Grade 12 MathsPaper 1

Prelim Revision

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

Algebra

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)

• 1.1.3. 1 − 𝑥 𝑥 + 2 < 0(3)

• 1.1.4. 𝑥 + 18 = 𝑥 − 2(5)

Solve simultaneously for 𝒙 and 𝒚 (6)

• 𝑥 + 𝑦 = 3 and • 2𝑥2 + 4𝑥𝑦 − 𝑦 = 15

If n is the largest integer for which 𝒏𝟐𝟎𝟎 < 𝟓𝟑𝟎𝟎, determine the value of n (3)

Sequences and Series

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

2.1. 𝟕; 𝒙; 𝒚; −𝟏𝟏; is an arithmetic sequence. Determine the values of 𝒙 and 𝒚. (4)

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)

Functions

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)

4.2.4. Calculate the area of OCDE (3)

4.2.5. Determine the equation of 𝒈−𝟏, the inverse of g, in the form 𝒚 = … (2)

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)

5.1.Write down the coordinates of A. (1)

• 5.2. Determine the coordinates of B. (3)

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)

Finance

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)

Calculus

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.

7.1. Determine 𝒇′ 𝒙 from first principles if 𝒇 𝒙 = 𝟐𝒙𝟐 − 𝟏 (5)

7.2. Determine

• 7.2.1.𝑑

𝑑𝑥

5𝑥2 + 𝑥3 (3) • 7.2.2. 𝑓′ 𝑥 if 𝑓 𝑥 =

4𝑥2−9

4𝑥+6; 𝑥 ≠ −

3

2(4)

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)

8.4. If 𝒈′ 𝒙 = −𝟔𝒙𝟐 + 𝟔𝒙 + 𝟏𝟐, determine the equation of g. (4)

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)

Probability

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!

Free worksheets and simulator:

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