TOTAL 28 marks
1. Solve this equation \[\frac{2x+1}{3}-\frac{3(2-2x)}{5}=2\]
[4 marks]
2. An observer stands 100m from the foot of a pine tree and uses a clinometer to measure the angle of elevation (angle from the horizontal) to the top of the tree which comes out as $27^O$. How high is the tree?
[3 marks]
3. Solve these simultaneous equations algebraically:\[4x+3y=1\\-2x+5y=8\]
[4 marks]
4. In a survey of 45 people, 17 answered that their favourite colour was red. What angle would this be on a pie chart?
[2 marks]
5. Find the mean median mode and range of: 3, 5, -11, 7, 12, 10, 8, 5
[4 marks]
6. Find the gradient of this line: $4y-5x=20$ and use this value to find the gradient of a line which is perpendicular (at right angles) to this line
[4 marks]
7. Copy and complete the table. Use it to find an estimate of the mean height from this data: \begin{array}{|c|c|c|} \hline \text{Height in cm (h)} & \text{Frequency} & \text{M.P. $\times$ Frequency} \\ \hline \text{100 $\leq$ h < 120} & 3 & \\ \hline \text{120 $\leq$ h < 140} & 25 & \\ \hline \text{140 $\leq$ h < 160} & 17 & \\ \hline \end{array}
[3 marks]
8. HARD: Find the length of YZ
[4 marks]
In question 1 you need to multiply both sides by 15 to give \[5(2x+1)-9(2-2x)=30 \\ \therefore 10x + 5 - 18 + 18x =30 \\ \therefore 28x -13 =30 \] etc
ReplyDeleteAlso note that in question 8 the triangle is not right angled (RAT). The angle at X is 45 degrees. You should spilt the triangle into 2 RATs so you can do 2 lots of trig. There is another way also...
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