TOTAL 33 marks
1. Solve this equation \[\frac{2x+1}{4}-\frac{2(3-2x)}{3}=2x\]
[4 marks]
2. Copy and complete this table for a pie chart \begin{array}{|c|c|c|} \hline \text{Fav. colour} & \text{Frequency} & \text{Angle (1 d.p.)} \\ \hline \text{red} & 8 & \\ \hline \text{green} & 33 & \\ \hline \text{blue} & 19 & \\ \hline \text{pink} & 7 & \\ \hline \text{other} & 2 & \\ \hline \end{array}
[3 marks]
3. Draw a prime factor tree for 84 and list all the factors of 84
[2 marks]
4. The point (3, -5) is on this line $4x-2y=k$ What is the value of k?
[2 marks]
5. Express 156 as a product of it's prime factors and use this to work out how many factors 156 has without actually listing them all.
HINT: E.g. $392=2^3 \times 7^2$; add one to each index; $3+1=4$ and $2+1=3$; then multiply; So $392$ has $3\times 4 = 12$ factors
[2 marks]
6. Find the gradient of this line: $8y+4x=15$ and use this value to find the gradient of a line which is perpendicular (at right angles) to this line. Remember for perpendicular gradient: flip the fraction and change sign.
[4 marks]
7. Copy and complete the table.
\begin{array}{|c|c|c|}
\hline
\text{Age} & \text{Frequency} & \text{Age $\times$ Frequency} \\ \hline
\text{14} & 4 & \\ \hline
\text{15} & 11 & \\ \hline
\text{16} & 31 & \\ \hline
\text{17} & 27 & \\ \hline
\end{array}
Use it to:
a. Find the mean
b. Find the median
[4 marks]
8. Copy and complete the table.
\begin{array}{|c|c|c|}
\hline
\text{Weight (w) in Kg} & \text{Freq-Girls} & \text{M.P. $\times$ F} & \text{Freq-Boys} & \text{M.P. $\times$ F} \\ \hline
\text{10 $\leq$ w < 15} & 4 & & 10 \\ \hline
\text{15 $\leq$ w < 20} & 25 & & 15\\ \hline
\text{20 $\leq$ w < 25} & 31 & & 21\\ \hline
\text{25 $\leq$ w < 30} & 10 & & 26\\ \hline
\end{array}
Use it to:
a. Find an estimate of the mean for boys and girls
b. Draw a a fully labelled frequency polygon to include the data for the boys and girls on the same diagram
[8 marks]
9. HARD: Find the value of p by splitting the triangle
[4 marks]
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