IGCSEFurther MathsEdexcelExam QuestionsLogarithms, Indices & SurdsLogarithms, Indices & Exponentials

Logarithms, Indices & Exponentials (Edexcel IGCSE Further Pure Maths): Exam Questions

Exam code: 4PM1

1 hour8 questions
1a
2 marks

Complete the table of values for

y space equals space 2 to the power of open parentheses x over 2 plus 1 close parentheses end exponent plus 1

giving your answers to 2 decimal places where appropriate.

x

0

1

2

3

4

5

y

3

9

12.31

How did you do?

1b
2 marks

On the grid, draw the graph of y space equals space 2 to the power of open parentheses x over 2 plus 1 close parentheses end exponent plus 1 for space 0 less-than or slanted equal to x space less-than or slanted equal to space 5

Graph paper with x and y axes centred. X-axis ranges from -5 to 5, y-axis from -5 to 14, with grid squares visible.

How did you do?

1c
4 marks

By drawing a suitable straight line on the grid, obtain an estimate, to 1 decimal place, of the root of the equation log subscript 2 space left parenthesis 4 x space – space 6 right parenthesis squared space space – space x space equals space 2 in the interval 0 space less-than or slanted equal to space x space less-than or slanted equal to space 5

How did you do?

2
7 marks

Solve the equation log subscript 2 x space plus space 6 log subscript x space space 2 space equals space 7

How did you do?

3a
2 marks

Find the value of a such that log subscript a space 8 space equals space 3 over 4

How did you do?

3b
4 marks

Show that

3 x log subscript 2 x space minus space 4 log subscript 16 8 space plus space 6 x log subscript 4 8 space minus space log subscript 2 x space equals space log subscript 2 open parentheses 8 x close parentheses to the power of 3 x minus 1 end exponent

How did you do?

3c
3 marks

Hence solve the equation 3 x log subscript 2 x space minus space 4 log subscript 16 8 space plus space 6 x log subscript 4 8 space minus space log subscript 2 x space equals space 0

How did you do?

4a
4 marks

Solve the equation 5 open parentheses log subscript b 9 plus log subscript b 3 close parentheses equals 3

How did you do?

4b
7 marks

Solve the equation 3 space log subscript 3 x plus 3 space log subscript x 27 equals 8 space log subscript 4 128
Give your answers in exact form.

How did you do?

5
8 marks

Solve the equation

log subscript 2 x cubed plus log subscript 4 x squared minus 3 log subscript x 2 equals 0

giving your answers to 3 significant figures.

How did you do?

6
8 marks

Solve the simultaneous equations

space space space space space space space space space space space space space space space space space 2 log subscript 4 space x equals log subscript 3 space 3 y squared log subscript 2 space x cubed plus 8 log subscript 9 space y equals 13

Show your working clearly.

How did you do?

7a
2 marks

Complete the table of values for

y equals 0.5 to the power of open parentheses x over 3 plus 1 close parentheses end exponent plus 2

giving each value to 2 decimal places where appropriate.

x

-6

-5

-4

-3

-2

-1

0

y

4

3.59

3.26

2.5

How did you do?

7b
2 marks

On the grid opposite, draw the graph of y equals 0.5 to the power of open parentheses x over 3 plus 1 close parentheses end exponent plus 2 for negative 6 less-than or slanted equal to x less-than or slanted equal to 0

How did you do?

7c
6 marks

By drawing a suitable straight line on the grid, obtain an estimate, to one decimal place, of the root of the equation

log subscript 2 left parenthesis 2 x plus 2 right parenthesis cubed plus x plus 3 equals 0 in the interval negative 6 less-than or slanted equal to x less-than or slanted equal to 0

Graph with x-axis ranging from -7 to 1 and y-axis from -1 to 5, both labelled. Gridlines present for precision in plotting points.

How did you do?

8
8 marks

Giving each value in your solution to 2 decimal places, solve the simultaneous equations

space space space space space space space space space space space space e to the power of 2 y end exponent minus x plus 2 equals 0 ln left parenthesis x plus 3 right parenthesis minus 2 y minus 1 equals 0

How did you do?