Extra Exercises: Algebra II & Number Bases

If a jacket is priced at RM400 and is offered with a 10% discount, what will be the final price of the jacket?

• RM360

• RM370

• RM380

• RM400

Answer explanation

To find the final price after a 10% discount on RM400, calculate 10% of RM400, which is RM40. Subtract RM40 from RM400 to get RM360. Therefore, the final price of the jacket is RM360.

Which symbol represents 'Not equal'?

• <

• >

• ≠

• ≤

Fill in the blank: The algebraic expression for '3 subtracted from m' is (a)  

• m - 3

• m / 3

• 3m

• m+3

Answer explanation

The phrase '3 subtracted from m' means we take 3 away from m, which is represented as m - 3. Therefore, the correct algebraic expression is m - 3.

Solve the following simultaneous equations: 2x + 3y = 12 and x - y = 1. What is the value of y?

• A) 2

• B) 3

• C) 4

• D) 5

Answer explanation

To solve the equations, substitute x from the second equation into the first. From x - y = 1, we get x = y + 1. Substituting into 2x + 3y = 12 gives 2(y + 1) + 3y = 12. Simplifying leads to y = 2. Thus, the correct answer is A) 2.

Fill in the blank: For the equations x + 5y = -13 and 2x - y = 7, the value of x is ​ (a)   .

• 2

• -3

• 4

• -5

Answer explanation

To find x, solve the system of equations. From the second equation, 2x - y = 7, express y in terms of x: y = 2x - 7. Substitute into the first equation: x + 5(2x - 7) = -13. Simplifying gives x = 2.

What is the solution to the system of equations: 3x + 4y = 18 and 2x - y = 1?

• x = 2, y = 3

• x = 3, y = 2

• x = 4, y = 0

• x = 1, y = 4

Answer explanation

To solve the system, substitute y from the second equation into the first. From 2x - y = 1, we get y = 2x - 1. Substituting into 3x + 4(2x - 1) = 18 gives x = 2. Then, y = 3. Thus, the solution is x = 2, y = 3.

• y = 2x - 7

• y = 7 - 2x

• y = x + 7

• y = -2x + 7

Answer explanation

To solve for y in the equation 2x - y = 7, rearrange it to get y = 2x - 7. This expression is then substituted into the equation x + 5y = -13.

A stadium sells 1,200 tickets for a football match. VIP tickets cost $50, and general tickets cost $30. The total revenue collected was $42,000. How many VIP tickets were sold?

VIP Ticket:​ ​ (a)  

• 700
• 800

• 900

• 300

Answer explanation

Let x be the number of VIP tickets sold. Then, 1200 - x are general tickets. The equation is 50x + 30(1200 - x) = 42000. Solving gives x = 300. Thus, 300 VIP tickets were sold.

A basket contains apples and bananas. There are 40 fruits in total. An apple weighs 150g, and a banana weighs 120g. The total weight of the fruits is 5.4 kg. How many apples and bananas are there?

• apple = 20, banana = 20

• apple = 40, banana = 20

• apple = 20, banana = 40

• apple = 40, banana = 40

Answer explanation

Let a = number of apples and b = number of bananas. We have a + b = 40 and 150a + 120b = 5400. Solving these, we find a = 20 and b = 20. Thus, the correct choice is apple = 20, banana = 20.

Answer explanation

To solve the inequality -5z + 7 ≤ 2z - 14, first isolate z. Adding 5z to both sides gives 7 ≤ 7z - 14. Adding 14 results in 21 ≤ 7z. Dividing by 7 yields z ≥ 3, making the correct choice z ≥ 3.