GCSE GCSE Mathematics 3 — Questions and Answers
Question 1: What is the interquartile range (IQR)?
- The difference between the maximum and minimum values
- The middle value of a data set
- The difference between the upper quartile and lower quartile (Correct answer)
- The average of all values
Correct answer: The difference between the upper quartile and lower quartile
The interquartile range (IQR) = Upper Quartile (Q3) − Lower Quartile (Q1). It measures the spread of the middle 50% of data and is less affected by outliers than the range.
Question 2: What does a negative correlation on a scatter graph show?
- As one variable increases, the other increases
- As one variable increases, the other decreases (Correct answer)
- There is no relationship between the variables
- The data is incorrect
Correct answer: As one variable increases, the other decreases
A negative correlation means there is an inverse relationship: as one variable increases, the other decreases. The scatter points slope downwards from left to right on the graph.
Question 3: What is 3.6 × 10⁴ written as an ordinary number?
- 36,000 (Correct answer)
- 360,000
- 3,600
- 0.000036
Correct answer: 36,000
Multiply 3.6 by 10⁴ = 10,000: 3.6 × 10,000 = 36,000. Moving the decimal four places to the right gives 36,000.
Question 4: In a right-angled triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. What is sin θ?
- 0.6 (Correct answer)
- 0.8
- 0.75
- 1.2
Correct answer: 0.6
sin θ = opposite/hypotenuse = 6/10 = 0.6. The SOH-CAH-TOA rule: Sin = Opposite/Hypotenuse.
Question 5: What is the equation of a line parallel to y = 2x + 1 passing through (0, −3)?
- y = 2x − 3 (Correct answer)
- y = −2x + 1
- y = 3x − 3
- y = 2x + 3
Correct answer: y = 2x − 3
Parallel lines have the same gradient. The original line has gradient 2. Through (0, −3), the y-intercept is −3. So the equation is y = 2x − 3.
Question 6: What is the value of 2⁵?
- 10
- 16
- 25
- 32 (Correct answer)
Correct answer: 32
2⁵ = 2 × 2 × 2 × 2 × 2 = 32. Index notation means multiplying the base by itself the number of times shown by the power.
GCSE GCSE Mathematics 3
What is the interquartile range (IQR)?