Cambridge Lower Secondary Stage 8 — Challenge Paper (Calculator Permitted)
A laptop costs $800. It depreciates by 25% in year 1 and 20% in year 2. Find the value after 2 years. Is the total percentage decrease more or less than 45%? Enter value after 2 years.
Calculate (3.2 × 105) ÷ (8 × 10−2). Give your answer in standard form.
Three friends share a bill. Ratio of contributions is 2 : 3 : 5. The middle person pays $42. What is the total bill, and what does the largest contributor pay?
Total: Largest:A train travels at 90 km/h. Convert this to m/s (1 d.p.). Then find how far it travels in 25 seconds.
Speed m/s: Distance: my is inversely proportional to x². When x = 3, y = 8. Find y when x = 6.
Expand and simplify: (2x + 3)(x − 4)
Solve the inequality: 2(3x + 1) > 5x + 8. List the first three integer solutions greater than the boundary.
Boundary x > First 3 integers:f(x) = 2x − 1 and g(x) = x² + 3. Find: (a) gf(3) (b) fg(2) (c) f⁻¹(9)
gf(3) = fg(2) = f⁻¹(9) =The nth term of a sequence is 4n − 3. Find the first term, the 10th term, and which term equals 97.
T₁ = T₁₀ = n =Two lines: L₁: y = 3x − 2 and L₂ passes through (0, 5) and is perpendicular to L₁. Find the equation of L₂ and their intersection point.
A rectangle has length (3x + 2) cm and width (x + 1) cm. Its area is 52 cm². Form a quadratic equation and solve for x (take positive solution only, 1 d.p.).
A hemisphere has diameter 12 cm. Find: (a) its total surface area (= 2πr² + πr² = 3πr²) (b) its volume. Give both answers to 1 d.p.
SA: Vol:Two similar solids have volumes in ratio 27 : 125. Find the linear scale factor and the ratio of their surface areas.
Scale factor: SA ratio (smaller:larger):A 3D shape has 6 faces, 12 edges. Using Euler's formula, find the number of vertices. Name a common solid with these properties.
V = Name:A shape is enlarged by scale factor 2 from centre (0, 0). The original triangle has vertices A(1, 2), B(3, 2), C(2, 4). What are the coordinates of B'?
B' =A composite shape is a rectangle (8 cm × 5 cm) with a semicircle of diameter 5 cm removed from one end. Find the area. (2 d.p.)
The back-to-back stem-and-leaf diagram shows test scores for two classes:
| Class A (leaves) | Stem | Class B (leaves) |
|---|---|---|
| 8 6 4 | 3 | 2 5 7 |
| 9 7 5 2 | 4 | 0 3 6 8 |
| 8 6 1 | 5 | 2 5 9 |
| 4 | 6 | 1 |
Find the median of Class A.
Which class has the higher median?
A bag has 4 red and 6 blue balls. Two balls are drawn WITHOUT replacement. Find P(both red).
A grouped frequency table:
| Time (min) | Frequency |
|---|---|
| 0 – 10 | 3 |
| 10 – 20 | 7 |
| 20 – 30 | 15 |
| 30 – 40 | 10 |
| 40 – 50 | 5 |
Find: (a) estimated mean (1 d.p.) (b) frequency density for the 20–30 class
Mean: Freq density:P(A) = 0.5, P(B) = 0.4. A and B are independent. Find: (a) P(A and B) (b) P(A or B) (c) P(neither)
P(A∩B) = P(A∪B) = P(neither) =