Question
Calculate the length of AB.
……………………………………….
(b) The point P has co-ordinates (10,12) and the point Q has co-ordinates (2,-4)
Find
(i) the co-ordinates of the mid-point of the line PQ.
(………………….. , …………………..)
(ii) the gradient of the line PQ
…………………………………………
(iii) the equation of a line perpendicular to PQ that passes through the point (2,3)
…………………………………………
Answer/Explanation
(a) 10.8 or 10.81 to 10.82
(b)(i) (6, 4)
(ii) 2
(iii) \(y=-\frac{1}{2}x+4\)
Question
(a) Calculate 20.7.
Answer/Explanation
Ans: 1.62 or 1.62…
(b) Find the value of x in each of the following.
(i) 2x= 128
Answer/Explanation
Ans: 7
(ii) 2x × 29 = 213
Answer/Explanation
Ans: 4
(iii) 29 ÷ 2x = 4
Answer/Explanation
Ans: 7
(iv) \(2^{x} = \sqrt[3]{2}\)
Answer/Explanation
Ans: \(\frac{1}{3}oe\)
(c) (i) Complete this table of values for y = 2x.
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| y | 0.125 | 0.5 | 2 | 4 | 8 |
Answer/Explanation
Ans:
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| y | 0.125 | 0.25 oe | 0.5 | 1 | 2 | 4 | 8 |
(ii) On the grid, draw the graph of y = 2x for –3 ≤ x ≤ 3.
Answer/Explanation
Ans: Correct curve
(iii) Use your graph to solve 2x= 5.
Answer/Explanation
Ans: 2.3
(iv) Find the equation of the line joining the points (1, 2) and (3, 8).
Answer/Explanation
Ans: y = 3x – 1 oe 3 term equation
(v) By drawing a suitable line on your graph, solve 2x– 2 – x = 0.
Answer/Explanation
Ans: –1.7 to –1.5 and 2