Psychological Bulletin, 145(11), 1029 to 1052.
  3. Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81 to 112.
  4. Bjork, E. L., & Bjork, R. A. (2011). Making things hard on yourself, but in a good way: Creating desirable difficulties to enhance learning. In M. A. Gernsbacher et al. (Eds.), Psychology and the real world (pp. 56 to 64). Worth Publishers.
  5. Pan, S. C., & Rickard, T. C. (2018). Transfer of test-enhanced learning: Meta-analytic review and synthesis. Psychological Bulletin, 144(7), 710 to 756.
  6. Carpenter, S. K., Pan, S. C., & Butler, A. C. (2022). The science of effective learning with spacing and retrieval practice. Nature Reviews Psychology, 1(9), 496 to 511.
  7. Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., & Rohrer, D. (2006). Distributed practice in verbal recall tasks: A review and quantitative synthesis. Psychological Bulletin, 132(3), 354 to 380.
  8. Weinstein, Y., Madan, C. R., & Sumeracki, M. A. (2018). Teaching the science of learning. Cognitive Research: Principles and Implications, 3, 2.

Practise MATH130 the way it is examined.

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