BECE - Basic Education Certificate Examination Algebraic Expressions and Equations Questions and Answers 1 — Questions and Answers

Question 1: Simplify the expression: 5(x + 2y) - 3(2x - y)

13y - x (Correct answer)
11y - x
7y - x
-x - 13y

Correct answer: 13y - x

First, distribute the numbers outside the brackets to the terms inside. 5 * x = 5x, and 5 * 2y = 10y. So the first part is 5x + 10y. For the second part, -3 * 2x = -6x, and -3 * -y = +3y. So the second part is -6x + 3y. Now combine the two parts: (5x + 10y) + (-6x + 3y). Group like terms: (5x - 6x) + (10y + 3y). This simplifies to -x + 13y, which is the same as 13y - x.

Question 2: Ama is twice as old as her brother Kofi. In 5 years, the sum of their ages will be 28. How old is Kofi now?

8 years
6 years (Correct answer)
12 years
9 years

Correct answer: 6 years

Let Kofi's current age be 'k'. Then Ama's current age is '2k'. In 5 years, Kofi's age will be k+5 and Ama's age will be 2k+5. The sum of their ages in 5 years will be (k+5) + (2k+5) = 28. Combine like terms: 3k + 10 = 28. Subtract 10 from both sides: 3k = 18. Divide by 3: k = 6. Therefore, Kofi is currently 6 years old.

Question 3: If 4(x - 3) = 2x + 6, what is the value of x?

3
5
9 (Correct answer)
-4

Correct answer: 9

To solve for x, first distribute the 4 on the left side of the equation: 4x - 12 = 2x + 6. Next, gather the x terms on one side by subtracting 2x from both sides: 2x - 12 = 6. Then, gather the constant terms on the other side by adding 12 to both sides: 2x = 18. Finally, divide by 2 to find x: x = 9.

Question 4: Which of the following expressions is equivalent to 3x² + 9x?

3x(x + 3) (Correct answer)
3(x² + 9)
9x(x + 1)
3x²(1 + 3x)

Correct answer: 3x(x + 3)

To find the equivalent expression, we need to factorize 3x² + 9x. The greatest common factor (GCF) of 3x² and 9x is 3x. When we factor out 3x, we divide each term by 3x. 3x² / 3x = x, and 9x / 3x = 3. Therefore, the factored form is 3x(x + 3).

Question 5: A rectangle has a length that is 5 cm more than its width. If the perimeter of the rectangle is 38 cm, what is its width?

12 cm
9 cm
14 cm
7 cm (Correct answer)

Correct answer: 7 cm

Let the width be 'w'. The length is 'w + 5'. The formula for the perimeter of a rectangle is P = 2(length + width). So, 38 = 2((w + 5) + w). Simplify inside the bracket: 38 = 2(2w + 5). Distribute the 2: 38 = 4w + 10. Subtract 10 from both sides: 28 = 4w. Divide by 4 to find the width: w = 7 cm.

Question 6: Solve the equation: (2y/3) - 1 = 5

y = 6
y = 12
y = 9 (Correct answer)
y = 4

Correct answer: y = 9

First, isolate the term with the variable 'y'. Add 1 to both sides of the equation: 2y/3 = 5 + 1, which simplifies to 2y/3 = 6. To solve for y, multiply both sides by 3: 2y = 6 * 3, so 2y = 18. Finally, divide both sides by 2: y = 9.

BECE - Basic Education Certificate Examination Algebraic Expressions and Equations Questions and Answers 1

Simplify the expression: 5(x + 2y) - 3(2x - y)