MATHS

Question 1:

The diagram shows a **pyramid** with a **horizontal rectangular base**.

Given:

• Base length = **4.8 m**
• Base width = **3 m**
• Height of the pyramid = **4 m**

(i) Calculate **y**, the length of a **sloping edge** of the pyramid.
Answer: **............................... m** [4]

(ii) Calculate the **angle between a sloping edge and the rectangular base** of the pyramid.
Answer: **...............................** [2]

Question 2:

The diagram shows a **pyramid** on a **rectangular base ABCD**.
Given:

• AB = **8 cm**
• BC = **6 cm**
• PM = **9 cm**
• AC and BD intersect at **M**, and **P is vertically above M**.

(a) **N** is the **midpoint** of **BC**.
Calculate **angle PNM**.
Answer: **...............................°** [2]

(b) Show that **BM = 5 cm**.
Answer: **............................... cm** [1]

(c) Calculate the **angle between the edge PB and the base ABCD**.
Answer: **...............................°** [2]

(d) A **point X is on PC** so that **PX = 7.5 cm**.
Calculate **BX**.
Answer: **............................... cm** [6]

Question 3:

(a) In the **pentagon ABCDE**, given:

• **Angle ACB = Angle AED = 90°**
• Triangle **ACD is equilateral** with **side length 12 cm**
• **DE = BC = 6 cm**

(i) Calculate **angle BAE**.
Answer: **...............................°** [4]

(ii) Calculate **AB**.
Answer: **............................... cm** [2]

(iii) Calculate **AE**.
Answer: **............................... cm** [3]

(iv) Calculate the **area of the pentagon**.
Answer: **............................... cm²** [4]

(b) The diagram shows a **cuboid** where:

• **AB = 8 cm, BC = 4 cm, CR = 5 cm**

(i) Write down the **number of planes of symmetry** of this cuboid.
Answer: **...............................** [1]

(ii) Calculate the **angle between the diagonal AR and the plane BCRQ**.
Answer: **...............................°** [4]

Question 4:

A **rod of length 145 cm** is placed inside a water tank.

• One end of the rod is at the **bottom corner** of the tank.
• The other end is **x cm below the top corner** of the tank.

(c) Calculate the value of **x**.
Answer: **............................... cm** [4]

(d) Calculate the **angle** that the rod makes with the base of the tank.
Answer: **...............................°** [3]

Question 5:

**(a)** A, B, and C are points on horizontal ground. BT is a **vertical pole**. Given:

• AT = **60 m**
• AB = **50 m**
• BC = **70 m**
• Angle ABC = **130°**

(i) Calculate the **angle of elevation** of T from C.
Answer: **...............................°** [5]

(ii) Calculate the length **AC**.
Answer: **............................... m** [4]

(iii) Calculate the **area of triangle ABC**.
Answer: **............................... m²** [2]

**(b)** A **cuboid** has:

• Length = **45 cm**
• Width = **22 cm**
• Height = **12 cm**

Calculate the length of the straight line **XY**.
Answer: **............................... cm** [4]

Question 6:

The diagram shows a **tent ABCD**.

• The front of the tent is an **isosceles triangle ABC**, with **AB = AC**.
• The sides of the tent are congruent triangles **ABD** and **ACD**.

**(a)** Given:

• BC = **1.2 m**
• Angle ABC = **68°**

Find AC.
Answer: **............................... m** [3]

**(b)** Given:

• CD = **2.3 m**
• AD = **1.9 m**

Find **angle ADC**.
Answer: **...............................°** [4]

**(c)** The floor of the tent, **triangle BCD**, is an **isosceles triangle** with **BD = CD**.
Calculate the **area of the floor of the tent**.
Answer: **............................... m²** [4]

**(d)** When the tent is on horizontal ground, **A is 1.25 m above the ground**.
Calculate the **angle between AD and the ground**.
Answer: **...............................°** [3]