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Edexcel IAL Mathematics P1.1.9 solve linear and quadratic inequalities

Use factorisation and critical values carefully: inequality marks depend on choosing the correct inside or outside intervals and preserving strict signs.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • Solve linear inequalities while keeping the inequality direction and exact bounds correct.
  • Factorise quadratics to find critical values before choosing inside or outside intervals.
  • Combine separate solution sets into final allowed x-ranges, including exact surd bounds.

P1.1.9 - Solving linear and quadratic inequalities question 1

[Maximum number: 3]

Students on a psychology course were given a pre-test at the start of the course and a final exam at the end of the course. The teacher recorded the number of marks achieved on the pre-test, p, and the number of marks achieved on the final exam, f, for 34 students and displayed them on the scatter diagram.

The equation of the least squares regression line for these data is found to be
f=10.8+0.748p

For these students, the mean number of marks on the pre-test is 62.4

Considering the equation of the regression line, Priya says that she would expect someone who scored 0 marks on the pre-test to score 10.8 marks on the final exam.

Later the teacher discovers an error in the recorded data. The student who achieved a score of 98 on the pre-test, scored 92 not 29 on the final exam.
The summary statistics used for the model f=10.8+0.748p are corrected to include this information and a new least squares regression line is found.
Given the original summary statistics were,
n=34
sum p=2120
sum pf=133486
Spp=15573.76
Spf=11648.35

Find the range of values of p for which this regression model, f=10.8+0.748p, predicts a greater number of marks on the final exam than on the pre-test.

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