A straight line passes through the points S(x, 4) and T(5, 1).
(a) In terms of x, find the gradient of this line.

(b) Given that the length of the line ST = 5 units, find the values of x.

f ( x ) = 2 x − 3 and g ( x ) = 4 x
Find:
(a) g ( 0.5 )

(b) x when f ( x ) = g ( x )

The diagram shows a straight line AB of gradient − 3 4.

(a) Find:
(i) The coordinates of A
(ii) The distance AB
(iii) The equation of a line parallel to line AB passing through (0, 2)
(b) C is the image of A under reflection in x=1. Find the coordinates of the point C.

f : x → x − 5 2
Find the value of:
(i) k if f : − 3 → k

(ii) h if f : h → 7

(a) A straight line passes through the points (−1, −2) and (0, −3).
(i) Find the gradient of the line.
(ii) Write the equation of the line.
(b) Here is a mapping.

(i) Complete the rule for the mapping.
(ii) Complete the table for this mapping.

(a) If f ( x ) = 3 x + 2, find f ( − 2 ).

(b) f ( x ) = 2 x + 5. Find f ( − 1 ).

In the diagram, B is the point (0, 8) and C is the point (0, 2).
The sloping line through B and the horizontal line through C meet at the point A.

(a) Write the equation of the line AC.
(b) Given that the gradient of the line AB is 2, find the equation of the line AB.
(c) Find the coordinates of A.
(d) Work out the area of the triangle ABC.

(a) Plot the point B (2,-2).
(b) Find the gradient of the line AB.
(c) Write down the column vector AB→.

f(x)=2x+3
Find f(2)

Given that f(x)=1-3x, find f(2).

In the diagram, A is the point (0,4) and B is the point (3,0).

Find:
(a) The gradient of AB
(b) the equation of the straight line AB

Mpho is n years old and her brother, Pule, is n + 7 years old.
Their mother is 3 times as old as Mpho.

(a) The father will retire at 60 years old when he is $2n+22$. Find Pule's age.

(b) Calculate the sum of the ages of Mpho and her mother.

(c) Find the mother's age when Pule was born.

The table shows the corresponding values of y for every value of x for $y=x^2+bx-4$.

x	−5	−4	−3	−2	−1	0	1	2
y	6	0	−4	−6	−6	−4	0	6

(a) Use the information from the table to calculate the value of b in $y=x^2+bx-4$.

(b) The line L is drawn on the grid. On the same grid draw the graph of $y=x^2+bx-4$ for $-5\le x\le 2$.

The diagram shows patterns with shaded and unshaded squares. Pattern 4 is incomplete.

(a) Complete the 4th pattern.

(b) Complete the table.

Pattern number	1	2	3	4
Unshaded squares	1	4	...	...
Shaded squares	4	4	4	4
Total number of squares	5	8	13	...

(c) Find the number of unshaded squares in the 21st pattern.

(d) Find the pattern number with a total number of 965 squares.

$f\left(x\right)=\frac{3x+2}{2}$
Find:
(a) $\frac{1}{2}f\left(x\right)$

(b) $f\left(2\right)$

The diagram shows a sequence of patterns made from shaded and unshaded squares.

(a) Complete the table.

Pattern number	1	2	3	4
Number of unshaded squares	1	3	...	...
Number of shaded squares	0	2	8	...
Total number of squares	1	5	13	...

(b) Write an expression in terms of n for the number of unshaded squares in pattern n.

(c) In another sequence the nth term is given by $n^2-n+30$.
(i) Write the second term of the sequence.

(ii) What term number is 102?

(a) Complete the table of values for $y=x^2+x-6$.

x	−4	−3	−2	−1	0	1	2	3
y	6	0	−4		−6	−4		6

(b) On the grid, draw the graph of $y=x^2+x-6$ for $-4\le x\le 3$.

$f\left(x\right)=1-x$
Find:
(a) $f\left(3\right)$,
(b) $f(k+4)$, in terms of $k$,
(c) $k$ when $f(2-\frac{k}{4})=3$.

The table shows some values of $y=x^2+x-2$.

x	−2	−1.5	−1	0	0.5	1	1.5	2
y	0	−1.25	−2	−2	p	0	q	4

(a) Calculate the value of p and the value of q.

(b) On the grid, draw the graph of $y=x^2+x-2$ for $-2\le x\le 2$.

(c) Write the equation of the line of symmetry of the graph.

(d) (i) On the same grid, draw the graph of $x+y=2$.

(ii) Write down the coordinates of the point where the two graphs intersect for $-2\le x\le 2$.

The point A(1, 5) is the midpoint of B(a, 3) and C(a + 1, 7).
(a) Show that $a=\frac{1}{2}$.

(b) Find the equation of a straight line passing through point A with y-intercept 5.

(c) Calculate AB.