Assessment

Core Skills Required for Entry to Maths G12

No Calculators of Any Kind May be Used

Reasoning: 

Numerical Reasoning:  Write down  the next number in the sequence


1:     2; 4; 6; 8; ?                         a: 6  b: 10  c:  9     

2:     17; 21; 25; ?                       a: 30  b: 29 c: 28


Answer 2 of the following

Various Sequences
  

Quadratic Equations:


  1. Factorize and solve    x^2 -x -12 = 0
  2. Confirm you answer by completing the square.  Show all working.
  3. Confirm again by using the quadratic formula

Numbers:

  1. If (100 000 000 - 1) = 99 999 999.0,  express 99 999 999.0 as a product of its prime factors
        without using a calculator OR using division.  Multiplication tables may be used.

       2.  Given the sequence 2; 8 ; 18; 32; ...   Write down or calculate the next term   


Graphs of Functions:



  
Graph of Quadratic Equation

  The graph above shows part of the function f(x) = ax^2 + bx + c


  1. Find the values of a, b and c.                                 (2)
  2. Find the co-ordinates of the vertex (minimum)     (3)
  3. Write down the domain of f(x)                              (1)
  4. Write down the range of f(x)                                (1)


Linear Programming:


In a certain army a platoon consists of 20 men plus a lieutenant in command.  All the men except the lieutenant may carry rifles and 80 rounds of ammunition each. A platoon may carry up to 4 light machine guns (LMGs) each with 400 rounds of ammunition:  One man carries the LMG and another carries the ammunition.  Battalion orders require that each platoon carry at least one LMG.  A military manual suggests 4 rifles per LMG.  Due to a shortage of rifles only 15 are actually available per platoon.  Let x be the number of rifles and y be the number of LMGs.  Determine the constraints upon the arms carried by a platoon.


  1.  Write down the max. possible number of rifles (LMGs = 0).  Mark this constraint. (1)
  2.  Write down the maximum possible number of LMGs.  Mark this constraint.             (1)
  3.  How many rifles can be carried if maximum LMGs are carried?                               (2)
  4.  For the line  relating x and y  determine the coordinates when x=maximum rifles
        and when y = maximum LMGs.  Connect the points.                                                       (4)
    5.  Mark the minimum LMG and maximum rifle constraints                                               (2)
    6.   Draw the line resulting from the military manual y = ?x                                              (4)
    7. 
Mark the feasible reason                                                                                              (3)

Write down the ammunition equation A = ?x + ?y  
                                                                                              (1)
Determine the gradient of the ammunition line.                                                                                                 (2)
Determine the values of x and y for maximum fire-power (max ammo. carried).                     (4)         


Trigonometry: 

  1.        Determine the value of Cos(240) x Sin(330)    
  2.        If Tan(t) = -1 and Sin(t)  > 0
 2.1  determine t                                                                  (1)
 2.2   determine Cos^2(t) - Sin^2(t)                     (2)


Trigonometry:

  • The Ratios
  • Identities
  • Special Angles
  • Reduction Formulae
  • Trigonometric Equations
  • Sine, Cosine and Area Rules. 
  Data Handling:
  • Statistics
    • Central Tendency
    • Cumulative Frequency
    • Bivariate Data
    • Grouped Data
      • Standard Deviation
Shapes:
  • Regular Solids