x² - x -12 =0

a. 2x² - 5x -11 = 0 [4 marks]

b. 2x³ - 5x² - 11x = 0 [2 marks]

-3(x+7)(x-5) < 0

Given: y + 2 = x and y = X² – x – 10

Solve for x and y simultaneously

Simplify: (3²⁰¹⁵ + 3²⁰¹³) / ( 9¹⁰⁰⁶)

Given the geometric sequence: 7 ; x ; 63 ; ...

Determine the possible values of x.

T₁₀

S₉

Write down the value of the 191^st term of the sequence.

Determine the sum of the first 500 terms of this sequence.

Calculate the first term of the series `sum_(k=2)^20 (4x - 1) `^k if x = 1

For which values of x will `sum_(k=1)^oo(4x - 1)`^k exist?

Determine a formular for the n^th term of the sequence.

Write down the 4^th, 5^th, 6^th and 7^th terms of the sequence.

Write down the remainders when each of the first seven terms of the sequence is divided by 3.

Calculate the sum of the terms in the arithmetic sequence that are divisible by 3.

T₅

T₅₀

Write down the coordinates of y-intercept of f.

Determine the coordinates of the x-intercepts of f.

Determine the coordinates of the turning point of f.

Sketch the graph of y=f(x), clearly showing the coordinates of the turning points and the three intercepts with the axes.

Determine the value of K.

Give the equation of g^-1 in the form of y= ...

For which value(s) of x is g^-1 (x) `<=` 0?

Write down the domain of h if h(x) = g-1(x-3).

Sketch the graph of the inverse of y=1.

Is the inverse of y = 1 a function. Motivate your answer.

Determine the values of D and P.

Show that the equation of f can be written as y= -3/x+1 +1.

Write down the coordinates of P.

Write down the coordinates of the image of B(2;0) if B is reflected about the axis of symmetry y= x+2.

The expomential funxtion, g(x) = p.2^x + q has a horizontal asymptote at y=1 and passes through (0 ; -2). :

Calculate the effective annual interest rate of Mpho's investment.

Determine the value of k.

Calculate the maximum amount that the bank will allow Darrel to spend each month on his bond repayments, if Darrel earns R18 480 per month.

Suppose at the end of each month, Darrel repays the maximum amount allowed by the bank. How much money does Darrel borrow if he takes 25 years to repay the loan at an interest rate of 8% p.a., compounded monthly?

(The first repayment is made one month after the loan is granted.)

Determine f'(x) from first principles.

A(X; 23) Where X > 0, and B(-2; y) are points on the graph of f.

Calculate the numerical value of the average gradient of f between A and B.

Differentiate y =`(x+5)/sqrt(x)` with respect to x.

Determine the gradient of the tangent of the graph of f(x) = -3x³ - 4x + 5 at x = -1.

Show that a=1 and b=-1.

Hence, or otherwise determine the x-coordinate of R.

Write down the coordinates of the turning point of h if h is defined by h(x)=2f(x)-4

After how long will the water be flowing at the maximum rate?

After how many seconds does the water stop flowing?

Write down the contraints that govern this system.

Sketch the system of contraints (inequalities) and clearly indicate the feasible region.

Write down the profit function.

Detemine the number of short-sleeved and long-sleeved shirts that must be manufactured per day to provide the company with maximum profit.

If the objective profit function is given by P = ax + by, determine (a/b) if P is maximised at each value of y between 100 and 160.