4MA0 Foundation January 2016 Paper 1 Q4
4 Rayna has a fair 4-sided spinner.
The spinner can land on 3, 5, 7 or 9
Rayna spins the spinner 20 times.
She records the score for each spin.
Here are her scores.
3 9 5 7 9 5 3 3 5 9
9 9 7 5 9 7 5 9 3 7
(a) Complete the frequency table for these results.
(2)
| Score | Tally | Frequency |
|---|---|---|
| 3 | ||
| 5 | ||
| 7 | ||
| 9 |
(b) Write down the mode of her scores. (1)
(c) Find the range of her scores. (1)
Rayna says that 3, 5, 7 and 9 are all prime numbers.
(d) Explain why Rayna is wrong. (1)
Rayna now spins her spinner twice.
She adds the two numbers together to get the total.
(e) Complete the table to show the total for each possible outcome.
Five of the totals have been done for you.
(2)
Five of the totals have been done for you.
| 1st spin | |||||
|---|---|---|---|---|---|
| 2nd spin | 3 | 5 | 7 | 9 | |
| 3 | 6 | 10 | |||
| 5 | 10 | 12 | |||
| 7 | 10 | ||||
| 9 | |||||
Rayna spins the spinner twice.
(f)
(i) Write down the probability that she will get a total of 10
(ii) Write down the probability that she will get a total greater than 12
(3)| Scheme | Marks |
|---|---|
| 4, 5, 4, 7 | B2 |
| (2) |
Notes
B2: for correct frequencies
B1 for at least 2 correct frequencies or tallies
| Scheme | Marks |
|---|---|
| 9 | B1 |
| (1) |
Notes
B1: ft from (a) or 9
| Scheme | Marks |
|---|---|
| 6 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| eg. 3 is a factor of 9 | B1 |
| (1) |
Notes
B1: for identifying 9 with a correct reason
| Scheme | Marks |
|---|---|
| (6), 8, (10), 12 8, (10), (12), 14 (10), 12, 14, 16 12, 14, 16, 18 | B2 |
| (2) |
Notes
B2: B1 for at least 4 correct entries
| Scheme | Marks |
|---|---|
| (i) \(\dfrac{3}{16}\) oe | B2 |
| (ii) \(\dfrac{6}{16}\) oe | B1 |
| (3) |
Notes
B2: B1 for \(\dfrac{a}{16}\) with \(a \lt 16\) or \(\dfrac{3}{b}\) with \(b \gt 3\) or
3 and 16 used with incorrect notation (eg. 3 : 16)
ft from complete table for numerator only
B1: ft from complete table for numerator only