NABTEB Mathematics May/June Exam Prep.

Welcome to today’s NABTEB Mathematics tutorial, brought to you by AllCBTs. In this guide, we’re working through core questions that appear regularly in the NABEB examination (May/June). So grab your calculator and writing materials — let’s dive into the key math problems and their step-by-step solutions.

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You can watch the full class in the video below:

Question 1: Simplify 1142+14×28\frac{1\frac{1}{4}}{2 + \frac{1}{4} \times 28}2+41​×28141​​

Step-by-Step Solution:

We apply BODMAS — Brackets, Orders, Division, Multiplication, Addition, and Subtraction.

1. First, calculate the multiplication in the denominator: 14×28=7\frac{1}{4} \times 28 = 741​×28=7
2. Add to the 2 in the denominator: 2+7=92 + 7 = 92+7=9
3. Convert the numerator 1141\frac{1}{4}141​ to an improper fraction: 54\frac{5}{4}45​
4. Now the entire expression becomes: 54÷9=54×19=536\frac{5}{4} \div 9 = \frac{5}{4} \times \frac{1}{9} = \frac{5}{36}45​÷9=45​×91​=365​

Final Answer: 536\frac{5}{36}365​

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Question 2: Triangle Ratio and Perimeter

Problem:

The sides of a triangle are in the ratio 4:7:8 and the perimeter is 38 cm. Find the length of each side.

Solution:

1. Add the ratio parts: 4+7+8=194 + 7 + 8 = 194+7+8=19
2. Find the value of one part: 3819=2\frac{38}{19} = 21938​=2
3. Multiply each ratio by 2:
   • 4×2=8 cm4 \times 2 = 8 \, \text{cm}4×2=8cm
   • 7×2=14 cm7 \times 2 = 14 \, \text{cm}7×2=14cm
   • 8×2=16 cm8 \times 2 = 16 \, \text{cm}8×2=16cm
4. Confirm: 8+14+16=38 cm✔8 + 14 + 16 = 38 \, \text{cm} ✔8+14+16=38cm✔

Final Answer: 8 cm, 14 cm, 16 cm

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Question 3: Solve the Simultaneous Equations

{3x+5y=142x+4y=6\begin{cases} 3x + 5y = 14 \\ 2x + 4y = 6 \end{cases}{3x+5y=142x+4y=6​

Elimination Method:

1. Multiply:
   • First equation by 2: 6x+10y=286x + 10y = 286x+10y=28
   • Second equation by 3: 6x+12y=186x + 12y = 186x+12y=18
2. Subtract: (6x+12y)−(6x+10y)=18−28⇒2y=−10⇒y=−5(6x + 12y) – (6x + 10y) = 18 – 28 \Rightarrow 2y = -10 \Rightarrow y = -5(6x+12y)−(6x+10y)=18−28⇒2y=−10⇒y=−5
3. Substitute back to find x: 3x+5(−5)=14⇒3x−25=14⇒3x=39⇒x=133x + 5(-5) = 14 \Rightarrow 3x – 25 = 14 \Rightarrow 3x = 39 \Rightarrow x = 133x+5(−5)=14⇒3x−25=14⇒3x=39⇒x=13

Final Answer: x = 13, y = -5

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Question 4: Solve the Exponential Equation

43×2=8×8x÷44^{\frac{3x}{2}} = 8 \times 8^x \div 4423x​=8×8x÷4

This question involves exponential simplification and laws of indices. Let’s break it down clearly in the full tutorial (next section coming soon!).

Watch more educational videos and past questions: https://youtube.com/@allcbts

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Why These Questions Are Essential

These questions cover common NAP math themes:

• Simplification and fraction operations
• Ratios and perimeter calculations
• Simultaneous equations
• Exponents and indices

They’re perfect for boosting confidence ahead of the May/June NAP exams.

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