How to Prepare for Högskoleprovet Math: XYZ, KVA, NOG and DTK

In April 2026, 78,397 people sat the quantitative part of Högskoleprovet. A 2.0, the top of the scale, took 76 correct answers out of 80, and only 1.2% of them reached it. A 1.0 took 45, just over half. The test's organiser, Universitets- och högskolerådet (UHR), pitches the mathematics at upper-secondary Matematik 1b, so what separates those two scores is not advanced knowledge. It is how many ordinary questions you answer correctly by hand, most of them on a budget of about a minute. The scale pays for steady accuracy, not brilliance.

Högskoleprovet is not a math exam, though. It is a general aptitude test with a verbal half (ORD, LÄS, MEK and ELF) and a quantitative half (XYZ, KVA, NOG and DTK), 80 questions each, and each half counts for exactly half of your result. This guide covers only the quantitative half. The test is open to non-Swedish citizens but given only in Swedish. The next sitting is on 18 October 2026, with registration closed; the one after is on 10 April 2027, with registration open from 7 to 14 January 2027.

Two Passes, Four Subtests, 55 Minutes Each

The test day has five passes of 55 minutes. Two hold the quantitative questions, two the verbal ones, and one is a try-out pass that trials questions for future tests and gives you no result. Each quantitative pass has 40 questions in four blocks, 80 questions and 110 minutes in all, and the October 2025 and April 2026 booklets used the same layout:

Subtest	What it asks	Questions per pass	Recommended time	Options
XYZ	Solve a mathematical problem	12	12 min	A-D
KVA	Compare two quantities, I and II	10	10 min	A-D
NOG	Decide whether two statements give enough information	6	10 min	A-E
DTK	Read and interpret diagrams, tables and maps	12	23 min	A-D

The minutes are the booklet's recommendations, not separate clocks. The only hard limit is 55 minutes for the whole pass, so a minute lost in XYZ comes out of DTK.

There is no calculator. The permitted aids are a pencil, an eraser, a straight ruler, a highlighter and simple earplugs; anything that can store or receive information, phones and smart watches included, is banned from the desk. Bring the ruler; DTK is where it earns its place.

The Math Is Matematik 1b, the Pressure Is the Clock

UHR puts the theoretical difficulty of the math questions at upper-secondary Matematik 1b (Matematik A in the old system). XYZ, the problem-solving subtest, draws on arithmetic, algebra, geometry, functions and statistics. Treat that list as the syllabus for the whole quantitative half.

The difficulty lives in the clock: twelve XYZ questions get a recommended twelve minutes and ten KVA questions get ten, about a minute each, reading included. Without a calculator, a fraction division or a percentage of a percentage can eat most of that minute.

Take a price that rises by 20% and then falls by 20%. Step by step, that is two calculations with a chance of a slip in each. With multipliers, it is one product you can do in your head, $1.2 \times 0.8 = 0.96$, so the price ends 4% below where it started. Fast hand calculation mostly looks like that: fewer steps rather than quicker ones. The percentages guide builds this habit, and the mental math tricks cover the estimation and round-and-adjust moves that keep a one-minute question inside its minute.

KVA: Compare, Don't Compute

Every KVA question shows two quantities, I and II, sometimes under a condition or a figure, and offers the same four answers: A, I is greater than II; B, II is greater than I; C, I is equal to II; D, the information is insufficient.

That changes the job. You are not asked for a value, only for a relationship, and it has to hold in every case the information allows. If the comparison comes out one way for one allowed value and another way for another, the answer is D.

So test values on purpose: a positive number, a negative number, zero and a fraction between 0 and 1, as far as the condition allows. Say $x > 0$, quantity I is $x^{2}$ and quantity II is $x$. With $x = 2$, I is 4 and II is 2, so I is greater. With $x = \frac{1}{2}$, I is $\frac{1}{4}$ and II is $\frac{1}{2}$, so II is greater. Two allowed values, two different answers: D. Anyone who tried only 2 marks A and moves on, confident and wrong.

Without a variable, simplify before you compute. Adding the same amount to both sides, or multiplying both by the same positive number, never changes which side is greater. If I is $\frac{7}{9}$ and II is $\frac{8}{11}$, cross-multiply, 77 against 72, and I is greater without a single decimal.

Choose D because you found two cases that disagree, never because a question feels vague.

NOG: Is There Enough Information?

NOG looks like nothing else on the paper. Each question comes with two statements, (1) and (2), and your job is not to answer it but to decide whether the statements are enough to do so. The wording is fixed, "Tillräcklig information för lösningen erhålls" (sufficient information for the solution is obtained), and so are the five options. A: (1) is enough but (2) is not. B: (2) is enough but (1) is not. C: you need both together. D: each statement is enough on its own. E: even both together are not enough.

UHR describes NOG as testing mathematical and logical problems, so expect logic as well as numbers. Whatever the content, work in a fixed order. Is (1) alone enough? Is (2) alone enough? If neither is, are they enough together? The order guards against the most tempting reflex here: combining the statements at once and marking C when one of them already did the job.

Try one. A rectangle has an area of 24 square centimetres; what is its perimeter? (1) The length is 6 centimetres. (2) The length is twice the width. Statement (1) gives a width of 4, so it is enough. Statement (2) gives $2w \cdot w = 24$, so $w^{2} = 12$. Stop there. That equation has exactly one positive solution, so there is one rectangle and one perimeter, and (2) is enough too: D. Working out the perimeter would be correct and pointless.

Six questions in a recommended 10 minutes means about 1 minute 40 seconds each, the most generous pace after DTK. Spend it on the logic.

DTK: The Biggest Slice of the Clock

DTK closes every quantitative pass with 12 questions and a recommended 23 of the 55 minutes, just under two minutes each.

UHR's preparation advice for this part is short: practise reading diagrams and tables, and use a transparent ruler to follow scales and rows. Treat DTK as reading first and arithmetic second. Before the first question, read the source: the title, what each axis measures, the units, whether figures are in thousands or percent, and the footnotes. A chart in minutes per day and a question in minutes per week is a reading test before it is a multiplication.

Estimate before you calculate. If the options are far apart, a rough reading settles the question; if they are close, the estimate shows where the careful work has to go.

Keep percent and percentage points apart. A share that rises from 20% to 25% has gone up by 5 percentage points, which is an increase of 25%. When a question compares percentages, decide which of the two it wants before you touch the numbers. The statistics guide covers the means, medians and spreads underneath this subtest.

How the Score Works

Each correct answer gives one point, and a wrong answer costs nothing. Your quantitative raw score, out of 80, is converted to a normed score from 0.0 to 2.0 in steps of 0.1, separately from the verbal part. Your final result is the mean of the two normed scores, from 0.00 to 2.00 in steps of 0.05. So a strong quantitative score lifts your result by half as much as it lifts the quantitative normed score: going from 1.2 to 1.4 on the quantitative part raises the final result by 0.10.

Selected rows from the April 2026 quantitative norm table:

Correct answers (of 80)	Normed score
0-17	0.0
30-33	0.6
45-47	1.0
57-60	1.3
64-66	1.5
70-71	1.7
74-75	1.9
76-80	2.0

Is 1.0 hard? It took 45 correct answers, 56% of the questions, and 56.6% of test-takers scored 1.0 or lower. The quantitative mean was 0.95, against 0.88 for the whole test, so a 1.0 is a little above the middle, not a high score. Has anyone got 2.0? Yes, 959 people in April 2026, none of whom could afford more than four wrong or blank answers.

Do not read the table as a forecast. In October 2025, 44 correct answers were enough for 1.0 and 76 again for 2.0. UHR is explicit that on a relatively hard test a lower raw score earns the same normed score, and the reverse on an easier one, which is why it calls old norm tables unsuitable for estimating a new result. Use them for the shape of the scale, not for your number. The latest tables, with the April 2026 questions and answer keys, are on the official results page.

Two rules lower the stakes of any one sitting. A result stays valid until the end of the calendar half-year eight years after the test, and admissions always use your best valid result. At least a third of study places are filled through the selection group for Högskoleprovet results, and applicants with both grades and a test result compete in several groups at once. Ties in the test group are settled by lottery, so a single 0.05 can matter.

Diagnose Before You Plan

Before the plan, sit one recent official quantitative pass cold: 40 questions, 55 minutes, no calculator, answers marked on a separate sheet. UHR's own advice is to take past tests on time, as if it were a real test day, and the papers and answer keys are free to download from the official archive, which goes back to 2013. Mark any question that took clearly longer than its share of time, right or wrong.

The score matters less than the error map. Sort every miss and every marked question by subtest, then into five bins by cause, because each bin needs different medicine. Concept gaps need explanation and a few clean examples. Slow but right answers need timed drills, since only the speed is missing. Careless slips need a habit: write the intermediate step, reread the question. Format misreads, like A in KVA after one test value or C in NOG when one statement was enough, need the logic above drilled until it is automatic. Running out of time needs the checkpoint plan below and a look at where the minutes went, because DTK comes last and inherits every earlier overrun.

Then use the subtest sort to stretch or shorten the blocks below: ten misses spread evenly call for a different plan than seven in NOG and DTK.

The 12-Week Study Plan

Six two-week blocks: three rebuild the mathematics, two train the formats, and the last rehearses the day. Counted back from 10 April 2027, week 1 starts in mid-January, just after registration closes on 14 January. So register first: the window is one week, the fee is 550 kr, and there is no late registration.

In every session, keep the calculator out of reach and finish with ten minutes of mixed questions from earlier blocks, so January's work survives until April; the guide to spaced repetition for math practice explains the reasoning.

Weeks 1 and 2: arithmetic by hand. Fractions, percentages, powers, roots and ratios, in short daily sets at the one-minute pace of XYZ and KVA. Treat a ratio as a comparison, not a part: saving a third of a salary puts saving and spending at 1 to 2, not 1 to 3, a distinction the ratios and proportions guide takes apart. Adaptive practice in an app such as Math Zen can carry these daily hand-calculation drills through the first six weeks; the KVA, NOG and DTK formats still come from past papers.

Weeks 3 and 4: algebra. Expressions, linear equations, inequalities and rearranging formulas. Turn short word problems into equations by naming the unknown first. Give inequalities extra time: multiplying by a negative number flips the sign, and a condition on the sign of x can flip a KVA comparison the same way.

Weeks 5 and 6: geometry and functions. Angles, the Pythagorean theorem, area and volume, circles and coordinates, then linear functions and exponential change, which is percentages again: growing by 10% a year means multiplying by 1.1 every year. Sketch any geometry question that comes without a figure.

Weeks 7 and 8: KVA and NOG. One KVA block and one NOG block from past papers per session, 20 minutes combined, as the booklet recommends. Run the four test values in KVA and the fixed order in NOG until both are automatic, and for every miss, name the habit that failed.

Weeks 9 and 10: DTK and statistics. Mean, median, percentage change, percentage points, basic probability and chart reading, then full DTK blocks at 23 minutes with a transparent ruler. Read the source first, estimate, then calculate.

Weeks 11 and 12: full rehearsals. Two complete quantitative passes per session, as on the test day, with a short break between them. Use the checkpoints below, answer every question, and review every miss before the next session. Add nothing new in the final days.

If you are registered for 18 October 2026, two weeks from now, go straight to that last block. Two weeks will not rebuild your arithmetic, but they can make the timing, the KVA and NOG logic and the guessing routine automatic.

Exam-Day Pacing for a 55-Minute Pass

Turn the booklet's recommended times into checkpoints: XYZ (questions 1 to 12) done by minute 12, KVA (13 to 22) by minute 22, NOG (23 to 28) by minute 32, leaving 23 minutes for DTK (29 to 40).

If you reach a checkpoint late, do not try to win the time back where you are. UHR's own advice is not to get stuck: skip hard questions and come back later. Four minutes spent fighting one XYZ question is the time of two DTK questions.

Mark answers on the answer sheet as you go, or at least at every checkpoint; only what is on the sheet when time runs out counts, and the booklet is just scrap paper. In the last two minutes, fill in a guess for every blank. With no minus points, an empty box is the only answer guaranteed to score nothing.

Pace the day too. Pass 1 starts at 09.00 and pass 5 ends at 16.25, with breaks and lunch in between. In April 2026 the quantitative passes were 3 and 5, so the second ended the day, and the try-out, as UHR confirmed when it published the questions, was pass 1. Treat every pass as one that counts.

The Bottom Line

The quantitative half of Högskoleprovet is half of your result: 80 questions at Matematik 1b level, 110 minutes, no calculator and no penalty for a wrong answer. In April 2026, 45 correct answers earned a 1.0 and 76 a 2.0, so accuracy beats flair. Prepare accordingly: rebuild arithmetic and algebra by hand, drill the KVA and NOG logic until it runs on its own, read every DTK source before its questions, and finish with timed passes from the official archive. Register in that January week, start in mid-January, and arrive on 10 April 2027 knowing where every minute of each pass goes.