grade 12 maths paper 1 prelim revision - mathsatsharp.co.za
TRANSCRIPT
What’s in Paper 1?
• Algebra
• Patterns (Sequences and Series)
• Functions
• Finance
• Calculus
• Probability
Before We Begin
• Make sure you get enough sleep.
• Start studying for maths long in advance
• Practice, practice, practice
• Don’t check the answer before you have actually tried the question
• Eat healthy
• Bring a spare pen, pencil and eraser.
• Make sure your pens work (and your calculator works)
• Don’t talk to your friends about the exam before you start writing
• Form a study group
• Ask for help
• Bring a watch if you can
How you will be tested
• 4 levels of questions:• Knowledge – 20%
• Routine – 35%
• Complex – 30%
• Problem Solving – 15%
Calculating how much time you have for each question• Exam total = 150 marks
• Time = 3 hours
• That means = 180 minutes
• So you have 150 ÷ 180 =5
6mark per minute
• If a section is 22 marks , you
have 5
6× 22 = 18
1
3minutes to
complete it
Right before the exam
• Read through the exam paper
• Calculate how much time you need to spend on each section.
• Make sure you are comfortable
• Close your eyes, breath deeply and count to ten.
• Think about what you want to be doing after the exam
Example of the memo
• Do you see the OR’s?
• Do you see that each tick is given a reason?
• So, you can use different methods
• And you must show ALL your working out
Things to Remember
• Factorising• Completing the square
• Trinomials where a ≠ 1
• Quadratic Formula• Memorise the formula
• Logs and exponent laws
Question 1.1. Solve for x:
• 1.1.1. 𝑥2 − 6𝑥 = 0 (2) • 1.1.2. 𝑥2 + 10𝑥 + 8 = 0(correct to TWO decimal places) (3)
Things to Remember
• Linear / Arithmetic Patterns• 𝑇𝑛 = 𝑎 + 𝑛 − 1 𝑑
• Sum: 𝑆𝑛 =𝑛
22𝑎 + 𝑛 − 1 𝑑
• Same difference
• Geometric • 𝑇𝑛 = 𝑎𝑟𝑛−1
• 𝑆𝑛 =𝑎(𝑟𝑛−1)
𝑟−1
• 𝑆∞ =𝑎
1−𝑟• Same ratio
• Quadratic• 𝑇𝑛 = 𝑎𝑛2 + 𝑏𝑛 + 𝑐
• 𝑎 + 𝑏 + 𝑐 = 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚
• 3𝑎 + 𝑏 = 𝑓𝑖𝑟𝑠𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒• 2𝑎 = 2𝑛𝑑 𝑐𝑜𝑚𝑚𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒
Given the quadratic pattern -3; 6; 27; 60…
• 2.2.1. Determine the general term of the pattern in the form 𝑇𝑛 = 𝑎𝑛2 + 𝑏𝑛 + 𝑐 (4)
Given the quadratic pattern -3; 6; 27; 60…
• 2.2.2. Calculate the value of the 50th term of the pattern. (2)
Given the quadratic pattern -3; 6; 27; 60…
• 2.2.3. Show that the sum of the 1st n first-differences of this pattern can be given by 𝑆𝑛 = 6𝑛2 + 3𝑛 (3)
Given the quadratic pattern -3; 6; 27; 60…
• 2.2.4. How many consecutive first-differences were added to the first term of the quadratic number pattern to obtain a term in the quadratic number pattern that has a value of 21 060? (4)
Things to Remember
• Remember your function theory
• Learn your formulae • Recognise a graph by its
formula, or shape, or characteristics
• What is an asymptote?
• How does shifting a graph• Up and down work?
• Left and right work?
• Straight Line
• Parabola
• Hyperbola
• Exponential
• Inverse Functions
Given 𝒉 𝒙 =−𝟑
𝒙−𝟏+ 𝟐
• 4.1.2. Determine the equation of the axis of symmetry of h that has a negative gradient. (2)
Given 𝒉 𝒙 =−𝟑
𝒙−𝟏+ 𝟐
• 4.1.3. Sketch the graph of h, showing the asymptotes and the intercepts with the axes. (4)
4.2.1. Write down the coordinates of A (2)
• 4.2.2. Write down the range of f. (1)
• 4.2.3. Calculate the values of m and n (3)
4.2.6. If 𝒉 𝒙 = 𝒈−𝟏 𝒙 + 𝒌 is a tangent to f, determine the coordinates of the point of contact between h and f. (4)
5.3.Write down the domain of 𝒇−𝟏 (2)
• 5.4. Describe the translation from f to ℎ 𝑥 =27
3𝑥(3)
• 5.5. Determine the values of 𝑥 for which ℎ 𝑥 < 1 (3)
Things to Remember
• The difference between a future value annuity and the present value annuity
• Formulae
• Study guide chapter
• Know how to use your calculator (make sure you bring it, and check that it works before the big day)
Things to Remember
• Your first principles • Always at least one question
• Your derivative quick rules
• Pay attention to your substitution
• Remember your k method for factorising (or use your table mode) – but be able to use both ☺
• Simplify roots, and powers and make sure you have separate terms before differentiating.
8.1. For which values of 𝒙 will 𝒈 increase? (2)
• 8.2. Write down the 𝑥-coordinate of the point of inflection of g. (2)
• 8.3. For which values of 𝑥 will 𝑔 be concave down? (2)
8.5. Determine the equation of the tangent to g that has the maximum gradient. Write your answer in the form 𝒚 = 𝒎𝒙 + 𝒄 (5)
Things to Remember
• Study Guide
• If it helps, draw a picture
• Don’t make it unnecessarily complicated.
• Think about what they are asking you and read the question carefully.
Thank you for your valuable time!
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