1.1.1
1.1.2
(Correct to TWO decimal places)
1.1.3
1.1.4
1.2 Solve the following equations simultaneously:
2.1 Simplify the following fully:
2.2 Solve for x:
2.3 Rewrite the following expression as a power of x:
ACDF is a rectangle with an area of . B is a point on AC and E is a point
. B is a point on AC and E is a point
on FD such that ABEF is a square with sides of length (x-2)cm each.
Calculate the length of ED.
4.1 Show that the general term of the quadratic number pattern is given by
4.2 Which term of the quadratic pattern is equal to 128?
4.3 Determine the general term of the first differences.
4.4 Between which TWO terms of the quadratic pattern will the first difference be 599?
5.1 How many white squares will be in the FOURTH pattern?
5.2 Determine the number of white squares in the th 157 pattern.
5.3 Calculate the largest value of n for which the pattern will have less than 613
grey squares.
5.4 Show that the TOTAL number of squares in the th n pattern is always an odd number.
6.1 Write down the equations of the asymptotes of f.
6.2 Calculate the x- and y-intercepts of f.
6.3 Sketch the graph of f. Show clearly the intercepts with the axes and the asymptotes.
6.4 If y = x + k is an equation of the line of symmetry of f, calculate the value of k.
7.1 Write down the value of q.
7.2 If the graph of h passes through the point
.calculate the value of a.
7.3 Calculate the average gradient between the x-intercept and the y-intercept of h.
7.4 Determine the equation of p if
in the form
8.1 Write down the coordinates of C.
8.2 Determine the equation of f in the form
8.3 Determine the range of f.
8.4 Calculate the equation of g in the form
8.5 For which values of x will:
8.5.1
8.5.2
8.5.2
8.6 For what values of p will
have non-real roots?
8.7 T is a point on the x-axis and M is a point on f such that
. TM intersects g at P. Calculate the maximum length of PM.
9.1 A tractor bought for R120 000 depreciates to R11 090,41 after 12 years by using the reducing balance method. Calculate the rate of depreciation per annum. (The rate was fixed over the 12 years.)
9.2 Calculate the effective interest rate if interest is 9,8% p.a., compounded monthly.
9.3
Mrs Pillay invested R80 000 in an account which offers the following: · 7,5 % p.a., compounded quarterly, for the first 4 years and thereafter
· 9,2% p.a., compounded monthly, for the next 3 years
Calculate the total amount of money that will be in the account at the end of 7 years if no further transactions happen on the account.
9.4 Exactly 8 years ago Tashil invested R30 000 in an account earning 6,5% per annum, compounded monthly.
9.4.1 How much will he receive if he withdrew his money today?
9.4.2
Tashil withdrew R10 000 three years after making the initial deposit and re-invested R10 000 five years after making the initial deposit.
Calculate the difference between the final amount Tashil will now receive after eight years and the amount he would have received had there not been any transactions on the account after the initial deposit.
10.1 How many customers did NOT buy burgers on the day?
10.2 Are events B and C mutually exclusive? Give a reason for your answer.
10.3 If a customer from this group is selected at random, determine the probability that he/she:
10.3.1 Bought only a vegetarian burger
10.3.2 Bought a cheese burger and a bacon burger
10.3.3 Did not buy a cheese burger
10.3.4 Bought a bacon burger or a vegetarian burger
Given: P(A) = 0,12
P(B) = 0,35
P(A or B) = 0,428
Determine whether events A and B are independent or not. Show ALL relevant calculations used in determining the answer.
12.1 How many red marbles are in the bag?
12.2 Draw a tree diagram to represent the above situation.
12.3 What is the probability that Paballo will choose a GREEN and a YELLOW marble?
