LVL7 NSC 2026
S T U DY PACKS CAPS
Grade 12 Mathematics
Diagnostic
Kit for teachers and tutors
P1 and P2 ⋅ Pre-test + Post-test
4 tests ⋅ 56 questions ⋅ 306 marks
Tick-by-tick memos, NSC style
Topic and cognitive-level tags
Class marks template
Every numerical answer computer-checked
Teacher / Tutor licence: one school or tutoring centre, 2026/2027 school year
,LVL7 Grade 12 Mathematics ⋅ Diagnostic Kit How the kit works
TEACHER AND TUTOR GUIDE
How the kit works
Two original diagnostic tests per paper for Grade 12 CAPS Mathematics: a pre-test to find where a
class is losing marks before revision, and a post-test to measure what changed after it. Each pre-test
and post-test pair carries the same marks per topic, so topic scores can be compared directly.
Test Questions Marks Time Test page Memo page
Paper 1 Pre-test 15 79 95 min 4 19
Paper 1 Post-test 17 79 95 min 7 24
Paper 2 Pre-test 12 74 90 min 10 30
Paper 2 Post-test 12 74 90 min 15 33
Kit total 56 306
Running a diagnostic cycle
1 Pre-test the class under exam conditions (the time guide is 1,2 minutes per mark). Print the test
pages only.
2 Mark with the memo. One tick 3 is one mark, as in an NSC marking guideline. Method marks
stand even when the final answer is wrong.
3 Capture topic totals on the class marks template (page 37), using the topic score key at the top
of each memo.
4 Flag topic gaps. A class average under 50% in a topic marks it for reteaching; individual learners
under 40% in a topic need targeted support.
5 Reteach the flagged topics, then run the post-test and capture it on a fresh copy of the template.
6 Compare the pre-test and post-test percentage per topic. Same marks per topic means the gain
column reads directly.
What is in the kit Licence in one line
• 4 tests: Paper 1 and Paper 2, pre-test and Use with all learners you teach at one school
or tutoring centre for the 2026/2027 school
post-test
year. Print and copy as many test pages as
• 56 original NSC-style questions, 306 marks
those learners need. Full terms on page 38;
• Every question tagged by topic and class marks template on page 37; test blueprint
cognitive level on page 3.
• A tick-by-tick memo with mark allocation
Privacy
for every question
The kit is paper based. No learner data is
• A one-page class marks template for topic
collected by LVL7 or leaves your school.
gaps
• Every numerical answer computer-checked
before publication
© 2026 LVL7 Study Packs ⋅ Teacher/Tutor licence: one school or tutoring centre, 2026/2027 school year. Do not resell or share. 2
,LVL7 Grade 12 Mathematics ⋅ Diagnostic Kit Test blueprint
TEACHER AND TUTOR GUIDE
Test blueprint
Paper 1: questions and marks per topic
Topic Pre-test Marks Post-test Marks
1 Algebra, equations & inequalities Q1 to Q3 13 Q1 to Q3 13
2 Sequences & series Q4 to Q5 13 Q4 to Q6 13
3 Functions & graphs Q6 to Q8 18 Q7 to Q9 18
4 Finance, growth & decay Q9 to Q10 8 Q10 to Q11 8
5 Differential calculus Q11 to Q13 19 Q12 to Q15 19
6 Probability & counting Q14 to Q15 8 Q16 to Q17 8
Total 79 79
Paper 2: questions and marks per topic
Topic Pre-test Marks Post-test Marks
1 Statistics Q1 9 Q1 9
2 Analytical geometry Q2 to Q5 21 Q2 to Q5 21
3 Trigonometry Q6 to Q9 25 Q6 to Q9 25
4 Euclidean geometry Q10 to Q12 19 Q10 to Q12 19
Total 74 74
Cognitive levels: marks per test
Level CAPS guide P1 pre P1 post P2 pre P2 post
Knowledge 20% 0 (0%) 0 (0%) 0 (0%) 0 (0%)
Routine procedures 35% 35 (44%) 39 (49%) 42 (57%) 43 (58%)
Complex procedures 30% 38 (48%) 36 (46%) 25 (34%) 26 (35%)
Problem solving 15% 6 (8%) 4 (5%) 7 (9%) 5 (7%)
Each question carries one tag for its predominant demand, using the CAPS four-level taxonomy for Grade 10 to 12
Mathematics. Tags are LVL7’s editorial classification. Sub-questions within one question can sit at different levels, so
the percentages are a guide. These are diagnostic tests, so they lean towards routine and complex procedures, where
most class-level gaps show up; use full NSC papers for final exam practice.
© 2026 LVL7 Study Packs ⋅ Teacher/Tutor licence: one school or tutoring centre, 2026/2027 school year. Do not resell or share. 3
, LVL7 Grade 12 Mathematics ⋅ Diagnostic Kit Paper 1 Pre-test
LVL7 DIAGNOSTIC KIT ⋅ GRADE 12 MATHEMATICS
Paper 1 Pre-test
79 marks 95 minutes Topic Questions Marks
Name 1 Algebra, equations & inequalities 1 to 3 13
2 Sequences & series 4 to 5 13
Class
3 Functions & graphs 6 to 8 18
Date 4 Finance, growth & decay 9 to 10 8
5 Differential calculus 11 to 13 19
6 Probability & counting 14 to 15 8
Total 79
Instructions
• Answer ALL the questions on your own folio paper. Number your answers exactly as the ques-
tions are numbered.
• Show all calculations, diagrams and graphs you used. Answers only will NOT necessarily get
full marks.
• An approved scientific calculator (non-programmable, non-graphical) may be used unless stated
otherwise.
• Round to TWO decimal places unless the question says otherwise. Decimal comma: 2,69.
• Diagrams are not necessarily drawn to scale. Write neatly and legibly.
Question 1 Algebra, equations & inequalities ⋅ Routine procedures
Solve for 𝑥, correct to TWO decimal places: 2𝑥 2 − 5𝑥 − 1 = 0 (4)
Question 2 Algebra, equations & inequalities ⋅ Routine procedures
Solve for 𝑥: (𝑥 + 2)(3 − 𝑥) < 0 (3)
Question 3 Algebra, equations & inequalities ⋅ Complex procedures
Solve for 𝑥: (𝑥 2 − 2𝑥)2 − 11(𝑥 2 − 2𝑥) + 24 = 0 (6)
Question 4 Sequences & series ⋅ Complex procedures
The 7th term of an arithmetic sequence is 26 and the sum of the first 10 terms is 215.
(a) Determine the first term and the common difference. (5)
(b) Determine the smallest number of terms that must be added for the sum to exceed 1 000. (4)
[9]
© 2026 LVL7 Study Packs ⋅ Teacher/Tutor licence: one school or tutoring centre, 2026/2027 school year. Do not resell or share. 4
S T U DY PACKS CAPS
Grade 12 Mathematics
Diagnostic
Kit for teachers and tutors
P1 and P2 ⋅ Pre-test + Post-test
4 tests ⋅ 56 questions ⋅ 306 marks
Tick-by-tick memos, NSC style
Topic and cognitive-level tags
Class marks template
Every numerical answer computer-checked
Teacher / Tutor licence: one school or tutoring centre, 2026/2027 school year
,LVL7 Grade 12 Mathematics ⋅ Diagnostic Kit How the kit works
TEACHER AND TUTOR GUIDE
How the kit works
Two original diagnostic tests per paper for Grade 12 CAPS Mathematics: a pre-test to find where a
class is losing marks before revision, and a post-test to measure what changed after it. Each pre-test
and post-test pair carries the same marks per topic, so topic scores can be compared directly.
Test Questions Marks Time Test page Memo page
Paper 1 Pre-test 15 79 95 min 4 19
Paper 1 Post-test 17 79 95 min 7 24
Paper 2 Pre-test 12 74 90 min 10 30
Paper 2 Post-test 12 74 90 min 15 33
Kit total 56 306
Running a diagnostic cycle
1 Pre-test the class under exam conditions (the time guide is 1,2 minutes per mark). Print the test
pages only.
2 Mark with the memo. One tick 3 is one mark, as in an NSC marking guideline. Method marks
stand even when the final answer is wrong.
3 Capture topic totals on the class marks template (page 37), using the topic score key at the top
of each memo.
4 Flag topic gaps. A class average under 50% in a topic marks it for reteaching; individual learners
under 40% in a topic need targeted support.
5 Reteach the flagged topics, then run the post-test and capture it on a fresh copy of the template.
6 Compare the pre-test and post-test percentage per topic. Same marks per topic means the gain
column reads directly.
What is in the kit Licence in one line
• 4 tests: Paper 1 and Paper 2, pre-test and Use with all learners you teach at one school
or tutoring centre for the 2026/2027 school
post-test
year. Print and copy as many test pages as
• 56 original NSC-style questions, 306 marks
those learners need. Full terms on page 38;
• Every question tagged by topic and class marks template on page 37; test blueprint
cognitive level on page 3.
• A tick-by-tick memo with mark allocation
Privacy
for every question
The kit is paper based. No learner data is
• A one-page class marks template for topic
collected by LVL7 or leaves your school.
gaps
• Every numerical answer computer-checked
before publication
© 2026 LVL7 Study Packs ⋅ Teacher/Tutor licence: one school or tutoring centre, 2026/2027 school year. Do not resell or share. 2
,LVL7 Grade 12 Mathematics ⋅ Diagnostic Kit Test blueprint
TEACHER AND TUTOR GUIDE
Test blueprint
Paper 1: questions and marks per topic
Topic Pre-test Marks Post-test Marks
1 Algebra, equations & inequalities Q1 to Q3 13 Q1 to Q3 13
2 Sequences & series Q4 to Q5 13 Q4 to Q6 13
3 Functions & graphs Q6 to Q8 18 Q7 to Q9 18
4 Finance, growth & decay Q9 to Q10 8 Q10 to Q11 8
5 Differential calculus Q11 to Q13 19 Q12 to Q15 19
6 Probability & counting Q14 to Q15 8 Q16 to Q17 8
Total 79 79
Paper 2: questions and marks per topic
Topic Pre-test Marks Post-test Marks
1 Statistics Q1 9 Q1 9
2 Analytical geometry Q2 to Q5 21 Q2 to Q5 21
3 Trigonometry Q6 to Q9 25 Q6 to Q9 25
4 Euclidean geometry Q10 to Q12 19 Q10 to Q12 19
Total 74 74
Cognitive levels: marks per test
Level CAPS guide P1 pre P1 post P2 pre P2 post
Knowledge 20% 0 (0%) 0 (0%) 0 (0%) 0 (0%)
Routine procedures 35% 35 (44%) 39 (49%) 42 (57%) 43 (58%)
Complex procedures 30% 38 (48%) 36 (46%) 25 (34%) 26 (35%)
Problem solving 15% 6 (8%) 4 (5%) 7 (9%) 5 (7%)
Each question carries one tag for its predominant demand, using the CAPS four-level taxonomy for Grade 10 to 12
Mathematics. Tags are LVL7’s editorial classification. Sub-questions within one question can sit at different levels, so
the percentages are a guide. These are diagnostic tests, so they lean towards routine and complex procedures, where
most class-level gaps show up; use full NSC papers for final exam practice.
© 2026 LVL7 Study Packs ⋅ Teacher/Tutor licence: one school or tutoring centre, 2026/2027 school year. Do not resell or share. 3
, LVL7 Grade 12 Mathematics ⋅ Diagnostic Kit Paper 1 Pre-test
LVL7 DIAGNOSTIC KIT ⋅ GRADE 12 MATHEMATICS
Paper 1 Pre-test
79 marks 95 minutes Topic Questions Marks
Name 1 Algebra, equations & inequalities 1 to 3 13
2 Sequences & series 4 to 5 13
Class
3 Functions & graphs 6 to 8 18
Date 4 Finance, growth & decay 9 to 10 8
5 Differential calculus 11 to 13 19
6 Probability & counting 14 to 15 8
Total 79
Instructions
• Answer ALL the questions on your own folio paper. Number your answers exactly as the ques-
tions are numbered.
• Show all calculations, diagrams and graphs you used. Answers only will NOT necessarily get
full marks.
• An approved scientific calculator (non-programmable, non-graphical) may be used unless stated
otherwise.
• Round to TWO decimal places unless the question says otherwise. Decimal comma: 2,69.
• Diagrams are not necessarily drawn to scale. Write neatly and legibly.
Question 1 Algebra, equations & inequalities ⋅ Routine procedures
Solve for 𝑥, correct to TWO decimal places: 2𝑥 2 − 5𝑥 − 1 = 0 (4)
Question 2 Algebra, equations & inequalities ⋅ Routine procedures
Solve for 𝑥: (𝑥 + 2)(3 − 𝑥) < 0 (3)
Question 3 Algebra, equations & inequalities ⋅ Complex procedures
Solve for 𝑥: (𝑥 2 − 2𝑥)2 − 11(𝑥 2 − 2𝑥) + 24 = 0 (6)
Question 4 Sequences & series ⋅ Complex procedures
The 7th term of an arithmetic sequence is 26 and the sum of the first 10 terms is 215.
(a) Determine the first term and the common difference. (5)
(b) Determine the smallest number of terms that must be added for the sum to exceed 1 000. (4)
[9]
© 2026 LVL7 Study Packs ⋅ Teacher/Tutor licence: one school or tutoring centre, 2026/2027 school year. Do not resell or share. 4
