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Mathematics Methods - Foundation Level 3 Free Online - Pack 0

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TASC Mathematics Methods - Foundation Level 3

TASC Mathematics Methods - Foundation Level 3 — Free Online Pack 0

Read TASC Mathematics Methods - Foundation Level 3 online for free, including every question, worked solution, marking note and diagnostic action. No public PDF download or checkout is provided.

TASC Section B Calculator-Permitted Practice 2026 Edition - Pack 0 v1.1
TASC Mathematics Methods - Foundation Level 3 is free to read in your browser. There is no public checkout or PDF download.

Exam-pack paper structure

This full-length showcase paper is available to read online.

TASC Mathematics Methods - Foundation Level 3

20 questions

100 marks

Estimated duration: Approximately 100 minutes

Reading: Optional 15-minute preparation · Writing: Approximately 100 minutes

Read TASC Mathematics Methods - Foundation Level 3 online

Skill Align

Skill Align TASC Mathematics Methods - Foundation Level 3 (MTM315117) Section B Calculator-Permitted Practice Booklet Pack 0 - 2026 Edition

Current for 2026 | Course code MTM315117. This original Skill Align booklet practises Section B only: 100 marks, approximately 100 minutes and calculator permitted. The separate 80-mark, calculator-prohibited Section A booklet is not included, so this resource is not a complete three-hour external-examination simulation.

Paper
Section B Calculator-Permitted Practice Booklet Showcase
Preparation time
Optional 15-minute preparation
Suggested working time
Approximately 100 minutes
Assessment
100 marks

Section B conditions: TASC-approved calculators are permitted. The current TASC MTM315117 information sheet must accompany this booklet. Open the official information-sheet link displayed below and supply that sheet with this booklet. Internet access and external communication are not permitted during the practice session.

Official information sheet:Current TASC MTM315117 Information Sheet — Official TASC resource current for 2026. Supply this sheet with the practice booklet.

Part 1 - Algebra - Criterion 4 (20 marks)

Answer all four questions in this part. Each question is worth 5 marks. Show the mathematical setup, method, intermediate working and final answer.

Question 1

5 marks
For x > 0, simplify (27x⁶)^(1 / 3) / (3x).

Question 2

5 marks
Expand (2x - 3)⁴ and collect like terms.

Question 3

5 marks
Solve 2x + y = 11 and x - y = 1.

Question 4

5 marks
Factorise x³ - 4x² - x + 4 completely and hence state all real zeros.

Part 2 - Linear, Quadratic and Cubic Functions - Criterion 5 (20 marks)

Answer all four questions in this part. Each question is worth 5 marks. Show the mathematical setup, method, intermediate working and final answer.

Question 5

5 marks
Find the equation of the line through (2,5) perpendicular to 3x - 2y = 7, in y = mx + c form.

Question 6

5 marks
For f(x)=(x-1)(x-7), find the zeros, axis of symmetry, vertex and range.

Question 7

5 marks
Analyse f(x)=(x+2)²(x-3): state all zeros, their multiplicities, the y-intercept and the sign of f(x) on the three intervals determined by the zeros.

Question 8

5 marks
A ball's height is h(t)=-2(t-3)²+18 metres for 0 <= t <= 6. Find its initial height, maximum height and time, landing time, and range of h.

Part 3 - Logarithmic, Exponential and Trigonometric Functions - Criterion 6 (20 marks)

Answer all four questions in this part. Each question is worth 5 marks. Show the mathematical setup, method, intermediate working and final answer.

Question 9

5 marks
An investment is V(t)=1200(1.06)^t dollars. Find V(5) and the doubling time.

Question 10

5 marks
Solve log base 2 of (x-1) = 4, stating the domain condition.

Question 11

5 marks
Without a calculator, evaluate sin(5π / 6), cos(5π / 6) and tan(5π / 6).

Question 12

5 marks
For y=2sin(3x)-1, state amplitude, period, midline, range and the first maximum for x>=0.

Part 4 - Differential Calculus - Criterion 7 (20 marks)

Answer all four questions in this part. Each question is worth 5 marks. Show the mathematical setup, method, intermediate working and final answer.

Question 13

5 marks
For f(x)=x²-4x+7, find the average rate of change from x=1 to x=5.

Question 14

5 marks
Differentiate f(x)=4x³-5x²+7x-9 and find f'(2).

Question 15

5 marks
Find the tangent to y=x³-2x at x=2.

Question 16

5 marks
Find and classify the stationary points of f(x)=x³-3x²-9x+5 using a derivative sign analysis.

Part 5 - Statistics and Probability - Criterion 8 (20 marks)

Answer all four questions in this part. Each question is worth 5 marks. Show the mathematical setup, method, intermediate working and final answer.

Question 17

5 marks
Given P(A)=0.60, P(B)=0.45 and P(A intersection B)=0.25, find P(A union B), P(A only) and P(neither).

Question 18

5 marks
A bag has 5 red and 3 blue counters. Two are drawn without replacement. Find the probability both are red.

Question 19

5 marks
Of 80 students, 48 travel by bus and 32 by car. Of these, 30 bus travellers and 12 car travellers arrive early. Find P(early given bus) and decide whether early arrival and bus travel are independent.

Question 20

5 marks
A committee of 3 is chosen from 10 students, one of whom is captain. Find the total number of committees and the number that include the captain.

TASC courses, assessment and certification are administered by the Tasmanian Assessment, Standards and Certification office. Skill Align is an independent publisher and is not affiliated with, authorised by, sponsored by, approved by or endorsed by TASC or the Tasmanian Government. This is original Skill Align Section B-only practice material, not an official TASC assessment.

Copyright (c) 2026 Skill Align. Free for personal, non-commercial online viewing at https://skillalign.au. You may share the Skill Align page link. Except as permitted by law or with Skill Align's prior written permission, the pack itself must not be resold, copied, redistributed, republished, automatically extracted, or uploaded to a question bank.

Worked Solutions And Marking Guide

Question 1

Indicative answer: x

(27x^6)^(1/3) = 3x^2, so (3x^2)/(3x) = x.

Mark allocation

  • TASC-style partial-mark policy: one-mark items may receive 0.5 for valid working; items worth two or more marks receive consequential partial credit for correct later work after an earlier arithmetic slip.
  • A correct answer without required working is capped at 1.5 / 2 for a two-mark item and at half marks for an item worth three or more marks.
  • Accept algebraically equivalent methods and exact forms. Unless a question states otherwise, accept a correctly rounded decimal within + / -0.01 of the listed value.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Recognises 27^(1 / 3) = 3
  2. Applies (x⁶)^(1 / 3) = x²
  3. Forms 3x² / (3x)
  4. Cancels the numerical factor and one factor of x
  5. States x, consistent with x > 0

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 2

Indicative answer: 16x^4 - 96x^3 + 216x^2 - 216x + 81

Using coefficients 1, 4, 6, 4, 1 gives 16x^4 - 96x^3 + 216x^2 - 216x + 81.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Uses binomial coefficients 1, 4, 6, 4, 1
  2. Obtains 16x⁴
  3. Obtains -96x³
  4. Obtains 216x² and -216x
  5. States the complete expansion including +81

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 3

Indicative answer: x = 4 and y = 3

Adding the equations gives 3x = 12, so x = 4. Substitution gives y = 3.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Selects a valid elimination or substitution method
  2. Eliminates y to obtain 3x = 12
  3. Finds x = 4
  4. Substitutes to find y = 3
  5. Checks or clearly states the ordered solution

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 4

Indicative answer: (x - 4)(x - 1)(x + 1); zeros -1, 1 and 4

Grouping gives x^2(x - 4) - 1(x - 4) = (x - 4)(x^2 - 1) = (x - 4)(x - 1)(x + 1).

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Groups terms to expose x - 4
  2. Factors to (x - 4)(x² - 1)
  3. Recognises a difference of squares
  4. Obtains all three linear factors
  5. States all three real zeros

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 5

Indicative answer: y = -(2/3)x + 19/3

The given line has gradient 3/2, so the perpendicular gradient is -2/3. Substituting (2,5) gives c=19/3.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Rearranges the given line to identify gradient 3 / 2
  2. Finds perpendicular gradient -2 / 3
  3. Uses point-gradient form through (2,5)
  4. Finds c = 19 / 3
  5. States y = -(2 / 3)x + 19 / 3

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 6

Indicative answer: Zeros 1 and 7; axis x=4; vertex (4,-9); range f(x) >= -9

The zeros are 1 and 7, so the axis is their midpoint x=4. Then f(4)=3(-3)=-9. The parabola opens upward.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. States zeros x=1 and x=7
  2. Finds axis x=4
  3. Calculates f(4)=-9
  4. States vertex (4,-9)
  5. States range f(x) >= -9

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 7

Indicative answer: Zero -2 (double), zero 3 (single); y-intercept -12; negative for x< -2 and -2<x<3, positive for x>3

The factors give a double zero at -2 and a single zero at 3. f(0)=4(-3)=-12. The double root does not change sign; the single root does.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. States zero -2 with multiplicity 2
  2. States zero 3 with multiplicity 1
  3. Calculates y-intercept -12
  4. Gives the negative sign on both intervals left of 3
  5. Gives the positive sign for x>3

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 8

Indicative answer: Initial 0 m; maximum 18 m at 3 s; lands at 6 s; 0 <= h <= 18

h(0)=0. Vertex form gives maximum 18 at t=3. Solving h=0 gives (t-3)^2=9, so t=0 or 6; the later time is landing.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Calculates h(0)=0
  2. Identifies vertex time t=3
  3. States maximum height 18 m
  4. Solves h(t)=0 and selects landing time 6 s
  5. States range 0 <= h <= 18

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 9

Indicative answer: $1605.87; doubling time approximately 11.90 years

V(5)=1200(1.06)^5=1605.87. For doubling, (1.06)^t=2, so t=ln(2)/ln(1.06)=11.90.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Substitutes t=5
  2. Calculates V(5)=1605.87
  3. Forms (1.06)^t=2
  4. Uses t=ln2 / ln1.06
  5. States 11.90 years with context

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 10

Indicative answer: x=17, with x>1

The logarithm requires x-1>0. Converting to exponential form gives x-1=2^4=16, so x=17.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. States x-1>0
  2. Converts to x-1=2⁴
  3. Evaluates 2⁴=16
  4. Finds x=17
  5. Checks x=17 satisfies the domain

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 11

Indicative answer: 1/2, -sqrt(3)/2 and -sqrt(3)/3

The reference angle is pi/6 in Quadrant II, where sine is positive and cosine and tangent are negative.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Identifies reference angle π / 6
  2. Identifies Quadrant II
  3. States sin=1 / 2
  4. States cos=-√3 / 2
  5. States tan=-√3 / 3

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 12

Indicative answer: Amplitude 2; period 2pi/3; midline y=-1; range [-3,1]; first maximum (pi/6,1)

Amplitude is 2, period is 2pi/3 and vertical shift is -1. Maximum occurs when 3x=pi/2, so x=pi/6 and y=1.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. States amplitude 2
  2. States period 2π / 3
  3. States midline y=-1
  4. States range [-3,1]
  5. Finds first maximum (π / 6,1)

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 13

Indicative answer: 2

f(1)=4 and f(5)=12. The average rate is (12-4)/(5-1)=8/4=2.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Calculates f(1)=4
  2. Calculates f(5)=12
  3. Forms [f(5)-f(1)] / (5-1)
  4. Obtains 8 / 4
  5. States average rate 2

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 14

Indicative answer: f'(x)=12x^2-10x+7; f'(2)=35

Apply the power rule: f'(x)=12x^2-10x+7. Then f'(2)=48-20+7=35.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Differentiates 4x³ to 12x²
  2. Differentiates -5x² to -10x
  3. Differentiates 7x and the constant correctly
  4. States f'(x)=12x²-10x+7
  5. Calculates f'(2)=35

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 15

Indicative answer: y-4=10(x-2), or y=10x-16

At x=2, y=8-4=4. The derivative is 3x^2-2, giving gradient 10. Use point-gradient form.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Finds the point (2,4)
  2. Differentiates to 3x²-2
  3. Calculates gradient 10
  4. Uses point-gradient form
  5. States a correct tangent equation

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 16

Indicative answer: Local maximum at (-1,10); local minimum at (3,-22)

f'(x)=3(x-3)(x+1), so stationary x-values are -1 and 3. The derivative changes + to - at -1 and - to + at 3. Evaluate f(-1)=10 and f(3)=-22.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Finds f'(x)=3(x-3)(x+1)
  2. Finds x=-1 and x=3
  3. Uses sign changes to classify both
  4. Calculates f(-1)=10
  5. Calculates f(3)=-22 and states both points

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 17

Indicative answer: 0.80, 0.35 and 0.20

P(A union B)=0.60+0.45-0.25=0.80. A only is 0.60-0.25=0.35, and neither is 1-0.80=0.20.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Uses inclusion-exclusion
  2. Calculates union 0.80
  3. Calculates A only 0.35
  4. Uses complement of the union
  5. Calculates neither 0.20

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 18

Indicative answer: 5/14

P(RR)=5/8 times 4/7=20/56=5/14.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Uses first-red probability 5 / 8
  2. Uses second-red probability 4 / 7
  3. Multiplies the conditional probabilities
  4. Simplifies 20 / 56
  5. States 5 / 14

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 19

Indicative answer: 5/8; not independent

P(E|B)=30/48=5/8. Overall P(E)=42/80=21/40. Since 5/8 is not 21/40, the events are not independent.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Forms conditional probability of early given bus as 30 / 48
  2. Simplifies to 5 / 8
  3. Calculates P(E)=42 / 80=21 / 40
  4. Compares the two probabilities
  5. Concludes not independent

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Question 20

Indicative answer: 120 total; 36 include the captain

Total committees C(10,3)=120. If the captain is included, choose the other two from nine: C(9,2)=36.

Detailed marking criteria

Integrated response (5 marks)

Award one mark for each independently observable checkpoint. Apply consequential marking when a correct method uses an earlier incorrect value.

Mark-by-mark checkpoints:

  1. Recognises combinations rather than permutations
  2. Calculates C(10,3)
  3. States total 120
  4. Fixes the captain and forms C(9,2)
  5. States 36

Acceptable alternatives: Accept any mathematically equivalent method with sufficient working. Accept an algebraically equivalent exact form or a correct calculator-supported method when sufficient working is shown. Unless the question states another tolerance, accept a correctly rounded decimal within + / -0.01 of the listed answer.

Do not credit by itself: An unsupported answer or a correct value obtained from inconsistent working is not full-credit evidence.

Diagnostic Checklist

TopicQuestionsMarksMarks LostAction
Section B | Part 1 | Criterion 4 | Algebra | Skill: Apply index laws to a fractional power. | Expected evidence: x Q1 5 ___ Rework Question 1: Rewrite the cube root as a power before cancelling common factors. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 1 | Criterion 4 | Algebra | Skill: Use binomial coefficients with signed terms. | Expected evidence: 16x^4 - 96x^3 + 216x^2 - 216x + 81 Q2 5 ___ Rework Question 2: Write the five binomial terms before simplifying them. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 1 | Criterion 4 | Algebra | Skill: Solve a pair of linear equations exactly. | Expected evidence: x = 4 and y = 3 Q3 5 ___ Rework Question 3: Eliminate one variable, then verify both values in the original equations. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 1 | Criterion 4 | Algebra | Skill: Factorise a cubic by grouping and difference of squares. | Expected evidence: (x - 4)(x - 1)(x + 1); zeros -1, 1 and 4 Q4 5 ___ Rework Question 4: Look for a common binomial after grouping the first two and last two terms. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 2 | Criterion 5 | Linear, Quadratic and Cubic Functions | Skill: Use perpendicular gradients and a point. | Expected evidence: y = -(2/3)x + 19/3 Q5 5 ___ Rework Question 5: Rearrange the given line first, then use the negative reciprocal gradient. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 2 | Criterion 5 | Linear, Quadratic and Cubic Functions | Skill: Analyse a factored quadratic. | Expected evidence: Zeros 1 and 7; axis x=4; vertex (4,-9); range f(x) >= -9 Q6 5 ___ Rework Question 6: Use the midpoint of the roots, then evaluate the function and inspect the leading coefficient. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 2 | Criterion 5 | Linear, Quadratic and Cubic Functions | Skill: Interpret a factored cubic including multiplicity. | Expected evidence: Zero -2 (double), zero 3 (single); y-intercept -12; negative for x< -2 and -2<x<3, positive for x>3 Q7 5 ___ Rework Question 7: Use factor signs on one test value in each interval. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 2 | Criterion 5 | Linear, Quadratic and Cubic Functions | Skill: Interpret a quadratic model in vertex form. | Expected evidence: Initial 0 m; maximum 18 m at 3 s; lands at 6 s; 0 <= h <= 18 Q8 5 ___ Rework Question 8: Read the vertex, then solve the domain-valid intercept equation. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 3 | Criterion 6 | Logarithmic, Exponential and Trigonometric Functions | Skill: Evaluate and solve an exponential model. | Expected evidence: $1605.87; doubling time approximately 11.90 years Q9 5 ___ Rework Question 9: Substitute for the value, then isolate the exponential for doubling time. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 3 | Criterion 6 | Logarithmic, Exponential and Trigonometric Functions | Skill: Convert between logarithmic and exponential form. | Expected evidence: x=17, with x>1 Q10 5 ___ Rework Question 10: State the log argument restriction before solving. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 3 | Criterion 6 | Logarithmic, Exponential and Trigonometric Functions | Skill: Use reference angles and quadrant signs. | Expected evidence: 1/2, -sqrt(3)/2 and -sqrt(3)/3 Q11 5 ___ Rework Question 11: Identify the reference angle and apply the Quadrant II sign pattern. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 3 | Criterion 6 | Logarithmic, Exponential and Trigonometric Functions | Skill: Read and apply sinusoidal parameters. | Expected evidence: Amplitude 2; period 2pi/3; midline y=-1; range [-3,1]; first maximum (pi/6,1) Q12 5 ___ Rework Question 12: Use amplitude, angular frequency and vertical shift separately. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 4 | Criterion 7 | Differential Calculus | Skill: Calculate average rate of change. | Expected evidence: 2 Q13 5 ___ Rework Question 13: Evaluate both endpoints before forming the difference quotient. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 4 | Criterion 7 | Differential Calculus | Skill: Differentiate a cubic polynomial. | Expected evidence: f'(x)=12x^2-10x+7; f'(2)=35 Q14 5 ___ Rework Question 14: Differentiate term by term, then substitute only after simplifying. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 4 | Criterion 7 | Differential Calculus | Skill: Find a tangent to a cubic. | Expected evidence: y-4=10(x-2), or y=10x-16 Q15 5 ___ Rework Question 15: Calculate both the point and derivative gradient at the stated x-value. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 4 | Criterion 7 | Differential Calculus | Skill: Classify cubic stationary points using derivative signs. | Expected evidence: Local maximum at (-1,10); local minimum at (3,-22) Q16 5 ___ Rework Question 16: Factor the derivative and build a three-interval sign chart. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 5 | Criterion 8 | Statistics and Probability | Skill: Use inclusion-exclusion for two events. | Expected evidence: 0.80, 0.35 and 0.20 Q17 5 ___ Rework Question 17: Place the intersection first, then calculate exclusive and outside regions. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 5 | Criterion 8 | Statistics and Probability | Skill: Calculate sequential probability without replacement. | Expected evidence: 5/14 Q18 5 ___ Rework Question 18: Update both numerator and denominator after the first draw. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 5 | Criterion 8 | Statistics and Probability | Skill: Use conditional probability to test independence. | Expected evidence: 5/8; not independent Q19 5 ___ Rework Question 19: Compare the conditional probability with the corresponding marginal probability. Then compare the setup, intermediate result and final presentation with the worked solution.
Section B | Part 5 | Criterion 8 | Statistics and Probability | Skill: Count unordered selections with a required member. | Expected evidence: 120 total; 36 include the captain Q20 5 ___ Rework Question 20: Separate the fixed captain from the remaining selections. Then compare the setup, intermediate result and final presentation with the worked solution.

What is included

Section B Calculator-Permitted Practice Booklet Showcase questions (100 marks)

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Pack 0 includes one full-length showcase paper, worked solutions, marking guidance and diagnostic checklists, all shown online.

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